Time-Resolved Photoemission Electron Microscopy

ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL. 142

Time-Resolved Photoemission Electron Microscopy G. SCHÖNHENSEa , H.J. ELMERSa , S.A. NEPIJKOa , AND C.M. SCHNEIDERb a Institut für Physik, Johannes-Gutenberg-Universität, D-55099 Mainz, Germany b Forschungszentrum Jülich, IFF, 52428 Jülich, Germany

I. Introduction . . . . . . . . . . . . . . . . . . . . . . II. Imaging of Fast Magnetization Reversal Processes . . . . . . . . . . . A. Time Scales in Magnetization Dynamics . . . . . . . . . . . . . B. Experimental Technique of Stroboscopic XMCD-PEEM Imaging . . . . . . 1. Synchrotron Radiation as a Stroboscopic Light Source . . . . . . . . 2. Generation of Ultrafast Magnetic Field Pulses . . . . . . . . . . . 3. Magnetic Contrast in X-PEEM . . . . . . . . . . . . . . . 4. Layout of a Stroboscopic X-PEEM Experiment . . . . . . . . . . 5. Determining the Time Reference . . . . . . . . . . . . . . . C. Stroboscopic Imaging of Ferromagnetic Domains Exploiting X-ray Magnetic Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . 1. Dynamics of Domain Boundaries . . . . . . . . . . . . . . 2. Vortex Dynamics . . . . . . . . . . . . . . . . . . . 3. Transient Domain Walls and Vortices . . . . . . . . . . . . . 4. Rapid Formation of Stripe Patterns (Blocking Domains) . . . . . . . . 5. Magnetic Eigenmodes in Confined Systems . . . . . . . . . . . 6. Nonperiodic Switching into Metastable States . . . . . . . . . . . D. Observation of Magnetic Stray Field Dynamics . . . . . . . . . . . E. Nonstroboscopic Time-Resolved Imaging . . . . . . . . . . . . . III. Imaging of Transient States . . . . . . . . . . . . . . . . . . A. Investigations of Surface Melting and Thermionic Emission of Electrons . . . . B. Detection of Electrical Pulses in a Gunn Diode . . . . . . . . . . . C. Femtosecond Lifetime Contrast of Hot Electrons . . . . . . . . . . . D. PEEM Imaging of fs-Laser Excited Optical Near Fields . . . . . . . . . E. Interferometric Time-Resolved Two-Photon PEEM Imaging of Plasmon Eigenmodes IV. Time-of-Flight Spectromicroscopy . . . . . . . . . . . . . . . . A. Time-of-Flight Versus Dispersive Energy Filters for Spectroscopic Imaging . . . B. Basics of Time-of-Flight PEEM . . . . . . . . . . . . . . . C. Spectromicroscopy Exploiting the Time Structure of Synchrotron Radiation . . . D. Femtosecond-Laser-Based Spectromicroscopy . . . . . . . . . . . 1. Results for Ag and Cu Nanoparticles . . . . . . . . . . . . . 2. Results for MoS2 Nanotubes . . . . . . . . . . . . . . . . E. Time-Resolved Spin-Polarization Spectromicroscopy . . . . . . . . . V. Toward Aberration Correction by Time-Resolved Detection and/or Time-Dependent Fields A. Basic Considerations: Early Approaches of High-Frequency Lenses . . . . . B. Time-of-Flight Energy Filtering . . . . . . . . . . . . . . .

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159 ISSN 1076-5670/05 DOI: 10.1016/S1076-5670(05)42003-0

Copyright 2006, Elsevier Inc. All rights reserved.

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C. Novel Concepts of Aberration Correction . . . . . . . . . . . . . 1. Chromatic Correction by Time-Resolved Image Detection (Picosecond Time Slicing) 2. Inversion of Electron Energy Distribution . . . . . . . . . . . . 3. Correction of Spherical Aberration by Diverging Round Lenses with Negative cs . 4. Quantitative Estimations . . . . . . . . . . . . . . . . . VI. Conclusions and Outlook . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . .

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I. I NTRODUCTION The idea of time-dependent electron optics dates back to the time when Scherzer (1936) published his famous work on the impossibility of building an aberration-corrected electron optical system composed of round lenses only. This paper initiated intensive work on the search for “loopholes” in his theorem (it turned out that loopholes do not exist) and on ways to circumvent preconditions of Scherzer’s theorem. One of these preconditions is that the lens fields are static. So, as one possibility of aberration correction several authors considered time-dependent lens fields. Given the existing technical possibilities the approaches were based on microwave-excited highfrequency lenses acting on a bunched electron beam. Despite several elaborate attempts, aberration correction could not be proven because of the difficulties in fulfilling the crucial phase condition between the lens potential and the transit time and phase of the electron beam. Much later, time-resolved imaging was implemented into scanning electron microscopy (SEM) columns in terms of a fast beam-blanking unit for stroboscopic imaging of operating integral circuits (ICs) (Feuerbaum, 1982). Today, this electron beam tester is a powerful tool that found its way into semiconductor production lines. The time resolution can be as good as a few hundred picoseconds as sufficient for imaging of time-dependent operation of electronic devices. The advent of pulsed photon sources (synchrotron radiation, lasers) with excellent time structure down to the femtosecond range recently had a strong impact on the field of time-resolved electron microscopy, particularly on photoemission electron microscopy (PEEM). It opens new and highly promising means of exploiting the “old concepts” of aberration correction and novel concepts, such as spectroscopic time-of-flight (TOF) imaging, stroboscopic imaging of ultrafast processes, or interferometric time-resolved PEEM. Photon sources with a very high potential for various time-resolved experiments are the numerous synchrotron radiation facilities all over the world. Synchrotron radiation is naturally pulsed due to the bunched electron beam, and its tunability provides access to a wide spectrum of photon energies from

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the visible up to the hard X-ray range. Moreover, its variable polarization gives access to contrast mechanisms such as X-ray magnetic dichroism, which is used in many laboratories worldwide for magnetic spectroscopy and magnetic imaging. Stroboscopic illumination with circularly polarized X-rays combined with PEEM has been recently used by a few research groups for the analysis of ultrafast remagnetization processes in the regime of spin precession and for the observation of magnetic eigenmodes (i.e., normal or center modes, wall oscillation modes, and vortex modes) in confined magnetic structures. A time resolution of 15 ps has been reached in a special bunchcompression mode of the synchrotron source. Even higher time resolution is possible with pulsed laser sources. When a femtosecond laser beam hits a surface, intense photoemission signals arise due to two-photon or multiphoton transitions. Such lasers are therefore ideal excitation sources for time-resolved PEEM when there is no need for high photon energies. Using an all-optical pump-and-probe technique an ultimate time resolution of 30 attoseconds has been achieved (Kubo et al., 2005) that allows observation of the phase evolution of localized plasmon excitations. This time resolution corresponds to a fraction of T /20 of the period of an optical light wave (T = 1.3 fs). Also, hot-electron lifetimes in the femtosecond range could be exploited as contrast mechanism on heterogeneous surfaces. This chapter provides an overview of this rapidly developing field. The various aspects of time-resolved PEEM are outlined and illustrated by experimental examples from several groups. We discuss not only the specific electronmicroscopical issues but also recall the basic physics behind the experiments. In particular, introductions are given to the basics of ultrafast magnetization processes, the spatiotemporal nature of surface plasmon polariton excitations in inhomogeneous matter and nanoscale metal objects, and femtosecond dynamics of excited electrons (hot electrons) in metals and semiconductors. Although most of the discussed experimental work has been published within the past five years, the wealth of information accessible by the novel technique sheds light onto the future potential of time-resolved PEEM. Finally, the above-mentioned pulsed excitation sources, along with state-of-the-art electrical pulse generators, are paving the way toward aberration-corrected PEEM instruments (at least chromatic aberration-corrected). This stirs up old ideas of an unconventional way to circumvent Scherzer’s theorem.

II. I MAGING OF FAST M AGNETIZATION R EVERSAL P ROCESSES Ultrafast magnetization reversal processes are presently attracting much attention. Technologically, fast magnetic recording, advanced magnetic memory

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elements, and spinelectronics call for an in-depth understanding and control of fast magnetization reversal processes on the nanosecond and sub-nanosecond scale. More fundamental questions are associated with magnetic excitations (eigenmodes) and damping processes in confined magnetic structures. The fundamental time scales for magnetization reversal processes range down to a few femtoseconds while present technologically interesting time scales are on the order of sub-nanoseconds (see Section II.A). Since magnetization reversal generally involves inhomogeneous magnetization structures (i.e., magnetic domains), experimental methods providing high spatial resolution are of vital interest. The various microscopic methods of magnetic imaging have been summarized by Schneider and Schönhense (2002). The highest spatial resolution is offered by spin-polarized scanning tunneling microscopy (SPSTM) (Bode, 2003; Wulfhekel and Kirschner, 1999). At present no effort has been made to implement time resolution in an SPSTM experiment. In principle, the highest time resolution can be achieved in an all-optical Kerr microscopy experiment, whereas the spatial resolution for optical microscopy is limited. PEEM fills the gap by providing simultaneously high temporal and lateral resolution. Theoretically, the lateral resolution in PEEM can be driven down to the range of 1 nm (Fink et al., 1997; Wichtendahl et al., 1998). Practically, however, the ultimate obtainable resolution can be substantially determinated in cases of a geometric surface corrugation (Nepijko et al., 2000b) or be due to the presence of electric or magnetic microfields on the sample surface. These occur when the work function is not homogeneous (Nepijko et al., 2000c, 2001a, 2001b, 2002c) or for ferromagnetic samples with micromagnetic structures (Nepijko et al., 2002e). The behavior for slowly varying magnetic fields (quasi-static remagnetization) is quite well understood. In this regime, the magnetization almost instantaneously follows the applied field via the nucleation and motion of domain walls and vortices, magnetization rotation, and Barkhausen jumps. Such processes are discussed by Hubert and Schäfer (1998) and have been studied in detail using quasi-static Kerr microscopy. New experimental methods for the microscopic investigation of ultrafast processes have recently been developed on the basis of Kerr microscopy (Freeman et al., 1998; Neudert et al., 2005), full-field imaging transmission X-ray microscopy (Fischer et al., 2002; Stoll et al., 2004), scanning transmission X-ray microscopy (Warwick et al., 1998), and photoemission electron microscopy (Choe et al., 2004; Krasyuk, 2005; Krasyuk et al., 2003, 2004, 2005; Raabe et al., 2005; Vogel et al., 2003). Ultrafast techniques generally use pulsed optical lasers in a stroboscopic arrangement. Although very high time resolution can be achieved, the spatial resolution of optical experiments is diffraction limited

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by the wavelength of light. This limitation can be overcome by X-ray imaging techniques. The experiments discussed below are based on PEEM (see Section II.B). The invention of PEEM dates back to the early days of electron microscopy (Brüche and Johannson, 1932). A planar sample surface is illuminated by a photon beam (ultraviolet [UV], X-rays) leading to photoelectron emission. The lateral intensity distribution of the photoelectrons is imaged by a lens arrangement analogously to an optical microscope. Upon UV excitation the image is largely dominated by work function variations (work function contrast) and by topographic contrast as a result of the off-normal illumination. The X-ray absorption edges can be exploited in PEEM (X-PEEM) for element-selective imaging as was first demonstrated by Tonner and Harp (1988). If, in addition, X-ray magnetic circular (or linear) dichroism (XMCD, XMLD) in the photoemission signal is recorded as the contrast mechanism, the result is XMCD-PEEM that is extremely powerful for magnetic imaging and spectroscopy as was first demonstrated by Stöhr et al. (1993). A high time resolution can be implemented by using stroboscopic illumination and/or time-resolved image detection (see Section II.B). A few concepts of aberration correction in photoemission electron microscopes drive the resolution limit to a few nanometers (see Section V). This chapter addresses the topic of how time-resolved photoelectron microscopy can answer current questions in surface and thin-film magnetism. Typical devices such as magnetic random access memories, magnetic sensors, or elements of future spintronics devices pose a major challenge on both materials research and “design” and the development of appropriate analytical tools. The complex layer structure of device elements calls for element selectivity, a lateral resolution of the order of 20 nm or better (well below the critical size of the elements), high magnetic sensitivity for the study of the domain structure, capability of magnetic spectroscopy for an analysis of subtle features such as spin and orbital moments of the constituent elements, access to “living devices” on a chip and to buried layers and, finally, a very high time resolution in the picoseconds range for real-time observation of magnetic switching processes. We will demonstrate that time-resolved PEEM has the potential to fulfill all these requirements. The magnetization in a ferromagnet is a collective phenomenon of correlated electrons and can therefore be profoundly understood only by models considering many body wave functions. When the magnetization responds to an external field pulse, excitations and de-excitations of single spins, collective behavior of ensembles of spins (i.e., spin waves) or magnetization reversal by homogeneous rotation, generation and interaction of magnetic domains dominate the reaction, depending on the intensity and duration of the

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external excitation. The different excitations are related to time scales ranging from femtoseconds to microseconds. A. Time Scales in Magnetization Dynamics Magnetic excitations can be generated on a femtosecond time scale by use of intensive ultrashort laser pulses. For ferromagnetic transition metals such as nickel the spin system equilibrates within a few hundred femtoseconds at a reduced magnetization (Beaurepaire et al., 1996; Guidoni et al., 2002; Hohlfeld et al., 1997; Koopmans et al., 2000; Koopmans, 2003). At present there is no general agreement on the underlying physics enabling such an ultrafast response. It is widely believed that the demagnetization process is somehow completed during thermalization of the electron system, with no role for phonons (Guidoni et al., 2002). A phenomenological threetemperature model as introduced by Beaurepaire et al. (1996) describes the magnetization by a spin temperature, which equilibrates via energy exchange with the electron and phonon baths. The model fits experimental data and quantifies coupling terms; however, it does not explain the microscopic mechanisms. Moreover, it disregards the conservation of angular momentum. A fully quantum mechanical description of spin dynamics in nickel (Zhang and Hübner, 1999) considering the coherent propagation of the many-electron state (neglecting phonons and any source of dephasing) even predicts a reduction of the magnetization within tens of femtoseconds after excitation. The quantum mechanical model attributes the demagnetization to the simultaneous effect of spin-orbit interaction and presence of the laser field. However, the applicability to realistic experiments with the (at present) limited laser power is debatable (Koopmans, 2003). In a further approach spin dynamics were studied (Knorren et al., 2000) by solving the Boltzmann equations, neglecting phonons but using realistic exchange-split densities of states of Co, Fe, and Ni (Knorren et al., 2000). A reasonable agreement with spin-resolved lifetimes of optically excited carriers was found. In an alternative approach (Koopmans et al., 2005) the Boltzmann equation was solved for a simple model system, including an Elliot–Yafet-type of spin-orbit-induced spin scattering by assigning a spin-flip probability to each electron–phonon scattering event (Yafet, 1963). The spin flip occurs by emitting or absorbing a phonon that is assumed to carry the appropriate quantum of orbital moment to fulfill angular momentum conservation. On a macroscopic scale, the transfer of spin from or to the lattice will appear a finite rotation of the system as a whole, similar to the Einstein–De Haas experiment (Einstein and de Haas, 1915). The potential role of phonons to the ultrafast magnetic processes is of particular relevance, realizing that a realistic model

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must not violate conservation of angular momentum (Koopmans, 2003). It is often stated that exchange of orbital momentum from the spin system to the lattice is too slow, and, in particular, that the characteristic demagnetization time is necessarily longer than the energy-equilibration time of electron and lattice whenever phonons act as a sink for angular momentum. However, Koopmans et al. (2005) were able to show in their approach that even though the demagnetization in their model is mediated by phonon scattering, it is possible to derive a demagnetization time that is shorter than the electronphonon equilibration (and even thermalization) time. The final heat transfer during the spin excitation previously described limits potential applications because the repetition frequency is limited by the cooling time. Recently, it was demonstrated that circularly polarized femtosecond-laser pulses can be used to nonthermally excite and coherently control the spin dynamics in magnets by way of the inverse Faraday effect (Kimel et al., 2005). Such a photomagnetic interaction is instantaneous and is limited in time by the pulse width. Their finding thus reveals an alternative mechanism of ultrafast coherent spin control and offers prospects for applications of ultrafast lasers in magnetic devices. The transition between the ultrashort excitations described above and magnetization processes on a macroscopic scale forms the regime of spin waves and precessional motion of magnetization (Demokritov et al., 2001). This regime is often denoted as regime of magnetization dynamics (Figure 1) and takes place on time scales that usually prove longer than the time necessary in a metallic film to recover equilibrium between the electron gas and the spin bath after ultrashort excitation, a time of the order of a few

F IGURE 1. Relevant time scales and lateral dimensions for the regime of magnetization dynamics compared with experimental methods for magnetic microscopy.

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picoseconds at most. On the other hand, experimentally accessible frequencies are higher than the attempt frequencies in thermally assisted switching. Thermally assisted magnetization reversal of single particles can be described by an Arrhenius law with the prefactor τ0 denoting the inverse attempt frequency. The inverse attempt frequency poses a lower limit for thermally activated switching processes and was found experimentally as τ0 = 4 ns (Wernsdorfer et al., 1997) for ellipsoidal Co particles. Therefore a time window exists within which magnetization motion may not be considered primarily governed by thermal effects and within which macroscopic quantities such as saturation magnetization, exchange, and anisotropy constants may be considered constant at a given temperature (Miltat et al., 2002). The physics of magnetization precession is usually described by the Landau–Lifshitz–Gilbert equation:     α dM(t) dM(t) M(t) × = −γ μ0 M(t) × H (t) + . (1) dt Ms dt Neglecting any damping (α = 0), this equation denotes the quantum mechanical analogue to the classical mechanical equation relating the torque to the angular momentum. The prefactor γ comprises the ratio of angular momentum and magnetic moment, which is at least for 3d metals close to the value of the free electron. Assuming the magnetic field to be time independent, the equation describes a precessional motion of the magnetization around the applied field. For a sphere, the angular frequency is a linear function of the magnetic field, ω0 = γ μ0 H , that is, ω0 /2π ≈ 28 MHz/mT in units of μ0 H . The damping term results from the assumption that the effective field acting on the magnetization is reduced by an ohmic-type dissipation term. Experimentally determined phenomenological damping constants are of the order of 10−2 to 10−3 . A microscopic understanding of the damping mechanisms is still missing. Several contributions from the spin relaxation mechanisms discussed above are potential contributions to the damping (Miltat et al., 2002). Considering the dynamics of a soft thin platelet in the limit of homogeneous magnetization M = Ms (mx , my , mz ), the effective field H eff can be derived from the density functional of the magnetic free enthalpy (Gradmann, 1993): 1 (2) g = Kp,eff m2x + Keff m2z − μ0 (M · H ) − μ0 (M · H d ). 2 The first two terms define the magnetic in-plane Kp,eff and out-of-plane Keff anisotropy, where the constants summarize contributions from surface anisotropy, strain anisotropy, and crystal anisotropy (Gradmann, 1993). Only second-order anisotropies are considered, while higher-order anisotropies

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provide considerable contributions in some cases (Prokop et al., 2004). The second term represents the Zeeman energy (i.e., the interaction energy between the magnetization and the external field H ). The last term corresponds to the magnetostatic energy with H d being the demagnetizing field. The demagnetizing field depends on the size of the platelet: H d = −Ms (Nx mx , Ny my , Nz mz ), with Ni denoting the corresponding demagnetization factors. For a flat platelet with lateral dimensions l much larger than the thickness t, Nx ≈ Ny ≈ t/ l is quite small and Nz (z pointing along the surface normal) is almost unity. The field acting on M is then given by  2Kp,eff 1 ∂g = Hx + mx − Nx Ms mx , Hy − Ny Ms my , H eff = − μ0 Ms ∂m μ 0 Ms  2Keff (3) mz − Nz Ms mz . Hz + μ 0 Ms The quantity Hi = 2Ki /μ0 Ms has the dimension of a field and is therefore conventionally denoted as the anisotropy field. For sufficiently small damping Eq. (1) results in damped oscillations of the macrospin around its equilibrium position. Considering the case of a rectangular permalloy platelet after excitation (external field is zero), the acting field is mainly given by the demagnetizing field and the precessional frequency is equal to:  ω0 = γ μ0 Ms Nz (Nx − Ny ). (4) Anisotropy is typically very small in Permalloy and may be neglected. Assuming further for typical dimensions a dominating demagnetizing factor along the x-axis of Nx = 10 nm/5 µm = 2×10−3 , the precessional frequency exhibits a value of 1.25 GHz. This figure indicates the kind of temporal resolution to be achieved on a time-resolved experiment. In magnetic particles of submicrometer size the assumption of a macrospin behavior fails. Instead, the magnetization distribution is not homogeneous and consequently Eq. (1) can be applied only locally. An additional energy term enters Eq. (2) arising from the exchange energy: fexch = A(∇m)2 ,

(5)

which accounts for the additional energy caused by the magnetization being nonuniform. Equation (5) assumes that the magnetization can be described by a continuous function neglecting magnetization distribution on an atomic scale. Micromagnetics is the continuum theory allowing upon minimizing Eq. (2) for calculating the equilibrium state of the magnetization distribution (Hubert and Schäfer, 1998). Finite element methods have been developed to solve the variational problem numerically (see, e.g., Donahue and Porter,

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F IGURE 2. Torque acting on the magnetization in a thin-film element in a Landau flux-closure state. H p denotes the pulse field, M the local magnetization.

2005). The same methods can also be applied, considering Eq. (1), to calculate the dynamic behavior of an extended particle. In micron- and sub-micron-sized magnetic particles magnetic domains generally are separated by domain walls. In thin film squares or rectangles the energetically most favorable state forms a Landau flux-closure pattern that is characterized by minimized stray field energy. For a square platelet the Landau flux-closure pattern forms one of the key building blocks of general domain structures—it consists of four equally sized domains with a pair-wise perpendicular in-plane magnetization direction forming a vortex structure as depicted in Figure 2(a). To understand the dynamic behavior of the domain structure we first recall how the magnetization in each domain responds to an external field pulse. We choose a geometry in which the pulse field H p is directed along one of the edges of the square. Because of the domain structure, regardless of which way the external field is directed, it will always find a region in which a component of the magnetization vector points perpendicular to the external field. In the situation sketched in Figure 2(b), there is no initial torque on the magnetization in domains A and C. Domain A has zero susceptibility because M points along H p constituting the energetically most favorable state. The maximum initial torque acts on the domains with M⊥H p , that is, B and D. Although domain C has the highest energy with respect to the applied field (it is energetically least favorable), no initial torque acts on this domain in case it is ideally magnetized antiparallel to the pulse field. The torque causes a precessional motion of the magnetization inside the domains B and D, a motion of the domain walls, and finally a movement of the vortex in the center. The time scales of these three substructures may be addressed separately (as proposed by Raabe et al., 2005). The highest frequencies similar to values obtained from the macrospin model are found experimentally in the domains, while time scales of the domain walls and vortices are almost an order of magnitude longer (Raabe et al., 2005). The domain wall movement in the limit of high velocities can be described by a viscous behavior: the wall velocity is proportional to the driving field

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(Hubert and Schäfer, 1998): v(H ) = βi H,

(6)

where βi is the wall mobility. In the limit of the gyromagnetic regime, the wall mobility follows from a balance between the driving field and the dissipative term of the Landau–Lifshitz–Gilbert equation [Eq. (1)]. For a 180-degree wall one obtains βg = (γ μ0 /α)dw with domain wall width dw . For thicker films eddy current damping must be taken into account, which decreases the wall mobility. In the limit that eddy current damping dominates the mobility is given by βec = 7.73/(2μ0 Ms tσ ) (Bishop, 1984), where σ denotes the conductivity. For typical samples and fields described here, the wall velocity is limited by βg . As demonstrated by Slonczewski (1973), there exists an upper limit to the domain wall velocity given by vmax = cγ μ0 dw Ms with a constant c ≤ 1 depending on the effective anisotropy; that is, in Permalloy the wall velocity must not exceed a value of 5000 m/s. For driving fields exceeding H = Ms α stationary solutions must be replaced by spatially inhomogeneous, chaotic modes (Suhl and Zhang, 1987). On even longer time scales (t0  4 ns) magnetization processes are dominated by thermal activation behavior. For the magnetization reversal process in thin films proceeding by the displacement of magnetic domain walls (Pommier et al., 1990), inhomogeneities in the film act as pinning sites for the domain walls and, consequently, have a strong influence on the dynamics of the magnetization reversal. The propagation of domain walls is then thermally activated. In the limit of thermal activation wall velocities can be described by Kirilyuk et al. (1993):   2μ0 Ms Vp v(H ) = v0 exp (H − Hc ) , (7) kB T with a propagation volume Vp and propagation field Hc depending on details of the sample. Wall velocity ranges from zero to the order of centimeters per second. These inhomogeneities are formed by crystallographic defects or deviations of the film morphology from an ideal atomically flat surface and their influence is difficult to quantify and the actual mechanism for the pinning remains often unspecified. A more precise picture of the importance of the microstructure was developed by introducing well-controlled defects, such as step edges (Haibach et al., 2000). The most interesting time scale from the technological aspect is the regime of magnetization dynamics: ∼1 ps to ∼10 ns. It has been shown that excitation of magnetization reversal can be performed and controlled using magnetic fields generated by current pulses injected into coplanar waveguides. This is certainly an important precondition for producing electronic devices. In contrast to optically induced excitations, the repetition frequency is not

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limited by the heat transfer to the substrate. As discussed in Section II.C, high repetition frequencies of the order of gigahertz can be achieved using coplanar waveguides. This interesting time scale is indicated in Figure 1 by the horizontal bar. On the other hand, the relevant lateral sizes are given by the typical lateral dimensions of future electronic devices being certainly below 1 µm. Magnetization direction may change on a length scale given by the exchange length:  lex = 2A/μ0 Ms2 , (8) with A being the exchange stiffness. Thus, the exchange length, which is typically on the order of 10 nm, defines the lateral resolution to be achieved by a microscopic method. The demanding request for a high lateral resolution manifest, for example, in the topical discussion of energy dissipation: any experiment that measures the temporal evolution of some average of the magnetization distribution is bound to yield a value larger than the true Gilbert damping parameter because energy dissipation in short-wavelength excitations is overlooked. The interesting region of lateral sizes is indicated in Figure 1 by the vertical bar. Magnetic microscopy can be performed with very high lateral resolution by magnetic force microscopy (MFM), which has become a standard method for the investigation of magnetization structures. An even higher resolution can be achieved by scanning electron microscopy with polarization analysis (SEMPA). Ultimate lateral resolution could be achieved by SPSTM. All of these methods lack a sufficiently high temporal resolution, since the acquisition time for a magnetically resolved image counts at least in minutes. Very high temporal resolution can be achieved by all-optical methods such as Kerr microscopy. In a stroboscopic measurement, the time resolution is limited by the pulse length of ultrashort laser pulses. It has been shown that a time resolution of a few tens of femtoseconds could be achieved (Kimel et al., 2005). However, the lateral resolution is then limited by the wavelength of light: ∼500 nm. Photoemission electron microscopy fills the gap of providing simultaneously high temporal and lateral resolution (see Figure 1) as discussed in Section II.B. The main limitation of present-day instruments is the restriction of lateral resolution to typically 100 nm in synchrotron radiation-based experiments due to the chromatic aberration of the microscope optics. The base resolution below 20 nm can only be reached in threshold excitation (UVPEEM) owing to the narrow energy distribution. A few concepts of aberration correction in photoemission electron microscopes, driving the resolution limit to a few nanometers, are discussed in Section V.

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B. Experimental Technique of Stroboscopic XMCD-PEEM Imaging The relevant and interesting time scales in magnetism range from the nanosecond to the femtosecond regime. The following section focuses on imaging experiments, which access magnetization reversal processes that take place on the nanosecond and picosecond time scale. Imaging of these magnetodynamic processes has long been a domain of magneto-optical Kerr microscopy using an illumination with pulsed laser sources (Freeman and Hiebert, 2002). These studies have also introduced and developed the principles of stroboscopic pump-probe investigations. Such a stroboscopic approach is necessary, as the limitations in photon flux from the light source and detection efficiency during image acquisition do not allow a one-shot recording of a full image. On this basis, both scanning and full-field time-resolved Kerr microscopies have been developed (Freeman et al., 1998; Neudert et al., 2005). It was not until 2000, however, that the potential of synchrotron radiation for timeresolved experiments in magnetism was explored and demonstrated (Sirotti et al., 2000). 1. Synchrotron Radiation as a Stroboscopic Light Source We know from fundamental electrodynamics that an accelerated charged particle will emit electromagnetic radiation (Jackson, 1972). In the simplest case of an oscillating charge, the far-field distribution will have the wellknown dipole character. A relativistic version of this picture describes the situation in a synchrotron or storage ring. In a storage ring, the charged particles—often electrons—are moving with very high kinetic energies (one to several gigaelectron volts) and thus almost with the speed of light. In order to store the charges they are guided by magnetic fields along a closed path with a polygonal shape. At each corner of the polygon, the trajectories of the electrons are bent from one straight section to the next one, giving rise to a radial acceleration. This leads to the emission of electromagnetic radiation mainly along the tangential direction. Because of the relativistic speed of the charges in the laboratory frame, the radiation is strongly peaked into the forward direction. It is guided into a beamline, in which a specific photon energy out of the broad spectrum is chosen by a monochromator before it reaches the sample. In addition to a high photon flux and a wide range of photon energies, the synchrotron radiation has unique polarization properties. If only the radiation within the orbit plane is considered, it is 100% linearly polarized, with the electric field vector lying in the orbit plane. The radiation emitted above or below the orbit plane is elliptically polarized with a high degree of circularity. The helicity of the light reverses when moving from above to below the orbital plane.

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In third-generation synchrotron radiation sources, these bending magnet sections play only a minor role for the production of light. Most of the light is generated in dedicated periodic magnet structures (undulators) placed within the straight sections of the polygonal orbit (Wiedemann, 2003). The multiple deflections of the electrons in the undulator cause repeated emission events, which interfere on their way to the experiment, resulting in a highly intense beam with a narrow spectral distribution, a so-called harmonic. Depending on the magnet configuration of the undulator, the radiation is either linearly polarized within the orbit plane, or the polarization may be varied between linear (within or perpendicular to the orbit plane) and circular (both helicities). The energy of the harmonic is shifted over a broad interval by changing the strength of the magnetic field in the undulator. According to energy conservation laws, the emission of light takes place at the expense of the kinetic energy of the particles. This energy loss must be compensated to keep the electrons in the storage ring. This is performed by accelerating the electrons after each cycle through the ring by means of a radiofrequency (RF) electromagnetic field. This process is most efficient if the electrons are grouped in packets or bunches, rather than being evenly distributed along the orbit. From this bunch structure follows immediately that synchrotron radiation must have an intrinsic time structure, as light is only generated if a bunch passes through a bending magnet or undulator. The details of the time structure depend on the bunch pattern and the degree of filling. In Table 1, the characteristics of several storage ring facilities and various operation modes are compiled. In general, single-bunch and multibunch operation can be distinguished. In the first mode, only one bunch is circulating in the ring. It offers the longest repetition time of the order of microseconds. Compared to multibunch operation, the pulse length of the light is usually larger, as the singular bunch is wider due to the higher filling, and ranges between 50 and 100 ps. A particular short pulse mode is available at synchrotron source in Berlin (BESSY), providing pulse lengths as low as 3 ps (Abo-Bakr et al., 2003; Feikes et al., 2004). Due to its method of generation, synchrotron radiation provides a very stable time structure ideally suited for time-resolved experiments. For stroboscopic experiments, however, an additional reference signal is needed. This is usually taken from the “bunch clock,” a standard derived directly from the RF signal accelerating the electrons in the ring. An alternative way to generate this reference uses a fast photodiode placed upstream in the beamline. The diode receives a part of the light not reaching the experiment (e.g., in front of the exit slit of the monochromator). The stability of this reference is an essential factor in determining the ultimate time resolution of the entire experiment.

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TABLE 1 C OLLECTION OF C HARACTERISTIC DATA FOR T IME -R ESOLVED I MAGING AT S YNCHROTRON R ADIATION S OURCES BESSY single bunch

BESSY multibunch

BESSY low αbunch

ESRF 16bunch

ESRF multibunch

SLS “camshaft”

ALS two-bunch, or “camshaft”

Pulse width

100 ps (45 ps at 2 mA)

30 ps

<3 ps

48 ps

20 ps

70 ps

70 ps

Period

805 ns

2 ns

2 ns (also 805 ns)

176 ns

2.82 ns

1 µs

328 ns (656 ns)

nbunch Typical current

1 20 mA

350 260 mA

350 40 mA

16 90 mA

992 200 mA

1 2 mA

2 (1) 60 mA (10 mA)

Pulse widths correspond to rms values. Data were reported by Abo-Bakr et al. (2003), Feikes et al. (2004), Holldack (2005), Kalantari et al. (2004), and taken from homepages for ALS, BESSY, DESY, ESRF, and SLS Handbooks in http://www.lbl.gov, http://www.bessy.de, http://www.desy.de, http:// www.esrf.fr, and http://sls.web.psi.ch, respectively.

2. Generation of Ultrafast Magnetic Field Pulses In the PEEM experiments reviewed in this chapter, we are interested mainly in magnetization reversal processes. These processes are initiated and controlled by an external magnetic field. In order to achieve an appropriate time resolution in the experiment, the magnetic field must be pulsed and the pulses must have a rise time in the sub-nanosecond regime (i.e., they involve frequency components in the gigahertz range). Switching a magnetic field with these frequencies cannot be achieved by simple coils. Instead, specially designed waveguide devices with low inductivity must be used. This involves the preparation of thin film structures, such as the two examples shown in Figure 3. The coplanar waveguide in Figure 3(a) is also called stripline. Typical dimensions of a stripline are 5 mm×10 µm×500 nm (length×width× thickness). The structures are fabricated by optical lithography and etching techniques from Cu or Au films deposited onto SiO2 /Si or GaAs wafers. The current pulse I (t) passing through the central conductor generates a magnetic field H (t) (called Oerstedt field) around the conductor, which has a strong in-plane component Hy above the center of the stripline and a strong out-ofplane component Hz at the edges. Because the field decays rapidly with the distance from the stripline, the subject of investigation is best placed on the surface of the stripline. Usually this is done by a second lithography step, thereby microstructuring the magnetic materials after depositing the subject

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F IGURE 3. Microstrip line geometries for ultrashort magnetic field pulse experiments. (a) Linear waveguide for the generation of an in-plane field, and (b) microcoil geometry for the generation of an out-of-plane field.

on the stripline. Sometimes an additional insulating layer is inserted between the stripline and the magnetic sample. Care must be taken to etch the insulator down to the stripline metal to avoid charge-up problems in the PEEM. In this way, in-plane fields of several 10 mT may be obtained with pulses of a few nanoseconds in length. The thermal load and electromigration, however, limit the maximum field. The ring-shaped structure in Figure 3(b) is optimized for an out-of-plane field. For this purpose, the sample is placed in the center of the ring, where Hz is highest. In the simplest case, the current pulses driving the waveguide structures may be conveniently taken from a pulse generator. A number of commercially available devices deliver pulses of several 10 V height and 300–500 ps rise time into a 50 load resistance (Kentech Instruments Ltd., see http://www. kentech.co.uk; Avtech Electrosystems Ltd., see http://www.avtechpulse.com; Picosecond Pulse Labs, see http://www.picosecond.com). The pulse length is usually in the nanosecond range. Somewhat shorter and steeper pulses may be obtained from gigahertz signal generators (Hewlett-Packard, see http://www.hp.com), however, thereby sacrificing on output power and pulse height. A further reduction of the pulse length and increase of the rise time is only possible by invoking optical excitation mechanisms. For this purpose, a pulsed laser illuminates a photosensitive device connecting the power supply with the waveguide. In the simplest case, a fast photodiode is involved. During the illumination the diode is conducting, the circuit is closed and the current can flow through the stripline. A better control of the pulse shape, however, is achieved with so-called Auston switches (Smith et al., 1989). These are interdigital structures on GaAs. Upon illumination, electrons are excited into the conduction band of GaAs and establish the current. As this process is very fast, rise times of a few picosecond can be achieved if the switch is excited with a femtosecond-laser system. The trailing edge of the pulse, however, is

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F IGURE 4. Optical image of the coplanar waveguide carrying various Permalloy microstructures (a) and PEEM image of a Permalloy ring (b) microstructured on the waveguide surface. The device is mounted on an exchangeable sample holder (c) that can be inserted with MMCX microwave plugs into a carrier frame (d). A cross section of the microstripline with magnetic field distribution H (r) and a contour plot of |H (r)| are depicted in (e) and (f), respectively.

usually much wider, due to the slow charge carrier recombination in GaAs. By suitable measures (e.g., using low-temperature-grown GaAs with higher recombination rates) or active pulse-shaping (e.g., operating two Auston switches with a 180-degree phase shift and time delay [Keil et al., 1995]), also, the trailing edge may be considerably sharpened. In our time-resolved PEEM experiments, we have also realized a fast sample interchange as shown in Figure 4. For this purpose, the chips in image (a) carrying the stripline and magnetic structures (b) are mounted on a panhandletype sample plate (c). This sample plate also carries two high-frequency and ultrahigh vacuum (UHV)-compatible electrical connectors (MMCX-type). From these connectors wire-bonded Au leads carry the current pulse to the stripline. The sample plate fits into a receptacle in the microscope’s sample stage that also carries two high-frequency connectors (d). From there on, shielded coaxial cables transport the signal to a high-frequency (SMA-type) UHV electrical feedthrough. The entire setup is optimized for a 50 load and has a maximum transfer frequency (bandwith) of more than 5 GHz. The plots in Figure 4(e and f) depict the calculated spatial distribution (e) and absolute strength (f) of the magnetic field around the center conducting line of the microstrip arrangement. 3. Magnetic Contrast in X-PEEM The magnetic contrast in X-PEEM is achieved by exploiting the various X-ray magnetic dichroism phenomena. Most important for the study of ferromagnetic systems is the XMCD (Schütz et al., 1987). The interaction

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of the circularly polarized light with a magnetized system is characterized by a magnetic component to the absorption cross section μ, which depends on the magnetization M and the light helicity vector P circ as μm ∝ M · P circ = M · P · cos.

(9)

As a consequence, opposite magnetization directions give rise to a sizable difference in the absorption signal (i.e., a magnetic contrast). Alternatively, the contrast can be obtained by switching the light helicity. The XMCD effect is particularly strong at the L2,3 edges of the 3d transition metal ferromagnets. In order to exploit the XMCD as contrast mechanism in X-PEEM, the dichroism in absorption must be translated into an electron yield signal. This is achieved by a two-step process. In the first step, the core hole created by the absorption process is filled by an Auger transition. In the second step, the highly energetic Auger electron moves through the crystal and suffers multiple scattering processes, thereby creating a cascade of low-energy secondary electrons. The number of secondary electrons generated in this cascade is proportional to the original absorption process and therefore serves as a direct measure of the XMCD signal (Duda et al., 1994). The first magnetic imaging experiments exploiting XMCD were performed in 1993 (Schneider et al., 1993; Stöhr et al., 1993). A single X-PEEM image contains not only magnetic contrast, but also contributions from chemical and topographical contrast mechanisms. The magnetic contrast, however, can be conveniently separated by exploiting the fact that it reverses on helicity reversal [see Eq. (9)]. By means of image processing routines asymmetry images are derived from two raw images taken with right (r) and left (l) circular photon polarization and a subsequent pixelby-pixel calculation of the asymmetry AXMCD =

1 (Ir − Il ) , Pcirc (Ir + Il )

(10)

where Pcirc is the degree of circular polarization of the synchrotron radiation projected into the in-plane direction. AXMCD is proportional to the projection of the magnetization vector on the polarization axis AXMCD ∝ m · P /Pcirc . In this way, all contrast mechanisms other than magnetic cancel out, because they do not depend on photon helicity. In case the synchrotron radiation intensity depends on time, the two raw images must first be corrected for intensity variations before being fed into the asymmetry equation. Assuming in-plane magnetization and provided that the magnetization direction is known within certain domains, absolute directions can be determined. It is important to point out that the applicability of the X-PEEM technique is not limited to ferromagnets. In fact, it was shown in 1986 that linearly

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F IGURE 5. Schematic layout of a pump-probe PEEM experiment using a coplanar waveguide. The sample is pumped by a magnetic field pulse H (t), which is triggered by the bunch clock of the storage ring. A variable delay sets the time t with respect to the bunch clock. In some experiments, the image detector is additionally gated.

polarized light can be conveniently used to study the XMLD in antiferromagnetic materials (van der Laan et al., 1986). Laterally resolved investigations of antiferromagnets were demonstrated first for NiO (Spanke et al., 1998). 4. Layout of a Stroboscopic X-PEEM Experiment The general scheme of a stroboscopic PEEM experiment is sketched in Figure 5. The pulse generator driving the microstrip line is triggered by the bunch clock via a variable electronic delay, defining the separation t between pump (magnetic field) and probe (soft X-ray) pulse. The microscope is operated in the free-running mode—all events are recorded on the image detector and accumulated in the charge-coupled device (CCD) sensor. In this case, the time resolution of the experiment is mainly determined by the width of the light pulse (Table 1). A limiting factor, however, is the electronic jitter between the bunch clock and the pulse circuit, which may amount up to 10 ps. In this type of experiment, each light pulse from the synchrotron is used as a probe pulse. To obtain a sharp image, the light pulse must probe the magnetic system always in the same state, otherwise blurring of the image features will occur due to superposition of slightly different magnetic configurations. Consequently, the system must be pumped by the field pulse at the same

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repetition time T . In order to obtain an image with good contrast, one must integrate over about 108 pulses at a given setting t of the delay. The approach described above requires that the sample be pulsed with the frequency of the bunch pattern. In the case of a multibunch operation, the time distance of two light pulses is only a few nanoseconds. Depending on the magnetodynamic aspect to be studied, this time may be too short for the magnetic system to relax back into the ground state. Solving this dilemma involves additional gating schemes. The first approach uses so-called hybrid modes, in which a certain region in the multibunch pattern is emptied and a singular, highly filled electron bunch is placed in the center of this empty region, which may be several 10 ns wide. The image detector is then gated such that it only accepts events associated with this solitary bunch. In this way, an effective single bunch operation of the experiment is achieved. The repetition time in this experiment is then ∼1 µs. Usually the gating is achieved by varying the voltage of the image intensifier (MCP) or involving an additional retarding grid in front of the image intensifier, which is used to repel the unwanted electrons. The second approach enables a more flexible variation of the duty cycle. It requires an image detector with intrinsic time resolution, such as, for example, the delayline detector described in Section IV.B. The detector is gated with a fraction 1/n of the bunch clock signal to pick only those events of interest: those corresponding to the chosen time delay t and repetition time T = nT (T is bunch separation). In an advanced mode, events between t and t + T = t + nT , that is (t, t + T , t + 2T , . . .) may even be recorded. The time resolution of the delayline detector allows a separation (routing) of these events, resulting in acquisition of an entire time-dependent image sequence after the pump pulse. 5. Determining the Time Reference In the stroboscopic experiment, the time scale is measured with respect to the pump (magnetic field) pulse. Therefore, prior to any measurement the position of the pump pulse on the time line must be determined. In principle, this is necessary for each new sample, as the propagation of the pump pulse along the microstrip line may vary from sample to sample. As it happens, a very convenient method exists to determine the position and even the shape H (t) of the field pulse without resorting to changes in the magnetic configuration of the sample. The metal pads adjacent to the microstrip line are electrically grounded. When the current pulse propagates along the line, it is accompanied by an electric field E(t) built up between the center conductor and the ground pads. This field superimposes on the extractor field of the immersion lens. As a

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F IGURE 6. Action of the electric field pulse traveling along the waveguide on the image magnification of the microscope optics exploited as internal probe of the pulse profile. Top left: Images taken at times before the pulse onset and in the pulse plateau, respectively, revealing an increase of the image magnification during presence of the voltage pulse. Top right: Sequence of stripes across images taken with 500 ps time increment. Note the transient change of magnification in the pulse regime. Bottom: Resulting temporal pulse profile as measured in situ (circles) in comparison with the pulse profiles measured at the entrance and exit of the RF lines into the UHV chamber (full and dotted curve, respectively).

consequence, the imaging parameters change slightly and cause a small but noticeable change in the magnification. This effect is also known as chromatic aberration of the magnification (Hawkes and Kasper, 1996). The size of this image changes scale with the magnitude of the electric field pulse (i.e., current pulse). Therefore, by mapping the “breathing” of the image as a function of the delay time t, the shape of the field pulse in the field of view (FOV) can be determined in detail. This is an important aspect, because the pulse shape at the experiment is otherwise difficult to access (reconstruction of trajectories, example for pulse determination). An example for this procedure is given in Figure 6, which shows the breathing of the image of a ring structure, while the current or electric field

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pulse passes through the FOV (Neeb et al., 2005). To visualize this effect more clearly, we have copied a narrow stripe along the center of each image in the time sequence and compiled these stripes as a function of delay time t (Figure 6, top right). From this sequence the change in image magnification is clearly seen—in this case, by ∼14%—and an image shift, when the pulse passes through the FOV. This shift is due to the Lorentz force, which acts on the electrons on their way to the microscope lens and is caused by the magnetic field pulse. The pulse shape obtained from the in situ determination (circles in the bottom panel) is compared to the pulse shapes measured directly at the output of the pulser (full curve) and in the return path from the UHV chamber (i.e., after the pulse passed through the stripline and left the UHV chamber again [dotted curve]). The rise time of the effective field at the sample is 1.8 ns—about two times larger than the rise time of the pulse generator output. The slope in the steepest part of the leading edge is approximately 2 mT/ns. The following plateau is maintained for ∼5 ns, before the drop with a maximum slope of approximately 1 mT/ns sets in. The comparison also shows that the pulse in the return path is much broader and shows the characteristic shape of capacitive charging/decharging. It does not reflect the actual situation in the FOV of the microscope. It should also be noted that this change of magnification does not impair the image quality, as it can always be compensated by a slightly different setting of the focus voltage at the microscope. C. Stroboscopic Imaging of Ferromagnetic Domains Exploiting X-ray Magnetic Circular Dichroism 1. Dynamics of Domain Boundaries The equilibrium magnetization configuration of a ferromagnet in the absence of an external field is determined by competing interactions on very different length scales (Bertotti, 1998). The short-range interactions are the exchange coupling and the magnetocrystalline anisotropy. The exchange coupling leads to a parallel alignment of all spins in the ferromagnet (i.e., a spontaneous magnetization), whereas the anisotropy aligns the spontaneous magnetization along one of the easy axes of magnetization in the given crystalline system. In a finite sample, this homogeneous magnetization results in magnetic poles at the sample surface, from which a long-ranged dipolar magnetic field emanates. This magnetic stray field outside creates a demagnetizing field within the sample, which acts against the homogeneous magnetization distribution. The balance of these short- and long-range interactions determines the magnetic configuration or microstructure of the sample. It depends on the magnetic characteristics of a given material, as well as on the shape and size of

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the sample. In very small particles a homogeneous magnetization distribution is often found. If the sample size increases, noncollinear distributions may appear, which show the tendency of the system to reduce the energy contained in the dipolar stray field. In still larger samples, the energy reduction can only be realized efficiently if the magnetization breaks up into domains. The magnetization within the domains follows one of the easy axes of magnetization and the domain pattern is formed to minimize the external stray field. The neighboring domains are separated by domain walls. These particularly interesting objects are narrow regions with a highly noncollinear magnetization distribution, as the magnetization vector must continuously rotate when moving from one domain to the other. The domain walls play an important role in magnetization reversal processes and thus in magnetodynamics. A classical magnetization reversal process starts from a saturated state and proceeds via domain nucleation (i.e., domain wall formation and subsequent domain wall√propagation). The domain wall formation requires an energy of Ew = 4 A · K1 in the simplest case of a uniaxial system, whereby A and K1 denote the exchange coupling and the anisotropy energy density. The corresponding width of the wall is also determined by these quantities and is given, for example, for a Bloch wall in the above case as A δw ∼ . (11) K1 That is, the higher the magnetic anisotropy the narrower the domain wall. An important parameter with respect to magnetodynamics is the speed with which the domain wall can move through a given material. The viscous picture has been discussed in Section II.A [Eq. (6)]. The free motion, however, is often hindered by pinning of the domain walls at defects. Freeing the wall from the pinning site costs an extra energy, which must be provided by the external field or thermal excitation. As a result, one usually finds a staggered motion of the wall, that is, a sequence of Barkhausen jumps. The following text discusses some examples for PEEM investigations on magnetic domain walls. Domain Wall Motion in Ultrashort Field Pulse Experiments. The ultrashort magnetic field pulse may lead to a displacement of the domain wall depending on the configuration of the adjacent domains. Given typical values of the domain wall velocity of several 100 m/s, however, the displacement should be relatively small. Assuming a field pulse of 500 ps width and a domain wall velocity of 100 m/s, a maximum displacement of only about 50 nm can be expected during the action of the pulse. This is close to the

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F IGURE 7. Domain wall motion during a quasi-oscillatory excitation experiment. Top row: Initial domain configuration (left) and enlarged view of the magnetization distribution in a Néel-type 180-degree domain wall (right) in the vicinity of a wall vortex. Center row: Domain patterns as a function of delay time, ranging from t = 0 (a) up to 600 ps (g) in 100 ps steps. Bottom row: Development of the domain wall shift as a function of delay time (according to the images a to g) along the rising edge of the (bipolar) field pulse H p (t). The domain wall position is marked by line AB in (a).

lateral resolution limit of an X-PEEM and makes the investigation of domain wall motions in pulse fields a considerable challenge. Figure 7 shows the results of an experiment using a quasi-oscillatory excitation with a frequency of 500 MHz (Krasyuk, 2005). The sample is a 16 µm × 32 µm Permalloy element with 10 nm thickness. The magnetic ground state configuration is a classical Landau pattern with triangular closure domains at the top and bottom of the rectangle, which are connected by a

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domain wall. The film is not thick enough to support a Bloch wall; therefore this wall is of the Néel type: the magnetization vector in the wall rotates within the film plane. Exploiting the angular dependence of the magnetodichroic (XMCD) contrast, we have oriented the sample so as to emphasize the contrast from the wall. The magnetic contrast from the domains of the left- and righthand side of the wall disappears, because M lies perpendicular to the incident light. The magnetization component in the center of the wall has a large projection onto the incident light, and is thus responsible for the selective wall contrast. A closer inspection of the wall reveals a contrast change (black– white) along the wall, indicative of a change of the in-plane rotation sense of M within the wall and the formation of a vortex, as shown in the top right panel. This domain pattern is subjected to pulses with a width of ∼1 ns repeated every 2 ns. A negative voltage offset ensures that the field switches between positive and negative values are of approximately the same amplitude [also see Figure 21(a), curve II]. The response to the pulse train is, first, a global shift of the wall to the right-hand side of the sample. This phenomenon is discussed in detail in Section II.C.5. Here we are interested in small motions of the wall around this dynamic equilibrium position. For this purpose, we have analyzed the location of the wall (indicated by the line A-B) as a function of time during the rising edge of the field pulse. The displacement as a function of time is plotted in the bottom part of Figure 7. To a good approximation the dependence follows a linear behavior with a constant wall velocity of ∼103 m/s. This is more than an order of magnitude higher than values calculated for a quasi-static reversal process involving a solitary 180-degree Néel wall (Redjdal et al., 2002) in a Permalloy film of similar thickness, but only a factor of 2–3 higher than other experimental reports (Konishi et al., 1971). To understand this behavior another interesting observation must be included in this experiment. The dichroic contrast of the trapezoidal domains on either side of the vertical Néel wall changes as a function of time. Starting with a dark gray contrast at t = 0 ps (corresponding to the onset of the rising edge at a field value of μ0 H ≈ 0.16 mT), the contrast continuously brightens up to a time t ≈ 600 ps (corresponding to the maximum positive value of the field μ0 H ≈ 0.22 mT). As will be discussed in detail in Section II.C.5, this contrast change is due to a rotation of the domain magnetization vector into the direction of the applied field. It is part of a precessional motion of the magnetization vector taking place with a frequency of ∼1.25 GHz. From the magnitude of the contrast changes in Figure 7 it is obvious that this precessional motion involves large angle rotations of M. A quantitative analysis reveals rotation angles of up to ±45 degrees with respect to the equilibrium direction of M. The precession may also involve out-of-plane

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components, to which we are insensitive in this experimental geometry. The Néel wall also has the magnetization within the film plane. Thus in this situation the wall is immersed in a rapidly precessing environment. Considering the large angle rotation of M, this means that in this dynamic case the wall is not strictly a 180-degree wall. Instead the magnetization across the wall may include a significantly smaller or larger angle of rotation, depending on the phase angle of the precessional motion in the domains. We therefore suggest that this precession drags the wall structure with it and thereby enables very high wall velocities. Domain Wall-Dominated Relaxation Phenomena. Domain wall motion may also play an important role if relaxation phenomena are concerned. The following discussion concentrates on the relaxation behavior of a magnetic element during and after the trailing edge of a field pulse. For this purpose, the Permalloy element has been subjected to a rather long unipolar field pulse of 10 ns width and ∼20 Oe height to establish a metastable magnetic configuration from which the relaxation could occur. After the decay of the field pulse the system was given 176 ns time to relax back into the ground state. As will be detailed in Section II.C.4, this pulse indeed leads to the formation of transient domain configurations with a high density of small- and large-angle domain walls caused by incoherent rotation processes. Figure 8 shows two examples for a retangular and a ring-shaped Permalloy microstructure (Neeb et al., 2005; Schneider et al., 2004). In the case of the rectangle, we start from a well-defined Landau pattern, consisting of

F IGURE 8. Development of transient domain patterns along a field pulse of 10 ns width (pulse profile as in Figure 6). Top row: Rectangular structure of 16 µm × 32 µm and 8 µm × 32 µm (right and left element, respectively). Bottom row: Ring-type structure with 64 µm diameter. Note that the directions of pulse field and photon incidence are perpendicular.

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triangular and diamond-shaped domains. Apparently, the sample relaxes reproducibly back into this state, which also corresponds to the pattern in the static case. The situation is somewhat different for the ring structure. In the ground state, we would ideally expect a continuous rotation of the magnetization around the center of the ring. The ring has a small defect (a notch at about 5 o’clock on the inner circumference). This notch acts as a pinning site for domains. As a result, the pattern that we observe in the stroboscopic experiment is some metastable intermediate state and not the ideal ground state. Nevertheless, this metastable state also is reproducibly reached in the stroboscopic imaging; otherwise the image would be blurred. The transient state assumed on the pulse plateau (5 ns, 9 ns) is characterized by a very complex magnetization distribution with several small stripelike domains. These appear mainly in those regions of the ground state configuration, where the local magnetization is opposite to the pulse field direction (see Section II.C.3). Therefore, in the rectangle this behavior shows up alternatingly in the left- and right-hand triangular domains. In the ring, the response is different. Most of the domains coherently rotate into the field direction to form a transient onion state with the exception of a few areas that exhibit closure domains and small domains with invariable magnetization. When the field pulse is switched off, the demagnetizing field will try to restore the original starting configuration. Following the evolution of the magnetization along the falling edge of the pulse, we first note the formation of a finely striped pattern also in those regions of the rectangle, which on the field pulse plateau had a homogeneous contrast, because of M↑↓H . This is due to the fact that on the plateau the system has already settled into a new equilibrium state in the presence of the field Hp . Reducing the field acts on the system in the same way as applying a field – H (t) in the opposite direction. This leads to a stripe formation in all those domains with M antiparallel to H (t). This explains also why this process is so fast and cannot be related to simple domain wall propagation. Instead the domain and domain walls are formed by incoherent rotation events. Domain wall motion is visible behind the trailing edge of the field pulse. The movement of ∼7 µm measured between the 9 ns and 15 ns images reveals a domain wall speed of only 100 m/s, driven by stray field minimization. A similar process takes place in the ring. The formation of stripes is particularly strong on the top and the bottom of the structure, which are the regions with M↑↓H in the transient equilibrium configuration on the pulse plateau. With elapsing time this stripe pattern becomes sharper and some neighboring stripes appear to coalesce into larger blocks. This means that some of the domain walls are annihilated. This relaxation process, however, takes a much longer time than the buildup of such a stripe pattern during the rising edge of the pulse (visible already at 150 ps, see below). Even at

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t = 15 ns (i.e., ∼5 ns after the field has effectively turned down to zero), the stripe patterns persist. In addition, the changes between t < 10 ns and t = 15 ns are marginal. Some sample images taken at t = 20 or 30 ns indicated that the relaxation was indeed proceeding very slowly. This is likely due to the fact that in the absence of a fast pulsed field, exerting a strong torque, the magnetization can only change its direction by domain wall propagation, which is much slower than rotation processes, particularly if defects and pinning sites for domain walls are involved. In case of the rectangular structure, a full relaxation into the Landau pattern takes place somewhere between t = 30 and 50 ns. This is an example of how domain wall motion can slow down the magnetic relaxation in ultrafast timing experiments, provided the field pulse acts long enough to displace the domain walls from their equilibrium position. Domain Wall Dynamics in Coupled Systems. Magnetically coupled systems, such as spin valves or magnetic tunneling junctions, play an important role in applications. The element selectivity of the XMCD magnetic contrast allows unique access to the micromagnetic behavior of these chemically complex layer structures (Swiech et al., 1997; Schönhense, 1999, 2004). In particular, magnetic coupling phenomena can be addressed this way (Schneider et al., 2001, 2002; Kuch et al., 1998, 2004; Vogel et al., 2005). In the following, we briefly discuss an experiment addressing the domain wall mobility in a layered system of the type Co/Cu/Fe20 Ni80 (Fukumoto et al., 2005). This experiment involves a single-pulse procedure, which differs significantly from the stroboscopic approaches described previously. In the single-pulse case, the film system is subjected to a nanosecond magnetic field pulse of chosen width and height, and the resulting stationary domain pattern is imaged without time resolution. This pulse/imaging sequence is repeated several times. The motion of the domains and domain walls can be traced from a comparison of the subsequent images. The sample investigated by Fukumoto et al. (2005) was an extended trilayer comprising 5 nm Fe20 Ni80 / 10 nm Cu / 5 nm Co grown on a stepbunched Si(111) surface. The large Cu interlayer thickness inhibits a sizable interlayer exchange coupling between the ferromagnetic layers. However, the sample exhibits a considerable magnetostatic coupling contribution arising from the roughness at the step bunches (i.e., a particular type of “orange peel” coupling) (Néel, 1954). Details about the coupling of the magnetic field pulse to the extended sample are described in Vogel et al. (2003). As a starting state, the sample was first completely saturated and then subjected to a single field pulse of 5 mT height and 120 ns length. The rise time of the pulse is ∼10 ns, resulting in a field gradient of 0.5 mT/ns. This pulse field initiates the magnetization reversal process and leads to the nucleation

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F IGURE 9. “Single-pulse” experiment on a magnetically coupled trilayer structure. The sample was subjected to field pulses of 120 ns width and 5 mT (a–c) or 6.1 mT height (d, e). The circles mark the position of the tips in the jagged domain wall and the crosses their new position after application of a field pulse. From these motions a lower limit of the wall velocity can be estimated as 270 ± 80 m/s for 5 mT and 410 ± 20 m/s for 6.1 mT. (From Fukumoto et al., 2005.)

of a few small domains, giving rise to an almost homogeneous dark contrast and small white inclusions in the X-PEEM images taken at the Fe L3 edge [Figure 9(a)]. After a second pulse of the same field strength domains with a jagged boundary have formed [Figure 9(b)]. A third pulse moves the domain walls again [Figure 9(c)]. From these subsequent propagation steps an upper limit of the domain wall velocity of about 270 ± 80 m/s has been determined. If the same experiment is repeated at a higher field gradient and larger pulse height of 6.1 mT, similar observations are made [Figure 9(d, e)]. From these data wall velocities of about 410 ± 20 m/s can be extracted. Since in the viscous regime, the domain wall velocity scales with the external field amplitude (see Section II.A), a better quantity for comparison purposes is the domain wall mobility β, which can be extracted from the domain wall velocity v and the effective field Heff according to Eq. (6). In the present case it is important to distinguish between applied and effective field, because the dipolar coupling leads to a field contribution of ∼2 mT, which acts against the applied field. Taking this into account one arrives at a wall mobility of β = 100 m/(s·mT) for the Permalloy layer assuming that the wall has moved with a constant velocity during the pulse. Values of up to 400 m/(s·mT) have already been reported in the literature (Konishi et al., 1971). The reason for this difference may be sought in the morphological defect structure and the sample roughness.

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F IGURE 10. (a–e) Series of XMCD images showing the time evolution of the magnetic contrast in 6 µm Permalloy squares. (From Raabe et al., 2005.)

2. Vortex Dynamics Magnetic vortices can be described as magnetic curls appearing at intersections of Néel walls (see Figure 7, top panel) and in cross-tie walls. As recently shown experimentally (Wachowiak et al., 2002) vortices are threedimensional (3D) structures that possess nanometer-sized cores in which the curling magnetization turns out of plane, avoiding the high energetic cost of antialigned moments. Magnetic vortices can be trapped in lithographically defined rectangular or circular magnetic patterns. They are of considerable technological interest because the low magnetic stray field leads to high magnetic stability and minimizes the cross-talk between adjacent vortices. Because the diameter of the core is of nanometer size, magnetic microscopy with high lateral resolution is needed to explore the properties of vortices. Recently time-resolved X-PEEM has provided deeper insight into vortex dynamics (Choe et al., 2004; Raabe et al., 2005). It was shown that the dynamics of the vortex are controlled both by the magnetization curl around the vortex and by the independently directed perpendicular magnetization of its core. Figure 10 shows a series of XMCD images from an experiment performed in the hybrid camshaft mode at the Swiss Light Source (SLS) in Villigen. The series reveals the movement of a vortex in the center of a square platelet (Raabe et al., 2005). The sample in this case is a Permalloy square with 6 µm edge length and 30 nm thickness. The magnetization pulse is generated by a pulsed laser that illuminates a voltage-biased photodiode launching a current pulse into a coplanar waveguide (10 µm). The field amplitude is Hp = 6 mT, the pulse width is 450 ps, and the pulse is repeated every 16 ns. The magnetization pattern reveals only two different gray levels because the polarization of the incident X-ray beam is at 45 degrees to the magnetization direction in the four domains of the Landau pattern. All domains have a component of M perpendicular to H p and experience a torque

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of equal magnitude. At t = 300 ps the intensity has increased in all domains, consistent with equal precessional motion caused by the initial torque. For t = 1550 ps, a large vortex displacement is observed that is perpendicular to H p . In addition a bulging of the domain walls is observed. At t = 2550 ps the domain walls have bulged back while the vortex has not yet relaxed to the center of the square. For long delays (t ≥ 14.3 ns) the system has returned to the Landau pattern, ensuring that it starts from the equilibrium state when being reexcited after 16 ns. A quantitative analysis of the vortex motion gives a maximum velocity of the vortex of vvortex = 2000 m/s at the leading edge of the pulse and a much smaller velocity at the trailing edge (Raabe et al., 2005). The vortex displacement persists long after the field pulse is gone. For strong field pulses the observed vortex motion perpendicular to the exciting field has also been seen in micromagnetic simulations (Hertel and Kirschner, 2004). It may be depicted as an increase of the domain with favorable magnetization direction with respect to the external field and a decrease of the domain with unfavorable magnetization. Whereas in the previous example the out-of-plane magnetization direction of the vortex plays no role, a different behavior was predicted for the case of small and short field pulses (Argyle et al., 1984). A Magnus-type force based on the Landau–Lifshitz–Gilbert equation is acting on the vortex parallel to the initial field pulse and leading finally to a gyrotropic motion of the vortex core around the pattern center with a frequency in the sub-gigahertz regime (Argyle et al., 1984). Using time-resolved X-PEEM at the Advanced Light Source (ALS) in Berkeley, Choe et al. (2004) showed that the out-ofplane magnetization influences the rotational sense of the gyrotropic motion. The effect is illustrated in Figure 11. In contrast to the expected transverse movement of the vortex, the vortex center moves parallel to the field because, on a subnanosecond time scale, magnetic moment precession around the field direction dominates over damping in the field direction. When viewed along the direction of the field pulse H p , the magnetic moments in left- and righthanded vortex structures experience a clockwise precessional torque about the field direction (see Figure 11). In a left-handed vortex, the magnetization in domain 3 precesses in the direction of the core magnetization, which itself precesses in the direction of the magnetization in domain 1. This corresponds to an initial motion of the vortex core antiparallel to the applied field. In contrast, for a right-handed vortex, the magnetization in domain 1 precesses in the direction of the core magnetization, resulting in a parallel motion of the vortex. The vortex handedness thus controls the fast, precessional dynamics of a micron-scale vortex pattern. The displacement of the core after the field pulse causes an imbalance of the in-plane magnetization (domain 1 is larger than domain 3), which in turn creates a demagnetization field perpendicular

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F IGURE 11. (a) Spin structure (white arrows) of a left-handed (left side) and a right-handed (right side) square vortex. Small vertical arrows represent the precessional torque generated by the external magnetic field H . Hands illustrate the vortex handedness, and the large vertical arrows indicate the out-of-plane core magnetization, the arrows at their top indicate the acceleration direction in response to the field. Simulated trajectory of the core of (b) a left-handed and (c) a right-handed vortex during and after a field pulse. (From Choe et al., 2004.)

to the displacement. This demagnetization field, initially directed to the left in (b) and right in (c), acts in a similar manner as the external field and moves the vortex to the right (b) and left (c). In the case that the external field is zero, the demagnetization field is always directed perpendicular to the actual displacement of the vortex that drives the vortex on a spiraling trajectory. For all vortices, the sense of the gyrotropic motion is counterclockwise when the direction of the out-of-plane magnetization at the core points toward the viewer and vice versa. While the gyrotropic motion of the vortex core excited by a short field pulse was observed experimentally (Choe et al., 2004), the out-of-plane magnetization direction of the core could not be resolved (Figure 12). However, it could be shown that the curling orientation of the in-plane domain structure was not correlated with the initial acceleration or the rotation sense of the gyrotropic mode, which makes the behavior described above very likely. Recently a similar observation of a gyrotropic vortex motion was measured by Puzic et al. (2005) using scanning X-ray transmission microscopy. Eventual changes of the rotational sense observed for strong field pulses indicate induced switches of the core magnetization. Micromagnetic simulations of the core motion as depicted in Figure 12 confirmed the gyrotropic motion (Choe et al., 2004).

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F IGURE 12. (Top) Domain images of the in-plane magnetization of pattern 1 µm × 1 µm (a), 1.5 µm × 1 µm (b, c), and 2 µm × 1 µm (d), taken at the specified delay times after the field pulse. The images are part of a time series that extends over 8 ns and were chosen so that the horizontal displacement of the vortex has maximum amplitude. Hands illustrate the vortex handedness and the out-of-plane core magnetization as determined from the vortex dynamics. (Bottom) Trajectories of the vortex core. The dots represent sequential vortex positions (in 100 ps steps). Lines represent time-averaged positions with a Gaussian weight function of 100 ps (FWHM) for 0 to 1 ns and 400 ps (FWHM) for 1 to 8 ns. Straight arrows show the trajectory during the field pulse, curved arrows show the direction of gyrotropic rotation after the pulse, and stars show the vortex position for the shown domain images. (From Choe et al., 2004.)

During the external field pulse, the core moves either parallel or antiparallel to the pulse field, depending on the vortex handedness. Afterward, the trajectory turns parallel or antiparallel to the magnetostatic field and the core starts its gyrotropic motion, in agreement with the experiment. The speed v of the core as observed in Figure 12 can be estimated using v ≈ 2γ0 bH /π,

(12)

with γ0 = γ μ0 representing the gyromagnetic ratio (Choe et al., 2004). The formula reflects that the precession of core spins by π/2 corresponds to the

translation of the core by its diameter b. The core diameter b = 2 2A/μ0 Ms2 can be approximated from the exchange stiffness A and magnetization Ms . For the core diameter in CoFe and permalloy platelets b ≈ 10 and 40 nm, respectively. As a suggestive assumption the effective field driving the vortex can be approximated from the demagnetization field Hd = εNxy Ms /2 generated by the vortex displacement ε = 2x/ l, with lateral dimension l of the platelet and demagnetization factor Nxy = 2t/ l. For the case of Choe et al. (2004) a displacement of 50 nm in a CoFe square of length l = 1 µm and thickness t = 20 nm corresponds to a demagnetization field

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of only 4 mT, which is far too small to explain the velocity of 100 m/s. Therefore the internal field near the core must be considerably higher. This is in agreement with micromagnetic simulations (Choe et al., 2004), which show a considerably enhanced value at the core of 80 mT as a consequence of the deformation of the magnetic structure of the vortex core during its gyrotropic motion. The fact that the vortex velocity in the case shown in Figure 10 is an order of magnitude higher than the case of the gyrotropic motion expresses the different origin of the effect. In Figure 10 the vortex motion is driven by the inplane rotation of magnetization toward the favorable magnetization direction with respect to the external field pulse. The result is a transverse motion perpendicular to the field pulse and independent of the core magnetization. In Figure 12 the vortex motion is driven by the out-of-plane rotation of the magnetization perpendicular to the external field pulse. A precondition for its observation is certainly a relative suppression of the large effect described above by a large demagnetization factor Nxy = 2 × 10−2 in the case of Choe et al. (2004) and 5 × 10−3 in the case of Raabe et al. (2005). Moreover, the small radius of the gyrotropic motion requires a high lateral resolution. 3. Transient Domain Walls and Vortices As mentioned previously in Section II.C.1, domain wall motion is the dominant response mechanism of multidomain configurations on slow field variations. We found that a domain boundary may be displaced only a few hundred nanometers during the rise time of a fast magnetic field pulse. For the 2 mT pulses used in the measurements presented the leading edge is ∼500 ps wide (pulser output); for ultrashort pulses it can be up to a factor of 5 shorter. A magnetic element with a lateral size of several micrometers will thus not be able to react on the field pulse by large domain wall movements. Instead, magnetization reversal can only proceed through the damped precessional motion of the magnetization vector. In addition to magnetic eigenmodes and their excitation spectra, there is another striking difference between the magnetic response of a given thinfilm microstructure on a pulsed external magnetic field compared with the quasi-static magnetization reversal. This concerns the appearance of transient spatiotemporal domain patterns and particular detail features in the patterns that do not occur in the quasi-static case. This section presents examples of such patterns in Permalloy platelets of various shapes and sizes. In particular, we discuss the broadening of domain boundaries due to the precessional magnetization reversal, the formation of transient domain walls and transient vortices, as well as the emergence of stripelike domain patterns (blocking patterns).

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The spatiotemporal patterns of precessional remagnetization were observed via stroboscopic series of XMCD-PEEM images measured at the European Synchrotron Radiation Facility (ESRF) in Grenoble. The pulse and probe frequency here was 5.7 MHz (16 bunch mode at the ESRF), yielding a time interval of 176 ns for the sample to relax back into the ground state after the pulse excitation (Kuksov et al., 2004). Time resolution was ∼125 ps, the amplitude of the pulse field was μ0 H = 2 mT (for details of the setup, see Neeb et al., 2005). In all experiments presented here the Permalloy layer has been produced by sputter deposition onto a lithographically prepared Cu stripline surface. It was microstructured by means of optical lithography and ion beam milling, as described by Schneider et al. (2004). Broadening of Domain Boundaries due to Precessional Remagnetization. Figure 13 shows the magnetic response of a Landau flux-closure pattern (comparable to the one introduced in Figure 2) on a magnetic field pulse with the profile given in Figure 14(a). The pattern (20 µm × 20 µm) is actually the top region of a larger rectangular structure (20 µm×80 µm) that is fully shown in Figure 15 (right element). The top rows display the XMCD asymmetry images taken from a sequence with a 125 ps increment. The bottom rows show the corresponding difference images obtained by subtracting the image at t = 0 ps (equilibrium state) from the corresponding image in the top row. As explained in the context of Figure 2, the maximum initial torque acts on domains B and D with M⊥H p . We now address the question whether these domains respond coherently to the field pulse. The image sequence in Figure 13 answers that question. As discussed in Section II.B.3, the gray value in an XMCD image is proportional to the projection of the local magnetization vector M(r) onto the vector of the photon helicity P circ , giving rise to a cos dependence of the dichroic contrast. The gray values in the XMCD asymmetry images thus give direct access to the angle of M(r) with respect to P circ (pointing from left to right in these images). The XMCD asymmetry in regions E and F has been determined and translated into the rotation angle according to Eq. (9); it is plotted versus time in Figure 14(b). During the steepest part of the rising edge of the field pulse (i.e., between t = 0 and about 250 ps), the precessional motion is excited. The Fourier spectrum of the pulse contains high-frequency contributions and the steepest part of the edge “triggers” the high-frequency response. These precessional modes (comparable to the normal or center modes discussed, for example, by Park et al., 2003) occur in domains B and D. With increasing time the magnetization in domains B and D is rotated out of the equilibrium direction due to the damped precessional motion. In the difference images in Figure 13 this effect shows up in that domain B gets darker and domain D gets brighter.

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F IGURE 13. Series of XMCD-PEEM snapshots (upper rows) and corresponding difference images (second rows) of the domain pattern of a Permalloy element (40 nm thick) from a sequence with 125 ps increment. Only the upper quarter of the 20 µm × 80 µm platelet is shown. Schemes (a)–(d) denote schematic magnetization structures, domains A–D, microregions E–F, and position of the line scans (dashed line in a). Marks + and − denote magnetic charges.

The two curves in Figure 14(b), taken for regions E and F, show damped oscillations of the angle with a period of approximately 800 ps, corresponding to a frequency of 1.25 GHz. This value corresponds here to the case of a

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F IGURE 14. Field-pulse profile (a), micromagnetic response local rotation angle of regions E and F (b), apparent width δ of the domain wall (c) resulting from the line profiles shown in (d). Regions E and F and the line profile position (dashed line) are denoted in Figure 13(a). The pulse profile has been determined experimentally (dots), for comparison the output signal of the electronic pulse generator is shown (full line, adjusted in the maximum).

nonvanishing external field, as is clear by comparison with the field pulse profile in (a). The oscillation is superimposed on a gradual change of the angle (dashed curve) that shows the rotation of the in-plane effective field (i.e., it reflects the actual remagnetization process). The upper curve in Figure 14(b) is not the mirror image of the lower curve as might be expected. Instead, it appears more complicated and exhibits several extrema. This indicates that we actually see the coexistence of more than one mode as previously discussed by Park et al. (2003) and Raabe et al. (2005). This dyssymmetry is most likely due to the fact that the pattern shown in Figure 13 is actually the top part of a larger structure and its dynamic response is influenced by the behavior of the whole structure. Region E lies in the triangular closure domain B, whereas region F lies in a rectangular domain in “diamond” orientation as visible in Figure 15(b) and sketched in Figure 13(a). For the same reason the magnetization in domains B and D is slightly tilted in the t = 0 ps image, about 10 degrees away from the ideal equilibrium directions of 0 and 180 degrees,

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F IGURE 15. Series of XMCD-PEEM snapshots of transient domain patterns of two Permalloy elements (30 nm thick). The sizes are 40 µm×80 µm (left) and 20 µm×80 µm (right platelet). A strong unipolar pulse drives the pattern from the initial “virgin” state (a) through an intermediate state (c) into an almost saturated state (d) that gradually relaxes (e, f) into the final state (b) at t = 0 and 176 ns behind the field pulse. The pulse profile is identical to Figure 14(a). Arrows denote the local magnetization direction as deduced from the quantitative XMCD contrast.

respectively. The structure may possess a small remanence or may experience a stray field interaction with neighboring elements on the stripline. The initial phase is governed by the characteristics of the precessional motion that rotates the local magnetization direction in regions E and F by ∼50 degrees during the first 2 ns [see Figure 14(b)]. The initial magnetization rotation between 125 and 500 ps amounts already to more than 40 degrees in region E and 30 degrees in region F. Without damping, the magnetization would continue its precession. Damping, however, leads to energy dissipation from the precessional mode into the phonon system. As a related feature, the 90-degree Néel walls A/B and A/D appear diffuse for t = 250 ps and above. In the difference images (second rows in Figure 13), this effect appears as a pronounced dark and bright feature antisymmetric to the domain walls A/B and A/D. This effect starts in the center of the domain wall, leaving its outer end at the corner and central part close to the vortex initially unaffected. Because of its low velocity the vortex pins the domain walls in the center, whereas in the corners a high demagnetizing field stabilizes the wall position. In the central part of the walls a region emerges that exhibits a continuous variation of the local magnetization direction as sketched in the schematic domain pattern [see sketch (b) in Figure 13]. These regions rapidly widen during the leading edge of the field pulse. Finally, the new triangular regions sketched in image (c) unify with domain A, forming a W-shaped domain with essentially uniform magnetization directed along the field pulse [see 7250 ps image and sketch (d)]. The initial walls A/B and A/C appear displaced and the central vortex has completely disappeared. This state has a large net magnetic moment as indicated by the magnetic charges at the upper and lower end of the structure in (d). Following Chikazumi (1964), we use the concept of

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magnetic charges denoted by + and − (magnetic monopoles do not exist, of course). A very striking phenomenon is the appearance of a striped pattern in domain C that is discussed below. The region of continuous rotation of the magnetization can also be discussed in terms of a strong broadening of the 90-degree Néel wall. This is illustrated in Figure 14(c) showing the temporal evolution of the apparent width δ (20% to 80% value) of the wall. The quantity δ has been extracted from line profiles along the dashed line denoted in the scheme in Figure 13. Examples I, II, and III of resulting line profiles are shown in Figure 14(d). During the rising edge the Néel wall broadens very rapidly to ∼4 µm and during the pulse plateau it becomes narrower again, until it reaches its initial width at the end of the pulse. The true width of approximately 80 nm of the unperturbed Néel wall could not be resolved in these dynamic images. At this point it is important to recall that the images are measured in stroboscopic mode (i.e., each image represents the average over about 109 magnetization cycles). This means that the gray value represents the average in-plane component of M that undergoes a damped precession about the direction of the effective field H eff , which is not constant but varies with time. The high precessional frequency in the range of 1.25 GHz corresponds to a rotation of 90 degrees in roughly 200 ps. Our time resolution of ∼125 ps therefore does not allow us to take sharp snapshots of the precessional motion. Instead, we observe the rotation angle averaged over 125 ps. Figure 15 shows a sequence of snapshot images during the application of the same unipolar field pulse to a larger rectangular element with 40 µm × 80 µm (left) and to the 20 µm × 80 µm element, the top part of which was discussed above (right). The series starts from a slightly deformed Landau state (a) as a “virgin” state, before the first pulses are applied. The pulse train drives the large platelet from the seven-domain ground state (a) into an 13domain state (b) that is characterized by three additional 180-degree Néel walls. These run horizontally, indicating a unaxial anisotropy in horizontal direction. Image (b) was taken in the stroboscopic mode at a delay time corresponding to the onset of the field pulse [t = 0, cf. Figure 14(a)]. Upon action of the field pulse, the domain pattern runs through an intermediate state (c) into a state with large net moment (d). The medium gray level provides evidence of the fact that in most parts of the platelet the local magnetization is pointing upward as indicated by the arrows. Bright closure domains remain only at the top and bottom edges. At the left and right edges remnant weak closure-domain features are seen that are obviously correlated with features in the second platelet located parallel to the first one with a gap of only 6 µm. A dipolar coupling via the stray field stabilizes these remaining local domains. The large net moment gives rise to magnetic charges at the upper and lower end of the particle as denoted by + and − signs. These, in turn, create a

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considerable demagnetizing field that tends to compensate the pulse field, once the saturation is generated (image d). Behind the trailing edge (e) the domain pattern appears strongly distorted. Horizontal stripes are visible. Even at t = 19 ns, the pattern is still not relaxed (image f) in comparison with the t = 0 ns in image (b) that is equivalent to t = 176 ns after the preceding pulse. In contrast to the rapid precessional remagnetization during the rising edge of the field pulse, the relaxation behavior during the trailing edge and later proceeds much slower (see Section II.C.4). Obviously in this dynamic mode the domains being magnetized perpendicular to the field pulse are enlarged at the expense of the parallel and antiparallel domains. For the large platelet the latter domains are only an areal fraction of ∼30% in the dynamic mode [Figure 15(b)]. In the “virgin” state [Figure 15(a)] the parallel and antiparallel domains occupy almost 50% of the platelet, as it should be for an ideal Landau ground state. This is a consequence of the fact that the magnetization vector in perpendicular domains can adjust more rapidly to the external field pulse (via rotation) than parallel domains could and thus minimize the free enthalpy of the system. Formation of Transient Domain Walls and Transient Vortices. The nonuniform precessional motion can give rise to dynamic domain walls that form and vanish (or at least develop into small-angle walls) during the magnetization process. An example is shown in Figure 16 (a–e), showing the response of the same structure as Figure 15 to a bipolar pulse (profile shown in f). Close inspection reveals that a part of a given domain undergoes a precessional remagnetization, whereas other parts of the same domain remain unchanged. This effect is visible, for example, in the bottom white domain in images (c and d). The line scan (panel g) along the dashed line reveals that the border between the precessing and nonprecessing region is rather sharp— a transient domain wall becomes visible in the dynamic image sequence. The orientation of the wall is determined by the fact that the magnetization component perpendicular to the wall is continuous (flux conservation in the material); see magnetization arrows in (d). During this bipolar excitation the structure developed “spike domains” in the upper corners of the large element as discussed by Chumakov et al. (2005). The flux penetrates the element from the bottom to the top left corner for the positive pulse (image b) and from the top right corner to the bottom left corner in the negative field direction (image d) as indicated by the arrows. Close to the zero between positive and negative polarity the magnetization rotates into directions nearly perpendicular to H p (shown in image c). The direction of the magnetization in the corner domains is not changed due to the strongly reduced effective torque, caused by the large local demagnetizing field inside the corners.

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F IGURE 16. (a–e) XMCD-PEEM snapshots for the same elements as in Figure 15 but for the bipolar pulse plotted in the lower panel (f). This pulse does not saturate the magnetization but generates a high net magnetization in the positive (b) and negative (d) field maxima. The line profile of the transient domain wall along the dashed line in (d) is shown in panel (g).

Figure 17(a–c) shows XMCD-PEEM snapshots of another pattern at t = 0, 250 and 500 ps after the onset of the field pulse. This Landau-like domain structure occurred in a Permalloy ring due to a structural defect, as discussed in detail by Neeb et al. (2005). The magnetization of domain C rotates toward the direction perpendicular to H p . Obviously, the torque is clockwise for the upper half and counterclockwise for the lower half of the domain [see image (b)]. This behavior is caused by the interplay between the demagnetizing field and external pulse field. The mechanism is illustrated by the micromagnetic simulation shown in Figure 17(d and e). It has been performed for a small square element with an edge length of 1 µm and 18 nm thickness. Starting from the Landau pattern (d), the external field pulse of 5 mT with a leading edge of 100 ps generates at t = 340 ps (e) a displacement of the central vortex by 300 nm and a pair of antiparallel oriented domains as observed in the experiment. Magnetic charges at the upper and lower right part of the flux-closure structure are formed as a response to the field pulse. The

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F IGURE 17. Three snapshot XMCD asymmetry images of a Permalloy element (30 nm thickness) showing how a Landau flux-closure-like structure (a) is driven into a transient double-vortex state (b, c) in the leading edge of a field pulse. Vortex positions are denoted by circles. A micromagnetic simulation (1 µm × 1 µm, 18 nm thickness, 5 mT) starting from a Landau state (d) reproduces this double-vortex state and reveals strong emission of spin waves (e). In a simulation with changed parameters (1 µm × 1 µm, 3 nm thickness, 0.8 mT), the double vortex state is absent (f). Note that images (b, c, e) show a transient state that does not occur during quasi-static remagnetization.

demagnetizing field originating from these charges is added to the external field yielding the total effective field. H eff is thus significantly tilted away from the original field pulse direction H p . The tilt results in a torque on the magnetization in domain C. This torque, in turn, rotates the magnetization clockwise in the upper half of domain C and counterclockwise in the lower half. Thus a pair of antiparallel domains with M perpendicular to H p is formed. This domain structure contains two new vortices as indicated by the circles in Figure 17(c). Both structures are confirmed by the simulation (e). Another transient vortex is visible in Figure 18(b) (see circle). The importance of the stray-field energy was confirmed by a simulation for a square with the same lateral dimensions, but with a thickness of only 3 nm [see Figure 17(f)]. The antiparallel domains in the former domain C do not occur here. In this case the field pulse is so large that the demagnetizing field caused by the charges at the edges of domain C does not significantly change

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F IGURE 18. Striped domain pattern (b) emerging from the Landau state (a) in a Permalloy element during the onset of the field pulse in the domain originally magnetized opposite to the field pulse. In addition, a transient vortex appears as denoted by a circle. Image (c) shows further development of the magnetic structure. The mechanism is sketched in (d) and (e) (see text).

the direction of the effective field. The original single vortex is thus preserved and only deformed and displaced. These transient states are a particular feature of fast and ultrafast magnetization reversal processes. In order to observe the richness of features in detail, a high-resolution probe such as X-PEEM is mandatory. 4. Rapid Formation of Stripe Patterns (Blocking Domains) We return to the situation shown in Figure 2. In the ideal case, the initial torque in domain C is zero. However, as soon as the adjacent domains start to react on the field pulse, the local demagnetizing field gives rise to a local effective field H eff that deviates from the direction of H p . Consequently, a torque is exerted on domain C. Owing to the demagnetizing field the response of domains A–C is thus not independent from each other. The snapshots in Figure 18 show that here the initially antiparallel domain in image (a) exhibits a rapid formation of a characteristic stripe pattern (b). The magnetization within the stripes has a significant component perpendicular to the initial magnetization, as is obvious from the dark and bright contrast. During the presence of an almost constant external field during the pulse plateau the stripe pattern coarsens (c). The following text discusses driving mechanisms that can generate such a domain pattern.

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Time-resolved Kerr microscopy along with micromagnetic simulations revealed the emergence of such complex striped patterns in Permalloy microstructures of similar size (Freeman et al., 1998; Freeman and Hiebert, 2002; Hiebert et al., 1997, 2002). Starting from an initially saturated state, the response on a field pulse antiparallel to the initial static field was investigated. Above a certain field strength the appearance of complex stripelike domain phases was observed. This behavior was attributed to incoherent magnetization rotation processes. The homogeneous magnetization breaks up into a system of striped regions, in each of which the local magnetization vector rotates into an orientation toward M⊥H p (t). During the dynamic response, M is also transiently rotated out of the film plane. The authors attribute the origin of the striped domain pattern to a magnetization ripple in the equilibrium state (magnetic inhomogeneities or anisotropies in the film) and to structural imperfections (edge roughness) of the magnetic microstructure. Our image series in Figure 13 (t = 250 ps and higher) reveals that the stripes seem to nucleate at the Néel walls B/C and C/D, thus ruling out edge roughness as a predominant mechanism. The patterns show some similarities to the static van den Berg concertina patterns, blocking patterns, or buckling states (van den Berg and Vatvani, 1982; Decker and Tsang, 1980). Hubert and Schäfer (1998) have shown that these are composed of a system of interacting, low-angle Néel walls that stabilize themselves by dipolar fields. The patterns are caused by the interplay between the stray-field energy and the same mechanism that gives rise to the magnetization ripple, well-known for Permalloy (Hoffmann, 1968). Static concertina patterns are “highly repeatable” as noted by Chumakov et al. (2005). Regions with stronger and weaker rotation appear as domain-like areas, separated by domain boundaries. Figure 13 shows that the stripe pattern gets stronger in contrast with increasing time, indicating an alternating and increasing clockwise and counterclockwise rotation of M(r) despite the fact that shape anisotropy favors an alignment of the magnetization parallel to the edges of the structure. Once this multidomain state is generated, the magnetization reversal, as well as the later relaxation, is decelerated as is visible in the series in Figure 13. One contribution is due to the low mobility of the domain-wall network (Chumakov et al., 2005). In addition, magnetic charges at the upper and lower end of the striped domain, marked by + and − signs in image (c), partly compensate the effective field. The structure looks like a horseshoe magnet whose demagnetizing field is opposite to the external pulse field, thus effectively shielding the external field. The magnetic ripple consists of a small magnetization component perpendicular to the net magnetization M as depicted in Figure 18(d). The canting of the local magnetization direction leads to M × H = 0, and the torque is

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directed such that the canting angle is enhanced leading to the striped phase as sketched in (e). Figure 18(b) reveals that a typical distance of the initial striped pattern is of the order of 800 nm. During the plateau of the field pulse the stripe pattern coarsens, that is, the fine stripes partly unify as visible in (c). In the series in Figure 13 (at t = 7250 ps), similar to Figure 17(b, c), the domain pattern tends toward the two antiparallel domains that reduce the demagnetizing field of the magnetic charges at the end of the structure as discussed in the context of the transient vortices (see Section II.C.3). This is another driving mechanism that yields a local magnetization perpendicular to the pulse field in domain C. In the field plateau the magnetic charges generate the demagnetizing field H d that ideally compensates the external pulse field H p in the static limit so that H eff × M = (H p + H d ) × M = 0.

(13)

Due to this condition no torque is acting on the magnetization vector after the damped precession has stopped. Within several nanoseconds during the field plateau the magnetization pattern does not change substantially, except for the coarsening of the striped phase. The situation changes at the trailing edge where the rapid drop of the external pulse field leads to an imbalance of Eq. (13) such that the component of the effective field perpendicular to M becomes different from zero. The magnetic charges cannot follow the rapid drop of the external field instantaneously. In the leading edge the acting component of the effective field was directed upward, causing the striped phase at the right edge in Figure 15(c). In the trailing edge this component is directed downward. The image in Figure 15(e) reveals that the structure with magnetization direction antiparallel to the not acting field reacts by forming a striped phase, here affecting practically the entire structure. Behind the end of the field pulse at t = 19 ns in Figure 15(f) the demagnetizing field is still different from zero. The relaxation of the structure requires a long time as confirmed by the simulations. The image series reveals that the local magnetization processes are slowed because of the blocking pattern (see also Section II.C.3). Chumakov et al. (2005) observed that for similar elements the initial Landau ground state is reached after about 40 ns. In contrast to this work, however, we recognize a striped pattern also during the rising edge of the field pulse. This blocking of magnetization is also responsible for the stability of concertina patterns during quasistatic magnetization processes. The multidomain state significantly delays the relaxation into the Landau ground state due to the complicated wall and vortex structure and its low mobility.

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5. Magnetic Eigenmodes in Confined Systems Quantized spin-wave eigenmodes form the fundamental excitations in magnetic elements of micrometer and sub-micrometer size. They are of special interest from the fundamental point of view, since both the exchange and the magnetic dipolar interactions essentially contribute to magnetic confinement phenomena in such elements. While in the past spin-wave eigenmodes have been studied for elements possessing a monodomain state, recent experimental efforts allowed the investigation of eigenmodes in mesoscopic systems with inhomogeneous distribution of the static magnetization (Perzlmaier et al., 2005). The simplest of these systems is a magnetic disk in the vortex state characterized by an axial symmetry. The corresponding confined spin-wave modes are now intensively studied both theoretically and experimentally (Buess et al., 2004; Giovannini et al., 2004; Ivanov and Zaspel, 2002, 2005; Novosad et al., 2002; Park et al., 2003) and seem to be well understood. Another, more complex magnetic structure with reduced symmetry is a square in the fluxclosure Landau state with fourfold symmetry in the magnetization distribution (Landau and Lifshitz, 1935). Regarding the dynamic mode spectrum, no reliable theoretical prediction and only a few experimental findings have been reported up to now. Recently Raabe et al. (2005) reported eigenmode excitations using timeresolved X-PEEM in a square platelet comprising a Landau flux-closure pattern (Figure 19). This experiment was performed in the camshaft mode at the SLS. For the squares oriented parallel to the pulse field, the torque is zero in the black and the white domains. In the gray domains the torque tilts the magnetization away from its equilibrium state. Once the field pulse has decayed, the magnetization relaxes back, performing a damped precessional motion. The precession frequency is mainly determined by the dipolar energy, thus depending on the shape, size, and material parameters (Ms and A). After half a precession period (t = 300 ps) the magnetization has a maximum component along P , thus showing maximum intensity. The modes and their frequencies can be determined using a Fourier transformation of the image series (Buess et al., 2004; Park et al., 2003; Perzlmaier et al., 2005). Images of the spatially resolved Fourier amplitude for three frequencies are shown in the third row of Figure 19. At 230 MHz the intensity is highest along the domain walls, while at 1.9 and 2.4 GHz the intensity is highest within the domains. These frequencies correspond to a domain wall mode and two normal modes within the domain. The phase images of the 1.9 and 2.4 GHz modes show a uniform phase within the two domains but a 180-degree phase shift between the two modes. The frequencies of the eigenmodes can be analyzed further by analyzing the local intensity variations of the PEEM image. Averaging over regions

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F IGURE 19. Selected XMCD images showing the time evolution of the y component of the magnetization (bright areas are magnetized upward, dark areas downward) in 6 µm Permalloy squares (first row). Difference images obtained by subtracting the equilibrium state (t = 0) from each image (second row). The orientation of the exciting field pulse H p and the polarization P are sketched in the leftmost image. Sketches denote the prominent features for different delay times (third row). The fourth row shows images of the Fourier amplitudes obtained by Fourier transforming of the image sequence. (From Raabe et al., 2005.)

of interest yields the magnetization component My parallel to the photon polarization (Raabe et al., 2005). Black and white domains shown in Figure 19 with magnetization parallel to the pulse field show only a small variation of My . This is to be expected since there is no initial torque acting on it. In contrast, the gray domains (M⊥P ) show a damped oscillation. After the data were decomposed into an oscillatory part and a slowly varying background, the oscillatory part can be described by the sum of two damped oscillators with a phase shift of π and a single decay time τ :   My (t) = Ms A1 sin(ω1 t) + A2 sin(ω2 t + π ) e−t/τ . (14)

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From a fit of Eq. (14) one obtains ω1 /2π = 1.9 GHz and ω2 /2π = 2.5 GHz, and a decay time τ = 0.63 ns (Raabe et al., 2005). The fact that in the vortex states the normal mode frequencies split up has been predicted by Ivanov and Zaspel (2002, 2005). They analyzed the magnon mode excitation spectrum for vortex ground state in cylindrical nanomagnets using a linearized set of Landau–Lifshitz–Gilbert equations in an external magnetic field and showed that the splitting is due to magnon scattering at the vortex core. The magnetization dynamics in rectangular Permalloy platelets as investigated by means of time-resolved X-PEEM at BESSY in Berlin show an additional interesting behavior (Krasyuk et al., 2005). The 10 nm thick platelets of 16 µm × 32 µm size were excited by an oscillatory field along the short side of the sample with a fundamental of 500 MHz and considerable contributions of higher harmonics. In this case, the transient magnetization distribution was stroboscopically imaged using synchrotron light pulses of 3 ps width, yielding an effective time resolution of 15 ps. Selected XMCDPEEM images are shown in the upper row of Figure 20. The actual shape of the current pulse could be derived from the apparent change of the size of the rectangular platelet when the current pulse passes the FOV. The voltage pulse accompanying the current pulse changes the magnification of the electron optical lens slightly (Neeb et al., 2005). An absolute value for the magnetic field results from the voltage signal measured at the output of the waveguide using a fast oscilloscope (R = 50 , b = 50 µm). The maximum field values are of the order of 2 Oe [Figure 21(a)]. The output shield of the pulse generator was set to floating ground. Thus the mean current through the waveguide remains zero and the applied signal was merely a 500 MHz alternating current (AC) signal with considerable contribution of higher harmonical components (d) and synchronized with the X-ray pulses from the synchrotron. The stroboscopic illumination of the sample was achieved by X-ray pulses produced by electron bunches in the synchrotron ring (tFWHM = 3 ps in the low-alpha mode) with a repetition rate of 500 MHz (Abo-Bakr et al., 2003; Feikes et al., 2004). The AC driving current and the probe pulses are synchronized with a variable electronic delay. The sample is thus excited and probed every 2 ns. To acquire an image the signal is typically integrated for 30 s, thus averaging over 1.5 × 1010 pumpprobe cycles. Snapshots of the time evolution of the magnetization in the Permalloy platelet comprising a Landau flux-closure pattern are shown in Figure 20 for the smallest field pulse. The domains oriented parallel and antiparallel to P appear black and white, while the two domains oriented perpendicular to P both appear gray. A 180-degree Néel wall, along the y-axis separates the two large domains with magnetization upward (left) and downward (right). In the Néel wall the magnetization is oriented to the left; thus the Néel wall

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F IGURE 20. Selected XMCD asymmetry images showing the time evolution of the x component of the magnetization (bright areas are magnetized to the right, dark areas to the left) in a Permalloy platelet (16 µm × 32 µm, 10 nm thick). The delay times are t = 0 (a), 600 (b), 1100 (c), and 1400 ps (d). The orientation of the exciting AC field and the photon polarization P are in x-direction. Sketches of the corresponding domain patterns are shown in the second row. In the third row micromagnetic simulation results are shown for a Permalloy platelet with linearly reduced dimensions (8 µm × 16 µm × 5 nm, cell size 10 nm).

appears black. Because of the high exciting frequency the image at t = 0 corresponding to the onset of the field pulse does not represent the equilibrium case before the excitation. The system did not have enough time to relax back into the equilibrium state since the preceding pulse arrived. Instead the image already shows a dynamic state of the magnetization pattern. The 180-degree Néel wall is shifted to the right. Moreover, an inhomogeneous magnetization structure shows up in the left and right domain, which can be seen most prominently close to the vortex located at the upper end of the Néel wall. At t = 600 ps [image (b)] the intensity has increased in the left and right domain, indicating a rotation of the magnetization vector toward the direction of the applied field—clockwise in the left domain and counterclockwise in the right domain. At t = 1100 ps the left and right domains appear dark because the magnetization has rotated in the opposite direction. A second oscillation is indicated by the snapshot at t = 1400 ps (d).

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F IGURE 21. Quantitative analysis of the time-dependent magnetization extracted from the whole image series correspond to Figure 20(a–d) (top row). Two periods are shown to emphasize the repetition rate. (a) Time dependence of the exciting magnetic field Hx (t) for three pulse amplitudes I, II, and III. (b) Time evolution of Mx averaged over the boxes shown in the inset in Figure 22. (c) Displacement of the 180-degree Néel wall parallel to Hx (t). (d) Fourier decomposition of the pulse profile I in image (a).

Micromagnetic simulations were used to verify the experimental findings. Permalloy rectangles of the same aspect ratio were excited with periodic pulses of the same magnetic pulse shapes and strengths as the experimental

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samples. The time evolution of the magnetization was stored until the oscillations converged. The spin-wave eigenfrequencies were then determined by local Fourier transformations, and the local power density was integrated over the volume to a global power density. The local power density yields the location and relative phases of specific eigenmodes. The micromagnetic simulations yield very similar oscillations of the magnetization, even though the exact pattern has not been reproduced. In particular, the experimentally observed right shift of the Néel wall caused by the high-frequency excitation could be reproduced in the simulation when an initial small asymmetry is assumed. In the experiment shown in Figures 20 and 21 (Krasyuk et al., 2005) the dominating excitation mode is a precession of the magnetization in the two large domains. It is excited by the external field pulse directed perpendicular to the magnetization in these domains. Our observation of two pronounced maxima of the magnetization component parallel to the field confirms the dynamic motion of the magnetization. In our case, the excitation field can rather be described as an oscillating field with considerable contribution of overtones instead of a field pulse. Thus the system resembles a forced oscillator, and we observe the dynamic answer of the system to the excitation rather than a damped oscillatory relaxation to equilibrium. To determine the frequencies and amplitudes of the data shown in Figure 20 we analyze the rotation angle ϕ(t) = arccos(Mx /M) by averaging over the boxes defined in Figure 20. The intensity of the small closure domain (top and bottom domain) was taken as a reference since no initial torque acts on the magnetization within these domains. Because of the nonlinear mixing of oscillatory behavior of the system and the exciting field ϕ(t) cannot be described by a sum of only a few sinusoidal functions. Instead we describe the data by an approximate periodic function. The rotation angle shows pronounced extrema at t = 600, 1100, 1450, and 1900 ps in the left domain [Figure 21(b) for two pulse amplitudes I and II]. Data from the right domain show qualitatively the same behavior with slightly shifted extrema. A rough estimate of the eigenfrequency can be taken from the second oscillation of the magnetization. Within the excitation cycle the external field assumes an almost constant small negative value. In this case, the least altering of the eigenfrequency can be expected. For the left domain (1) we thus estimate a value of 1.25 GHz. For the right domain (2) the precession frequency is slightly higher as can be seen by the shift of the second and third maxima to shorter delay times. The domain walls and in particular the 180-degree Néel wall move only very little throughout the series shown in Figure 20. Close to the maximum of the field pulse at t = 600 ps [image (b)] the upper triangular domain with magnetization parallel to the field increases in size at the expense of the

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F IGURE 22. Snapshots of the Permalloy platelet with the domain pattern sketched in (a) excited with an oscillatory field with increasing amplitudes as depicted in Figure 21(a) as amplitude I (b), amplitude II (c), and amplitude III (d). A comparison of the numerical solution obtained from Eq. (22) (solid line) and the experimentally determined domain wall shift (dots) is shown in image (e).

lower black domain. This occurs through a bulging of the 90-degree domain walls downward. This bulging behavior is similar to an observation for square particles (Raabe et al., 2005). The movement of the 180-degree Néel wall is depicted in Figure 21(c). The wall velocity does not exceed 103 m/s in agreement with the result of Raabe et al. (2005). The 180-degree Néel wall movement is in close relation to the oscillation of the magnetization in the left and right domain. We do not observe a significant movement of the vortex. This is not a contradiction to the vortex motion perpendicular (Raabe et al., 2005) or parallel to the applied field (Choe et al., 2004) because in our case the excitation frequency is too high for the low frequency of the vortex mode and the slow velocity of the vortex (see also Section II.C.2). The most interesting phenomenon discussed here is the mean shift of the 180-degree Néel wall out of its symmetric position to the right [see Figure 22(b–d)]. The mean shift increases with increasing amplitude of the exciting field. This shift cannot be caused by the external field directly because the field is directed parallel to the magnetization in the domain wall and thus causes no torque. Moreover, the field is oscillating and the mean field averaged over one cycle is zero. A movement of the wall would, of course, be induced by a magnetic field along the y-axis. Since the domain walls can move freely in this low-anisotropy sample, the walls adjust in a quasi-static external field

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such that the sum of the demagnetizing field Hd and the external field is zero. Hd = Ny Mε is given by the magnetic moment m = MV ε of the particle (ε = 2x/w denoting the relative shift of the 180-degree domain wall), and the demagnetizing factor Ny = t/ l (thickness t and length l) roughly approximated assuming an ellipsoidal particle. The required external field for a domain wall shift to the right edge (ε = 1) is 3 Oe (i.e., on the same order of magnitude as the field amplitude). Such a large field component can certainly not be caused by a misalignment of the particle and the waveguide or by stray fields from the leads. One might assume that the shift is caused by the presence of a static field because of permanent magnets inside the vacuum chamber (the vacuum chamber itself is made of µ-metal to shield the earth magnetic field and further stray fields). However, in this case the shift of the domain wall would be independent of the exciting field. Contrarily, Figure 22 clearly shows that ε increases with increasing field amplitude. For the largest field amplitudes applied in this experiment the rectangular platelet is nearly saturated with the magnetization vector showing upward [Figure 22(d)]. The observed effect can only be explained by the following dynamic response of the system on the oscillating excitation. As a general physical principle, a system with a continuous source (exciting field) and sink (spin damping) of power assumes a state with maximum energy stored in the system and thus maximizes the entropy production. The energy stored in our particle is given by the magnetization precession in the large domains. The system is excited with a significant oscillating field component of 1 GHz—just below the resonance frequency of the free-running system. If the domain wall is shifted to the right the effective field determining the precession frequency and consequently the resonance frequency will be reduced in the left domain and vice versa in the right domain. As a consequence the amplitude of the precession will increase in the left domain and decrease in the right domain. Since the precession energy is proportional to the square of the amplitude the total energy has increased. Moreover, the domain size with the larger amplitude has increased, which also helps to increase the stored energy. The stored precession energy is finally balanced by the stray field energy because of the resulting finite magnetic moment of the particle. The initial domain wall movement can occur to the left or to the right. However, we observed exclusively a shift to the right. Small inhomogeneities or a small vortex motion as described by Choe et al. (2004) could be the reason. To substantiate this qualitative consideration we estimate in the following the contributing energies. The amplitude of a forced oscillator with small damping is given by  −1 A(ξ ) = C 1 − ξ 2 (15)

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at the exciting frequency ξ = ω/ω0 normalized to the resonance frequency ω0 . If ω0 is varied the amplitude will change by β=

2ξ 2 ω0 A (ξ ) ω0 = − . A(ξ ) 1 − ξ 2 ω0

(16)

The resonance frequency ω0 can be derived from the Landau–Lifshitz–Gilbert equation:

t π , (17) ω0 (ε) = γ μ0 M Nx − Ny ≈ γ μ0 M (1 + ε) w assuming demagnetization factors Ni for an ellipsoidal particle of similar dimensions as the magnetic domains. The resonance frequency decreases with increasing shift ε = 2x/w of the domain wall:   ω0 = (1 + ε)−1/2 − 1 . ω0 (0)

(18)

Using Eqs. (16) and (18) the change of the precession amplitude can be denoted as a function of the wall displacement: β(ε) = −

 2ξ 2  (1 + ε)−1/2 − 1 . 2 1−ξ

(19)

Note that for ε ≥ 0 (i.e., the wall is displaced to the right) and an excitation below the resonance frequency (i.e., ξ < 1), the amplitude in the left domain increases (β > 0), while it decreases in the right domain. The change of the precession energy is caused as well by the change of the precession amplitude as by the change of the domain size. For the left domain the precession energy Ep increases by Ep /Ep = ((1 + β)2 (1 + ε) − 1)/2, while it decreases in the right domain according to Ep /Ep = ((1 − β)2 (1 − ε) − 1)/2. Note that in the case of ξ < 1 both effects, change of area and amplitude, cooperate. We then calculate the change of the precession energy when the domain wall is shifted by ε as  Ep 1 = (1 + β)2 (1 + ε) + (1 − β)2 (1 − ε) − 2 Ep 2

(20)

and after some calculation Ep = β 2 + 2βε. Ep

(21)

Using the experimentally accessible amplitude of the magnetization component Mx = Mmx along the x-axis and the demagnetization factor Nx we can express the energy as Ep = V μ0 Nx M 2 m2x /2. The stray field energy

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Es balancing Ep also increases with increasing domain wall shift: Es = V μ0 Ny M 2 ε2 /2. From the equilibrium condition Ep = Es one obtains the implicit equation: Nx  2 β + 2βε m2x = ε 2 (22) Ny determining the shift ε as a function of the oscillation amplitude mx . If mx exceeds a critical value, a nontrivial solution ε = 0 exists. As expected ε increases with increasing amplitude of the oscillation. A comparison of ε(mx ) obtained from Eq. (22) to the experimental data is shown in Figure 22(e) with the parameter 2ξ 2 /(1 − ξ 2 ) = 3.8 corresponding to a relative exciting frequency ξ = 0.81 (i.e., ω ≈ 1 GHz). Even though the model presented above is a rough approximation of the contributing energies, the experimental data (dots) can be described by the model quite well. Further quantitative insight into the dynamic behavior will be gained from future micromagnetic simulations. Note that a nontrivial solution of Eq. (22) exists also in the case of an excitation above the resonance frequency, ξ > 1. However, in this case the change of the precession energy for a given excitation is much smaller. The contribution from the change in precession amplitude in the two domains counteracts the changes due to the domain sizes. Therefore much higher excitation energy is needed to shift the domain wall. To summarize, a magnetic moment is induced along the long side of a rectangular platelet by an exciting oscillatory magnetic field directed along the short side of the platelet. The observed phenomenon can be explained by a self-trapping spin-wave mode. When the system is excited just below the resonance frequency, the magnetization distribution adapts itself to gain more energy from the exciting field and thus maximize entropy. Above a threshold the near-resonance spin-wave mode thus causes an effective force perpendicular to the 180-degree Néel wall in the center of the rectangular particle that is balanced by the string force, which in turn is caused by the stray-field energy. 6. Nonperiodic Switching into Metastable States In several cases we observed that the structure did not relax back into the Landau ground state on a nanosecond time scale. Instead, metastable states persisted for macroscopic times, typically several hours. Since relaxation is then a thermally activated process at random times, stroboscopic or timeresolved imaging of switching dynamics is impossible. Two typical examples are shown in Figures 23 and 24. The behavior of a Permalloy square (40 µm × 40 µm, 40 nm thick) in “diamond” orientation is shown in Figure 23(a–d). A unipolar pulse train with

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F IGURE 23. Nonperiodic switching into metastable states. The initial Landau state (a) of a Permalloy square (40 µm × 40 µm, 40 nm thick) is switched by a short pulse train into metastable states (b, c for opposite field directions) that relax within hours back to the Landau ground state (d). This sequence of images has been taken using the delayline detector.

F IGURE 24. Two small rectangular platelets [4 µm×16 µm, 8 µm×16 µm; chemical image (a)] are driven into a long-lived striped pattern (b). This has significant stray-field energy but favorable anisotropy energy due to a unaxial anisotropy Ku in the film.

positive polarity drives the structure from the initial Landau ground state (a) to an “s-like” state (b), characterized by two 180-degree cross-tie walls. Closure domains with 90-degree walls are visible at the upper right and lower left edge of the structure. For a pulse train of opposite polarity the metastable pattern is reversed as in image (c). Only after several hours the structure was relaxed into the Landau ground state (d), which is practically identical to the initial state (a). The 180-degree walls suggest that a uniaxial anisotropy Ku is present. The 180-degree walls tend to align parallel to Ku . Obviously, the gain in anisotropy energy in patterns (b and c) is large enough to stabilize these patterns over macroscopic times despite the increased wall energy. An example with a different behavior is shown in Figure 24. Here two rectangular Permalloy platelets with different aspect ratio are studied, the “chemical” image taken at the Ni L3 edge is shown in (a). In this case, the unipolar field pulse train drives the structure into a concertina pattern (b) that did not relax over many hours. Again, a uniaxial anisotropy Ku leads to a gain of anisotropy energy if all domains are magnetized along Ku . In this case, not

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only enhanced wall energy but also considerable stray-field energy due to the magnetic charges at the two long edges is present. The concertina pattern is finer in the narrower microstructure. This happens because the demagnetizing factor of the narrower platelet is larger, thus increasing the stray-field energy for a given domain structure. The finer domain structure then decreases the stray-field energy on the expense of domain wall energy. D. Observation of Magnetic Stray Field Dynamics The time-resolved measurement of magnetic stray fields is very attractive for future investigations of magnetization dynamics. First, magnetic stray fields outside the magnetic particle provide the complementary information to the knowledge of the magnetization structure inside the particle. Uncompensated magnetic charges causing the stray fields simultaneously generate the nonlocal demagnetization fields that tremendously increase the numerical effort for simulating. The comparison of experimentally determined stray fields with simulated values would therefore considerably help to improve the understanding of the dynamic behavior. Second, the stray fields can be measured by their influence on the electron path and therefore no polarization detection is needed. Given an appropriate pulsed source of photons or electrons, no synchrotron radiation is needed and a laboratory-based experiment can be set up. The first quantitative measurement of the dynamics of the magnetic stray fields during a partial magnetization reversal of Co particles was reported by Krasyuk et al. (2004). As a very fast surface magnetometer a photoemission electron microscope was used exploiting the action of the Lorentz force adding to an image distortion. In this case, the magnetization structure could be observed simultaneously with the previously described X-PEEM method using circularly polarized synchrotron radiation. Magnetization dynamics were studied for flat Co particles of rectangular shape (45 µm × 30 µm and 45 µm × 15 µm) and 30 nm in thickness. They were located on top of a Cu microstrip line, which was 50 µm wide and 250 nm thick. Figure 25(a) shows the arrangement of the Co platelets on the Cu microstrip line. The sample surface was cleaned by mild ion etching (Ar+ , 1 kV, 30 min) prior to the measurements. The PEEM images were acquired with the help of a delayline detector (see Section IV.B). The electrons were excited by left- and right-handed circularly polarized light from the elliptical undulator beamline UE56/1-PGM at BESSY II in Berlin. The storage ring was operated in the single-bunch mode providing photon pulses of 100 ps width and 800 ns separation. Current pulses of 500 mA through the Cu microstrip line were synchronized with the synchrotron radiation pulses (repetition rate of 1.25 MHz). The

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F IGURE 25. (a) Optical microscope image of the Cu microstrip line (horizontal gray bar, 50 µm wide) with rectangular Co dots. The sizes of the dots are 45 µm×30 µm and 45 µm×15 µm, thickness 30 nm. Difference (b) and sum (c) images of Co particles shown in image (a) obtained before a passage of the magnetic pulse in a photoemission electron microscope under illumination with leftand right-handed circularly polarized synchrotron radiation at the Co L3 edge.

magnetic field induced by this pulse was 5–10 mT. The original width of the pulse injected into the stripline was 8 ns; however, the actual pulse profile at the Co platelets in the FOV was not known. Figures 25(b) and (c) show the difference and the sum PEEM images of the Co platelets, before passing the magnetic pulse through the Cu microstrip line. The difference image (b) exhibits the XMCD contrast (i.e., the magnetization structures inside the two particles). The domain pattern is quite complex and the arrows indicate only the average magnetization direction. Particularly, the domain walls are certainly not in a head-to-head configuration. Instead, the domain walls might be dominated by zig-zag-shaped configurations known from similar cases (Hubert and Schäfer, 1998) that are not resolved in this case. The magnetic field pulse amplitude was too small to achieve a complete magnetization reversal of the Co particles. As a result, the number of domains in the platelets remained almost constant. Details of the variations of the domain structure were reported by Krasyuk et al. (2003). The sum images [Figure 25(c)] eliminate the XMCD contrast and thus contain no contrast related to the domain structure. The apparent deformation of the particle shape, however, carries information of the external magnetic stray fields created by the internal domain pattern. The series of sum images in Figure 26 shows how the deformation of the Co particle shape in the region of the gap between the adjacent rectangles evolves dynamically during the passage of the field pulse. This region is marked by the white rectangle in Figure 25(c). For the sake of clarity, the images are horizontally stretched by a factor of 3 (the gap width between the particles is equal to 3 µm). As seen, the image of the gap between the particles has a nearly rectangular shape at t = 1 ns, and this shape is extremely deformed in opposite directions at t = 22 and 28 ns. In these early experiments the pulse shape was strongly

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F IGURE 26. Lorentz force–induced deformation of the image of the gap between two Co platelets during the passage of the field pulse. The region shown in the images is horizontally stretched by a factor of 3 and marked in Figure 25(c). The time between field-pulse onset and X-ray pulse is given in the images.

distorted by insufficient impedance matching and resulting reflections of the pulse at electrical interconnections. The PEEM image is deformed because the magnetic stray fields of the particle cause a Lorentz force acting on the photoelectrons. The reconstruction of the undistorted image from a deformed image of the ferromagnetic object with known geometry yields detailed information about the magnetic stray fields. This reconstruction approach has been presented by Nepijko et al. (2000a, 2002a, 2002b, 2003b) for the case of a steady-state distribution of the magnetic stray fields and by Krasyuk et al. (2004) for the dynamic case using the most simple approximation of the domain structure. The stray field determined from the image deformation in Figure 26 has a maximum amplitude of about 100 ± 20 mT. This is more than an order of magnitude higher than the pulse field (5–10 mT). The image deformation is thus essentially caused by the stray fields of the domain pattern and their temporal variation and not by the pulse field. Unfortunately, the signal-to-noise ratio (SNR) was too poor in this first approach to compare the variations of the

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magnetic stray fields directly with changes of the domain patterns obtained from difference images. In the future, this technique will provide an easy and very fast local surface magnetometer with a lateral resolution in the 20 nm range and a very high time resolution in the sub-picosecond range if a femtosecond laser source is used for illumination in the PEEM. In the range of threshold photoemission, there is another interesting magnetic contrast mechanism in PEEM: the threshold magnetic linear dichroism (TMLD) discovered by Marx et al. (2000). In principle, the TMLD also could be exploited as magnetic contrast mechanism for time-resolved imaging, although this has not been proven yet. E. Nonstroboscopic Time-Resolved Imaging There is an operation mode that does not require a time structure of the photon source, but instead it uses time-resolved image detection. The schematic setup is depicted in Figure 27. In this case the time resolution is defined by the minimum time window of the detector. CCD cameras with ultrafast optical intensifiers provide a time resolution of a few hundred picoseconds. However, the decay time of the fluorescence screen sets a practical limit to this kind of detection, even if a fast scintillator is used (Spiecker et al., 1998). Higher time resolution can be obtained using a 3D (x, y, t)-resolving image detector, the delayline detector (DLD) (Oelsner et al., 2001). Few experiments with this kind of detection have been performed up to now (Cinchetti et al., 2003b; Cinchetti and Schönhense, 2005; Oelsner et al., 2004a). The present resolution is ∼100 ps at a total count rate of several 105 counts per second. A new prototype reaches a time resolution ≤60 ps at a total count rate of several 106 counts per second (Surface Concept GmbH, see www.surface-concept.de). The detector is presented in Section IV.B. In the latter mode the time structure of the synchrotron radiation, although being present in all operation modes, is not exploited. At typical exposure times between several seconds and a few minutes per time slice the image is integrated over 108 –1010 photon pulses from the storage ring. The DLD receives the trigger signal of the magnetic pulse onset at t = 0 from the electrical pulse generator and detects every single electron in the image with respect to its lateral (x, y) and time coordinate (t). After image acquisition, picosecond time slices for the desired time interval (t, t) can be extracted from the 3D data stack by the image processing software. Figure 28 shows a typical example. Due to the nonsynchronous operation of the electrical pulser generating the magnetic field the synchrotron radiation acts as quasi-continuous wave (cw) source (no phase locking). In this mode the excitation source could as well be

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F IGURE 27. Nonstroboscopic magnetic imaging using PEEM equipped with a time-resolving image detector. Unlike in Figure 5, a time structure of the photon beam is dispensable. The pulse generator gives the time-zero trigger signal to the delayline detector and all picosecond time slices are acquired simultaneously.

F IGURE 28. Time-resolved domain image taken with the delayline detector. (a) Raw image; (b) XMCD asymmetry image.

a true cw source. In principle, even laboratory photon sources like Hg lamps or UV lasers can be used if a suitable contrast mechanism like TMLD (Marx et al., 2000; Marx, 2001) or Lorentz-type contrast in PEEM (Nepijko et al., 2000a, 2002a, 2002b, 2003b) is exploited.

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In stroboscopic operation the small repetition time of the order of 2 ns in multibunch operation (see Table 1) is not sufficient for a full relaxation of the magnetic system as seen in Section II.C. In the future, this drawback can be overcome by routing of images via combination of stroboscopic illumination providing high time resolution (see Section II.B) combined with time-resolved image detection using the DLD. In this mode the DLD only needs to separate the signals originating from adjacent photon pulses, separated by about 2 ns. In other words, the features explained in Figures 5 and 27 are combined. A useful setting will be to run the electric pulse generator at 20 MHz (i.e., at a period of T = 50 ns that is sufficient for a full relaxation of the system). Using a variable delay between 0 and 2 ns and routing the signal of 25 adjacent photon pulses via the DLD yields 25 time slices at each delay setting t. In this way, the whole interval between 0 and 50 ns after the onset of the magnetic field pulse is imaged stroboscopically. The time resolution limit is given by the width of the photon pulses, provided the electronic jitter can be sufficiently reduced. In conclusion of Section II, stroboscopic XMCD-PEEM has been used by several groups for the study of ultrafast magnetization phenomena in small thin-film elements, being important for future memory or spintronics elements. The response of multidomain flux-closure structures (Landau states) in micrometer-sized magnetic thin-film elements on fast magnetic field pulses leads to the excitation of magnetic eigenmodes (vortex modes, wall modes, and normal or center modes) and to transient spatiotemporal domain patterns that do not occur in quasi-static remagnetization. Results have been presented for permalloy platelets of various shapes and sizes. Dynamic series of domain patterns with variable delay between field pulse and photon pulse (synchrotron radiation) have been taken using stroboscopic XMCD-PEEM. Examples for all three kinds of modes have been discussed. Further, the rapid broadening of domain boundaries due to the precessional remagnetization, the formation of transient domain walls and transient vortices as well as the fast formation of a striped domain phase (blocking pattern) have been demonstrated by typical examples. In addition to XMCD, a Lorentz-type contrast in PEEM can be exploited for ultrafast imaging of stray-field dynamics. A novel type of 3D (x, y, t)-resolving electron image detector with a time resolution of ≤100 ps allows a nonstroboscopic operation mode that can use cw sources for excitation.

III. I MAGING OF T RANSIENT S TATES Short-lived electronic states in metals or semiconductors can be probed by time-resolved PEEM or mirror electron microscopy. Using excimer laser

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radiation structural transitions such as surface melting or the dynamics of thermionic electron emission could be observed in single-shot experiments. The propagation of electrical pulses in a p–n junction was detected combining PEEM with a streak camera-like device. The optical near fields of localized surface plasmons (LSPs) can be visualized exploiting two-photon photoemission (2PPE) in PEEM. Femtosecond laser radiation in a pump-probe arrangement was used to obtain electron lifetime contrast. Interferometric time-resolved PEEM in a similar arrangement allowed observation of the phase lag of the plasmon eigenoscillation in relation to the phase of the exciting light wave. A. Investigations of Surface Melting and Thermionic Emission of Electrons Time-resolved PEEM can also be used for studies of fast nonperiodic processes. For example, Bostanjoglo and Weingärtner (1997) have succeeded in visualizing the initial stage of melting. They used a single-shot approach combining two powerful lasers in a pump-probe arrangement yielding enough signal for image formation within one pulse. Figure 29 shows a schematic section of the time-resolving photoemission electron microscope with an attached solid-state laser for in situ materials processing. The image-forming photoelectrons are released from the specimen surface by a pulse from a KrF excimer laser [wavelength 248 nm, pulse duration 4 ns full width half maximum (FWHM)]. The photoelectrons are accelerated by a two-electrode cathode lens, then focused to an intermediate image by a three-electrode einzel lens and finally projected by a magnetic lens on a fluorescent screen. The electron image on the screen is intensified by a MCP and registered by a CCD camera. A beam blanker, placed behind the einzel lens, directs electrons to the detector only during the emission of photoelectrons. Thus the interfering contributions to the image from longer-lasting thermal and ion-induced secondary electrons, produced by the processing laser beam, are effectively suppressed. The investigated fast processes are launched in the specimen by a focused Gaussian pulse from a Q-switched, frequency-doubled Nd:YAG laser (wavelength 532 nm). This laser is powerful enough to initiate a melting process, but its quantum energy is less than the work function of the sample hν = 2.33 eV < φ; therefore its contribution to the photoemission signal is negligible in comparison with the KrF laser for which hν = 5 eV > φ. The imaging 4 ns photoelectron pulse can be produced at a well-defined time delay with respect to the processing Nd:YAG laser pulse. The time jitter is below ±2 ns. Further improvement of this technique lies in the possibility to switch off the accelerating voltage within 20 ns after the image acquisition to

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F IGURE 29. Single-shot time-resolving photoemission electron microscope with an attached solid-state (Nd:YAG) laser for in situ materials processing (pump beam) and powerful excimer laser (probe beam) for photoemission.

avoid breakdown due to the plasma produced by the processing laser pulse (Bostanjoglo et al., 2000; Weingärtner and Bostanjoglo, 1998). Of course, the precaution is only successful if the avalanche buildup takes longer than 25 ns (i.e., at not too high fluences). Figure 30 shows the Nd:YAG laser treatment of a 100 nm aluminum film on a silicon substrate (Kunze and Bostanjoglo, 2003). Wavelength, pulse width, fluence, and spot size were 532 nm, 5 ns, 0.4 J/cm2 , and 20 µm, respectively. The times of exposure shown are counted between the peaks of the treating (processing) and imaging laser pulse. As can be seen, an increased emission is observed for a few nanoseconds after the treatment, which can be attributed to excited atom states generating Auger electrons (this emission is observed without the imaging laser). From 10 to 50 ns after the treatment the molten area shows reduced photoemission; beginning at 35 ns it is nonhomogeneous (photoemission in the center is enhanced in comparison to the rest of the molten area). The possible explanation is related to the changes of the work function due to the dissolving of a capping native oxide layer in the molten

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F IGURE 30. Time-resolved PEEM images of Nd:YAG laser treatment of a 100 nm aluminum film on a silicon substrate. The time refers to the delay time between the treating pulse (pump) and the probe pulse. (From Kunze and Bostanjoglo, 2003.)

metal and further diffusion of dissolved oxygen atoms. The final state shows enhanced emission corresponding to a surface cleaned from adsorbate layers. The lateral resolution in these measurements is limited not only by the lens aberrations, but also by the electron space charge, and, due to the short exposure times, by shot noise. The estimation of the lateral resolution is based on the Brüche–Recknagel formula: x = kE/eF,

(23)

where the parameter k is close to 1, e and E denote the charge and the energy spread of the electrons, and F is the electric field at the specimen. The feature of these measurements is the formation of a negative space charge in front of the specimen. This alters the accelerating field F (the component normal to the sample is diminished and a transversal component appears). This leads to a deterioration of the resolution. There is no simple relation between resolution and electron emission current density (Massey et al., 1981). However, adverse effects from space charges certainly can be neglected if the current density j of the photoelectrons stays well below the space charge-limited Child– Langmuir current density j ∗ , that is, 1 1 ∗ j = CF 3/2 d −1/2 , (24) 10 10 where C = 2.3 × 10−6 A/V3/2 and d is the spacing between the accelerating electrodes of the cathode lens. In addition, currents that are too low give rise to noisy images. j≤

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In the presence of shot noise, two neighboring areas with diameter x in the specimen can only be discerned if their SNR exceeds a minimum value (S/N > 1 should always be fulfilled). It is assumed that the number of detected photoelectrons scatters according to a Poisson distribution, and that the currents of the two regions are constant during the emission time t. Then the combined time/space resolution is easily shown to obey the law (Bostanjoglo and Weingärtner, 1997) t · x 2 ≥

2eα(S/N)2 , π K 2j

(25)

where K = |n1 − n2 |/(n1 + n2 ) is the contrast of the two regions that emit numbers of electrons equal to n1 and n2 , j is the average photoelectron current density, and α accounts for the detector noise (α = 1 for an ideal detector). Combining Eqs. (24) and (25) gives the resolution due to space charge and shot noise: t · x 2 ≥

20eα(S/N)2 d 1/2 . π CK 2 F 3/2

(26)

Inserting values typical for the used setup F = 5 × 106 V/m, d = 5 mm, K = 0.2, S/N = 5, α = 1.5 (guessed), and imaging time t = 4 ns, a spatial resolution of x = 0.8 µm is calculated for the aberration-free pulsed microscope. The resolution additionally is deteriorated by lens aberrations. Using Eq. (23) with E = 1.5 eV, the actual spatial resolution amounts to 1.3 µm. The time resolution of the experiment shown in Figure 30 is equal to 4 ns. This is sufficient for the studies of the dynamics of the melting processes. The combined time t and space x resolution is limited primarily by space charge, shot noise of the photoelectrons, and detector noise to t (x)2 ≥ 6.8 ns·µm2 . Similar studies were performed using a time-resolved electron microscope in the mirror operation mode (Kleinschmidt and Bostanjoglo, 2001). Schäfer et al. (1994) restricted the fluence of a Nd:YAG laser so much that the sample was heated but stayed under the melting point. They studied dynamics of the thermionic emission of electrons from a metal surface. The experimental setup was simpler because thermoelectrons were used for imaging, so the KrF laser was absent. Short-exposure time imaging is achieved with a beam-blanking capacitor between the objective and projective lens. Applying a constant voltage of typically 100 V prevents the stationary emission, if present, from reaching the detector. Short time exposures are realized by removing the deflecting field completely for a desired time with a compensating voltage pulse. The required pulse shape is generated with an avalanche transistor, discharging a coaxial cable. The exposure time is determined by the length

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F IGURE 31. Thermal electron emission images of a stationary (a) and a pulsed-laser (b–h) heated tungsten grain. The irradiated area is marked with a circle in the stationary image. Short time exposures of the laser-induced emission from grain boundaries in tungsten at different times are referred to the maximum of the laser pulse. (From Schäfer et al., 1994.)

of the cable. To avoid deterioration of the lateral resolution by streaking, the top of the pulse must be flat within 1–2% of the full amplitude as the required resolution δ is related to the fluctuation U of the voltage pulse U by U/U ≤ δ/D,

(27)

with D representing the diameter of the imaged area. The time resolution is defined primarily by the width of the image shifting pulse. In the measurements performed by Schäfer et al. (1994) time resolution was 10 ns (the pulse rise/fall times were 2 ns). Figure 31 shows a different emission contrast of grain boundaries in tungsten due to stationary [image (a)] and pulsed-laser heating [images (b–h)]. Laser fluences were far below the damage threshold (wavelength, pulse width, fluence, and exposure time were 532 nm, 10 ns, 0.2 J/cm2 , and 3 ns, respectively). The maximum current density is observed at ∼5 ns after the maximum of the pulse intensity. From this it can be inferred that the strong emission of the boundaries is not due to a photoeffect but is rather a consequence of the laser-induced temperature profile, peaking at the boundaries. Such a temperature distribution may be caused by a larger absorption of the grain boundaries compared with the grain, which has smooth surfaces.

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Single-shot (“flash-”) time-resolved photoelectron microscopy also is a suitable technique to investigate other fast processes in metals induced by laser pulses with fluences below the ablation threshold (mechanical deformations, chemical reactions, and so forth). Therefore, the emission electron microscope is found to be a sensitive probe for the study of nonrepetitive laser-induced modifications of the surface. B. Detection of Electrical Pulses in a Gunn Diode The spatiotemporal variation of the lateral electric field distribution in a Gunn diode has been studied in an early time-resolved emission electron microscope experiment by Sedov and Zlobin (1974). It was the first time-resolved measurement performed in emission electron microscopy (EEM). A special electron-optical system with a high-speed device for image recording was used there. This system operated on the same principle as a streak camera. The streak camera or chronography method is based on a linear image scanning with high speed. A scheme of the electron microscope-chronograph is given in Figure 32. The object under study is illuminated with the primary electrons from an electron gun. The triode electrostatic microscope objective forms a surface image of the object from the secondary electrons emitted by this object on a fluorescent screen. A slit diaphragm is placed in the path of these electrons. The diaphragm shades the entire image except for a narrow stripe of width y in the center of the screen. Deflecting plates are in place behind the diaphragm; they shift the image in the direction normal to the direction of the slit. The image of a preferred stripe is moved over the screen with a speed v under the action of a linear voltage drop applied to the plates. The image runs across the screen for a time comparable to the duration of the process being investigated. Thus, it is possible to observe the development of a 1D process on the object surface along the coordinate axis x swept along the coordinate y as shown in Figure 32. The time interval recorded in this case is T = D/v, where D is the microscope screen diameter. The time distribution is determined by the width of the selected area of the image and the scanning rate t = y/v. The specimen was illuminated with a long-focus pulsed electron gun with a directly heated V-type tungsten cathode. The gun operated in the regime was normally locked by a modulator, and it was opened only for the time of active scanning stroke. The duration τ of the activating pulse applied to the modulator varied from a few microseconds up to a few nanoseconds. The electron gun was characterized by a current density of several tens of mA/cm2 and by an exposure time (integral time) of 1 µs (it is determined from the

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F IGURE 32. Schematic view of the emission electron microscope-chronograph. Similar to a streak camera the image is swept across the screen at a high speed thus, displaying a 1D feature versus time.

condition that the density of blackening of the photographic plates is close to unit). The described scheme enabled the scanning rate v at the screen to be changed from 5 × 105 to 3 × 109 cm/s (v = D/T ; in the case of singleshot processes τ is used instead of T ). Considering the object illumination permitting the photographing with an exposure time of 1 µs, these scanning rates provided a time resolution of 1–0.1 µs for the single-shot or nonperiodic processes and of 30 ps under the study of periodic processes with a repetition rate of 10 kHz. From the technical point of view, it is possible to obtain a still higher scanning rate and, respectively, a time resolution of the order of 1 ps. However, such an increase of the time resolution imposes fundamental difficulties. Note the reasons limiting the time resolution of the microscopechronograph; one of them is the time chromatic aberration. It is caused by a spread of the initial velocities of electrons escaping from the same point of the specimen, as well as by a difference between the mean velocities of electrons escaping from different points of the object with a nonequipotential

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surface. Since the study of the dynamics of electrical microfields is of great interest, we consider the case of a nonequipotential object. Because of the potential difference applied to the specimen, the electron energy spread is usually significantly greater than the initial electron energy, which can be neglected. Then tchrom = tu/2U0 , where t is the time of electron transit through the region of the deflecting plates (it is equal to 1.2 ns) and U0 is the microscope accelerating voltage (20 kV). Under the potential difference U = 100 V applied to the specimen, the spread of transit time then amounts to 3 ps. The second reason for chronogram distortion is the time distortion. It is caused by the fact electrons escaping from the outer points of the specimen have a greater length of the optical path to the chronograph slit than the electrons escaping from the center. As a result, the line of constant time on a chronogram is not a straight line. The elapsed time is td = tα 2 , where α = 0.05 rad is the half angle of the pencil beam forming the image. In the case under consideration, td = 3 ps. The third, most important reason is related to the finite time of electron transit in the object microfield. For this reason the image contrast formed under the action of the time-dependent field will be weaker than in the case of observation of a stationary field. It is believed that the action of a microfield is completely negligible at a height equal to 10 times the width of the region of voltage drop on the specimen. Under the accelerating field of the microscope objective lens of 3 × 104 V/cm and the height of field action of a few tenths of a millimeter (the distance between cathode and anode on the Gunn diode comprised 240 µm), the transit time is estimated to be 10 ps. To decrease this contribution, it is necessary either to use a very strong accelerating field when the image is formed by the slow-moving electrons, or to use for image formation the electrons with high velocities in the region of the action of the microfield (high-velocity secondary, reflected, or passed primary electrons). In the studies of the Gunn diode described here the time resolution was ∼30 ps, which is close to the finite resolution for devices of this type (Sedov and Zlobin, 1974; Zlobin and Sedov, 1976). These experiments have been conducted on specimens prepared by the planar technology from n-type GaAs with an initial concentration of n0 = 3 × 1015 cm−3 and the mobility μ = 5300 cm2 ·V−1 ·s−1 . The specimens were 240–500 µm in length and 50 µm in width. Figure 33 shows chronograms obtained for two specimens. The dark regions in the images (between anode A and cathode K of the specimen) correspond to the regions (domains) of strong electric field. The process of formation of a running domain boundary is essentially different for the two specimens shown. In the first specimen [Figure 33(a)] the “highpotential” region is formed near the cathode and moves toward the anode with a constant speed of v ∗ = v × tgϕ = 1.2 × 107 cm/s. The invariable angle of

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F IGURE 33. Chronogram of the rapid movement of a domain of the electrical field in GaAs specimens with a homogeneous (a) and an inhomogeneous (b) distribution of the prethreshold field. The positions of anode A and cathode K are denoted by dashes. (From Sedov and Zlobin, 1974.)

inclination ϕ of the chronogram shown in Figure 33(a) confirms that the speed is constant. In the second specimen [Figure 33(b)] the strong field region behaves opposite. It is also formed near the cathode but does not start to move immediately. The voltage drop at the high-potential region increases and the domain finally detaches from the cathode at about t = 3.5 ns. Furthermore, the high-potential region also moves with a constant velocity. In the second specimen, the voltage of appearance of generation is higher than in the first one (the calculation technique of the electric fields from the measurements of current density distribution at the screen is described in detail by Nepijko et al., 2002d, 2003a, 2005). The total time for the transit of the high-potential region amounts to 2 and 5 ns for the first and second specimens, respectively. C. Femtosecond Lifetime Contrast of Hot Electrons The pioneering experiments combining PEEM with femtosecond-laser excitation have been performed by Schmidt et al. (2001, 2002) and Fecher et al. (2002). A frequency-doubled Ti:sapphire laser oscillator was used whose photon energy (typically 3.1 eV) lies below the work function threshold of most metals (e.g., ≥4.2 eV for Ag). Thus, the observed electron signal in the microscope results from 2PPE. Time-resolved 2PPE has been extensively investigated to understand electron dynamics at metal and semiconductor surfaces (Aeschlimann et al., 1996; Cao et al., 1998; Fann et al., 1992a; Haight, 1995; Hertel et al., 1996; Lehmann et al., 2000; Ogawa and Petek, 1996; Schoenlein et al., 1988; Schmuttenmaer et al., 1994; Williams et al., 1982; Yen et al., 1982). However,

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F IGURE 34. Schematic energy–time diagram for two-photon (or multiphoton) photoemission. The possible emission channels are: simultaneous excitation (a); cascade process (b); thermally assisted photoemission (c); thermionic emission (d). The Fermi distribution f (E) (left-hand side) develops through a transient “non-Fermi distribution” into a Fermi distribution corresponding to a higher temperature on a timescale of <100 fs (right-hand side). The intermediate state usually has a short lifetime of the order of a few femtoseconds.

as this technique is a spatially integrating method, it was not possible to systematically investigate, for example, local variations of the electron dynamics or the effect of surface inhomogeneities on the 2PPE process. A striking example is the nonlinear enhancement of the integral photoemission yield due to so-called hot spots at surfaces. This effect is the result of the interaction between the exciting intense laser field and surface defects (Aeschlimann et al., 1995; Schmidt et al., 2001). Of particular interest is the specific hot-electron dynamics of spatially heterogeneous systems. The approach we present in this section is the combination of time-resolved 2PPE and PEEM. The 2PPE process is illustrated in Figure 34. The first (pump) pulse populates an intermediate state |i located between the Fermi edge and the vacuum level; a second (probe) pulse photo-emits these electrons into the vacuum. A defined control of the temporal delay t between pump and probe pulse enables information about the decay dynamics of the photoexcited electrons to be captured. Because the 2PPE process is a nonlinear photoemission process, the overall photoelectron count rate in the case of coincidence or temporal overlap between pump and probe pulses [image (a)] is increased compared to the case in which both pulses are well separated [image (b)]. For identical collinear pulses and optimum spatial overlap, this enhancement results in a peak-to-background ratio of 8:1 for interferometric temporal resolution (i.e., phase-coherent constructive interference; see Section III.E) and 3:1 for phase-averaging resolution, respectively. The so-called autocorrelation trace reflects the finite lifetime of the electron population in the intermediate state.

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F IGURE 35. Schematic set-up for time-resolved (interferometric or phase-averaged) 2PPE electron spectromicroscopy. Behind the beamsplitter the probe beam is delayed optically and both pump and probe beams are fed collinearly to the sample.

Ideally, the lifetime of hot electrons in a free-electron gas is proportional to (E − EF )−2 , as follows from Fermi-liquid theory (Gasparov and Huguenin, 1993; Hawrylak et al., 1988; Quinn, 1962, 1963; Quinn and Ferrell, 1958). For metals, relaxation times down to the low femtosecond range have been observed. On the other hand, semiconductors (e.g., GaAs) show significantly longer lifetimes due to the restricted phase space for inelastic decay (Schmuttenmaer et al., 1996). The brightness of a PEEM image is proportional to the total electron yield of the photocurrent. Thus, PEEM is capable of directly visualizing material-dependent variations in hot-electron lifetimes on heterogeneous sample surfaces. This holds even in the energy-integrating mode, that is, without energy filter. Moreover, a microscopic imaging method is capable of separating off signals from defects at surfaces (hot spots) that could easily overwhelm the signals of interest. In fact, we frequently found inhomogeneities in the lateral distribution of 2PPE (e.g., the presence of hot spots on various sample surfaces; see below). A schematic of a typical experimental setup for time-resolved 2PPE electron spectromicroscopy (2P-PEEM) is shown in Figure 35. Schmidt et al. (2002) used a commercial instrument with a base resolution of ∼20 nm (Focus GmbH, see http://www.focus-gmbh.com). The electron-optical column is an electrostatic three-lens system with a contrast aperture and an octopole stigmator. It allows a zoom range from a FOV below 5 µm to ∼500 µm. The sample stage is piezomotor driven and integrated into the microscope column.

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The image is intensified by a multichannel-plate/YAG-screen arrangement. Images are acquired by a slow-scan CCD camera. Parallel full-field image acquisition, similar to an optical microscope, is ideally suited for a real-time observation of the spatial electron yield distribution (for the basics of contrast mechanisms, etc., see, Schneider and Schönhense, 2002). Typical exposure times in these experiments were in the range of 300 ms up to several seconds per image. A 82-MHz pulsed Ti:sapphire laser, tunable from 750 to 830 nm, was used as the excitation source. The system delivers pulses of up to 9 nJ/pulse with a duration of 40 fs. The output was frequency doubled in a nonlinear crystal to produce pulses at hν = 3–3.4 eV. Both the infrared and blue pulses can be focused on the same spot on the sample under a 65-degree incidence angle with respect to the surface normal. The blue pulses are split to equal intensity pump and probe pulses and later combined collinearly by a second beamsplitter. The probe pulse can be delayed with respect to the pump pulse by a computer-controlled optical delay stage. In this mode a series of images is taken at varying temporal delays t between the two beams. The investigation focused on patterned silver films on semiconductor substrates of silicon and gallium arsenide. Two different approaches of data analysis have been applied. In the decay mode, two images are taken at different temporal overlaps of the pump and probe pulses (e.g., 0 and 60 fs delay) and the ratio of the image intensities is calculated according to I (lifetime) ∝

I (60 fs) − I (∞) I (0 fs) − I (∞)

(28)

for every image pixel. I (0 fs), I (60 fs), and I (∞) denote the brightness values of the corresponding pixels of images taken at zero delay, at 60 fs, and at a large (infinite) delay, respectively. The found it important to subtract a background image taken at infinite delay from the other images before forming their ratio. This subtraction removed the contribution from photoemission by the single pulses alone that does not reflect the actual difference in the excited electrons’ lifetimes. In the FWHM mode the photoemission intensity from each pixel of the image is plotted as a function of delay between the pump and probe pulses. The resulting autocorrelation trace was smoothed numerically, resulting in the phase-averaged autocorrelation trace. The FWHM extracted from these autocorrelation traces reflects the lateral distribution of differences in the relaxation dynamics and can be displayed in terms of an FWHM map as described by Schmidt et al. (2002). Figure 36 summarizes results from a time-resolved 2P-PEEM scan. The sample chosen here is silver evaporated onto a masked GaAs substrate, (100)surface. A single pixel in these images corresponds to an area of ∼0.09 µm2 .

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F IGURE 36. Time-resolved 2P-PEEM images of hexagonal silver patches on GaAs. (a) PEEM image of the microstructured Ag layer (partly visible hexagonal patches) taken with 400 nm laser radiation. (b) FWHM image extracted from a pump-probe PEEM scan of the same area. The brightness value of each pixel corresponds to the FWHM of the respective autocorrelation trace. (c) Decay image exhibiting differences in the lifetime calculated for 60 fs delay (areas with shorter hot-electron lifetimes appear darker in the image). (d) Decay image for 200 fs delay.

Figure 36(a) is a 2P-PEEM image and shows the patterned silver film (hexagonal patches). The brightness values of the Ag hexagons and the GaAs substrate (bars) are approximately equal. Figure 36(c) shows a decay image obtained according to Eq. (28) calculated for 60 fs delay. The darker appearance of the hexagons reflects a shorter hot-electron lifetime of silver compared with the GaAs interstitial parts. Additional relieflike contrast is visible at the edges of the silver patches. It is connected with the intensity enhancement at the rims of the Ag islands as visible in image (a). For comparison, image (d) shows a decay image corresponding to a delay of 200 fs. It is obvious that at this large delay the lifetime contrast is significantly weakened. Obviously, most of the excited hot-electron population has decayed in both materials. The observed contrast between silver and GaAs is also reproduced in the FWHM image shown in (b). Again, the silver hexagons appear darker in comparison to the GaAs areas due to the smaller FWHM corresponding to shorter lifetimes. In the center part of the image, essentially no contrast can be observed between silver and GaAs in correspondence with a reduced contrast in the decay image (c). Comparison with image (a) indicates a correlation of this effect with an enhanced 2PPE yield. This is most likely caused by the presence of a silver cluster film in this boundary area as a result of the evaporation process. Particularly for small silver particles, effective coupling of the exciting laser light to localized plasmons can enhance the photoemission yield quite significantly (see next section). Both approaches of data analysis provided clear evidence of lateral variations in the hot-electron lifetime on heterogeneous microstructured sample surfaces. In conclusion, these experiments have successfully established a new experimental technique that is referred to as time-resolved 2P-PEEM. In general, it offers a new contrast method for PEEM by the use of a femtosecond-pulsed light source. However, even more important, this technique can investigate the characteristics of hot-electron dynamics of surfaces at a spatial resolution of

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20 nm and a time resolution that is given by the pulse length of the laser, i.e., the ten femtosecond range. It provides a new probe for the physics of charge carriers in nanostructured and low-dimensional systems. Implementation of energy discrimination in terms of an imaging energy filter (e.g., the TOF filter, explained in Section IV) is straightforward and facilitates, in addition, timeresolved spectroscopy at high spatial resolution. D. PEEM Imaging of fs-Laser Excited Optical Near Fields The interplay of electromagnetic field intensity and photoemission yield raises the question whether PEEM can be useful for the observation of the local optical field distribution on a conducting surface. It is known that the intensity of optical fields may be largely enhanced in the vicinity of nanoscopic metal objects. Extreme local field enhancement is believed to be responsible for the increase of the Raman cross section of organic molecules by up to a factor of 1014 (Nie and Emory, 1997) in the vicinity of stochastically roughened silver films. Fluorescence yield also is drastically altered by an enhanced optical near field (Lakowicz et al., 2004; Shimizu et al., 2002; Wokaun, 1985). Analogous to antennae used for radiation of lower frequency, small metal objects of certain dimensions can be regarded as antennae for the optical regime. These nanoscopic antennae are characterized by an overall optical resonance similar to the well-known plasmon resonance of spherical metal particles (Bohren and Huffmann, 1983; Kreibig and Vollmer, 1992). Such resonances have been observed for rods (Sönnichsen et al., 2002), closely spaced particle dimers (Okamoto and Yamaguchi, 2003), and nanorings (Aizpurua et al., 2003), to name only a few. In all these cases a strong dependence of the resonance wavelength on the geometry was found. These antennae have geometric features of very small dimension that concentrate electromagnetic energy to extremely highenergy density in volumes far below the diffraction limit. One prominent example is the nanoscopic gap that is formed between two almost-touching metal spheres (Aravind et al., 1981) or cylinders (Kottmann and Martin, 2001) or between a plane and a sphere (Aravind and Metiu, 1983). Sharp tips are another important example for nanoscale structures where it could be shown experimentally (Kramer et al., 2002) that the photophysics of a single fluorescent molecule is significantly altered by the large field enhancements, this result being in qualitative agreement with theory (Ditlbacher et al., 2002; Kottmann et al., 2001). Mapping of the near-field distribution down to the nanometer scale is the key to understanding and optimizing such antenna structures. Optical microscopy detects the far field and its resolution is diffraction limited.

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F IGURE 37. Hot spots in femtosecond-laser excited PEEM on various inhomogeneous metallic systems: Permalloy on Si (a), Pb on rough Si (b), Pb clusters on smooth Si (c), Ag hexagon on Si (d), Ag nanodots (e), rough Ag film (f), polycrystalline Cu (g), single-crystalline Cu (h). Other designations are given in the text.

Scanning probe tips provide good resolution (Frey et al., 2002), but they alter the near field substantially as they approach the nanostructure. An “inverted” approach using the high resolution of electron microscopy was demonstrated by Yamamoto et al. (2001). They detected light emission induced by an electron beam and were able to image multipolar patterns on small silver particles, taking advantage of the superior resolution of electron optics. Photoemission dynamics of deposited silver particles were studied in detail (Lehmann et al., 2000; Pfeiffer et al., 2004) and the influence of the collective electron dynamics could be quantified (Merschdorf et al., 2004; Scharte et al., 2001). However, the photoemission signal was recorded without spatial resolution. Since the first 2P-PEEM work of Schmidt et al. (2001), clear evidence of strongly enhanced optical near fields has been found for many inhomogeneous metallic systems; several examples are shown in Figure 37. Images (a, b, and d) are from Schmidt (2000) and Schmidt et al. (2001, 2002), images (c, e–g) from Cinchetti et al. (2003a, 2003b), Cinchetti (2004), and Cinchetti and Schönhense (2005), and image (h) from Ernst (2005). It became clear that a variety of nanostructural elements give rise to local field enhancement. Examples have been found for isolated spherical, hemispherical, oblate, or prolate nanoparticles, showing different dependences on photon polarization (Fecher et al., 2002), closed films with granular structure or rough surfaces, as discussed in terms of a fractal model by Shalaev et al. (1996), or single structural defects such as protrusions or voids on smooth surfaces or at grain boundaries of polycrystalline samples.

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F IGURE 38. Scanning electron micrograph of nanostructured silver crescents on Si. The inset shows a magnified view.

In addition, laterally resolved electron energy distribution spectra have shown that the surface plasmon-induced enhanced near field governs the photoemission and its dynamics to a large extent (see Section IV.D). However, the details of the structural features that produce the locally enhanced photoemission yield were not exactly known and remained speculative. Therefore, further experiments have been performed on well-defined metal structures that possess sharp tips as required for high local field enhancement. Cinchetti et al. (2005) successfully demonstrated that PEEM is capable of mapping the nearfield distribution of such objects. Nanoscopic crescent-shaped silver objects were prepared on a Si wafer using a combination of colloid templating, metal film deposition, and ion beam milling (Shumaker-Parry et al., 2005). Figure 38 shows a typical SEM image of the crescents with a diameter of roughly 400 nm and a thickness of 50 nm. Photoelectron emission was induced by illuminating the sample with two different light sources. A Hg deep-UV lamp (photon energy cutoff hνUV = 5.0 eV, wavelength λUV ≥ 250 nm), was focused on the sample at an angle of θ = 65 degrees with respect to the surface normal. The fundamental of a femtosecond Ti:sapphire laser (MaiTai Spectra Physics, wavelength tunable between 750 nm and 850 nm, repetition rate 80 MHz) was frequency doubled by a commercial device (3980 Spectra Physics), yielding a photon energy tunable between 2.9 and 3.3 eV and a pulse width below 200 fs. For this experiment the photon energy was fixed at hνL = 3.1 eV (λL = 400 nm). The frequency-doubled beam was focused on the sample at θ = 65 degrees, from the opposite direction in the same plane of incidence as the UV lamp. The obtained fluence per pulse was ∼6.4 J/cm2 . In a PEEM image, the brightness in a given area is proportional to the intensity of electron emission from that area. Thus, for the interpretation of the data it is important to know the physical processes leading to electron emission for a certain wavelength of the incident light. The work function φ of Ag ranges between 4.2 and 4.8 eV (Michaelson, 1977; Hölzl and

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Schulze, 1979), depending on crystal orientation. Upon illumination of the sample with the UV lamp, electrons are emitted by regular, one-photon photoemission (1PPE), since hνUV > φ. Conversely, under laser illumination at hν = 3.1 eV, the photon energy is smaller than the work function and photoemission requires a multiphoton process, where it can be expected that two-photon processes as lowest order dominate. The intensity of the 2PPE yield is proportional to the fourth power of the local electrical field E 4 , which, especially for plasmon-resonant metal particles, may significantly differ from the field of the incoming wave (Merschdorf et al., 2004; Messinger et al., 1981). The presence of a Fermi edge in the laterally resolved electron energy distribution spectra recorded from Cu and Ag nanoclusters (see Section IV) demonstrates that even in this case 2PPE contributes substantially to the recorded electron yield. As a first approximation it can thus be assumed that the electron emission yield scales with the square of near-field photon density (Shalaev et al., 1996), which is given by the local electric field to the power of four. Because of the inelastic mean free path of the electrons, PEEM probes only the first few nanometers (at our energies ∼5 nm) from the surface, thus providing a fingerprint of the electrical field in this region. This quantity is crucial to understanding the aforementioned luminescence enhancement effects. Details of the interaction of the local electric field E, with the electrons certainly must take into account the vector character of E, as well as the nature of the states from which the electrons are emitted. Figure 39 shows a UV-PEEM image (a) and a laser-PEEM image (b) of exactly the same region of the sample, containing one crescent in the orientation and size as shown in the SEM image (c), from Cinchetti et al. (2005). The dark spot in the upper left corner of images (a) and (b) is a defect on the screen. The images for UV and laser excitation reveal a marked difference. In particular, comparison to the orientation of the crescents (c) suggests that with UV illumination (a) electron emission is enhanced throughout the metal structure. Some localized features visible in the lower part are superimposed on this average behavior. Illumination at 400 nm (b), on the other hand, leads to an enhanced emission between the tips of the structure. These observations can be explained by consideration of the dielectric response of silver (Johnson and Christy, 1972). At the experimentally used wavelengths silver has a dielectric function of ε(250 nm) = −0.138 + 3.505i and ε(400 nm) = −4.460 + 0.215i. The dominating imaginary part for ε(250 nm) indicates that this radiation corresponds to an energy above the onset of interband transitions. The dominating negative real part of ε(400 nm) is typical for all energies below the interband transitions. This behavior rules the entire frequency range down to the static limit and may be termed the “metallic” response.

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F IGURE 39. (a) UV-PEEM image of a crescent at hνUV = 5.0 eV (250 nm). (b) Same region for illumination with the femtosecond-laser, hνL = 3.1 eV (400 nm). (c) Corresponding SEM image with identical orientation and scale. (d) Local magnitude of the electric field, calculated for a 2D geometry of silver in vacuum for light incident from the left with wavelength hνUV = 250 nm. (e) Same for λL = 400 nm. The gray scale bar indicates the enhancement factor of the squared field amplitude.

Model calculations were performed to illustrate the dependence of the optical response of silver on photon energy. For the calculations, the optical response of silver was described by literature values (Johnson and Christy, 1972) and a 2D geometry of an infinitely extending rod with a cross section similar to the crescents was considered. Maxwell’s equations were solved with a commercial finite element code (Femlab GmbH, see http://www.femlab.de). Figures 39 (d, e) show the calculated near-zone field for a cross section through a silver rod in vacuum to illustrate qualitatively the optical near-field distribution for these two cases. At 250 nm (d), there is an almost homogeneous field inside the silver, whereas at 400 nm (e) enhanced and highly localized optical fields are observed, especially near the tips. This calculation must not be regarded as a quantitative description of the electromagnetic response of the crescents since they are 50 nm thick structures on an interface between two media with highly different polarizabilities (vacuum and silicon), whereas the calculations are performed on infinitely extending rods in vacuo. Still, the central conclusion of a qualitatively different response of the metal objects to optical fields above and below the onset of interband transitions is justified and in agreement with theoretical studies on similar geometries (Kottmann and Martin, 2001; Kottmann et al., 2001).

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As a general trend, it can be stated that the particle plasmon wavelength given by Re(ε) = −2 (neglecting the substrate) roughly divides a regime of metallic behavior at lower photon energies where large field enhancements and optical resonances are observed from a nonmetallic regime, that is, a response without significant change of the field distribution of the exciting photon beam at higher energies. The experimental observations of Cinchetti et al. (2005) can be interpreted along these lines; homogeneous electron emission from the entire silver surface should ideally appear as a 1:1 image of the geometric shape of the crescents for the case of UV illumination above the particle plasmon energy (a). The metallic behavior clearly shows up in terms of an essentially dark crescent but a bright spot in the field enhancement region between the tips (b). For silver particles the peculiar property of a blue-shifted plasmon frequency for very small particles is observed (Liebsch, 1993), which may indicate another possible source for localized highly emissive spots at grains or cracks in the metal crescents in the UV. As a consequence of these superimposed effects, the signature of the opening of the ring, which in principle should be visible in (a), is obstructed. In the laser-PEEM image (b), the enhanced 2PPE yield at the gap position points toward a locally enhanced electrical optical field close to the tips of the structure, in agreement with the behavior that can be expected for a photon energy in the vicinity of the particle plasmon energy. E. Interferometric Time-Resolved Two-Photon PEEM Imaging of Plasmon Eigenmodes The study of femtosecond-laser-excited plasmon eigenmodes in metallic nanostructures was initiated by the accidental discovery of very intense electron emission centers in PEEM images by Schmidt et al. (2001). Figure 37 shows a collection of examples of such hot spots. The electron emission signal is strongly enhanced due to plasmon-assisted multiphoton photoemission. Meanwhile, an increasing number of groups worldwide use the PEEM technique for the study of plasmon excitations (Meyer zu Heringdorf, 2005; Cinchetti et al., 2004; Dürr et al., 2001; Ernst, 2005; Kubo et al., 2005; Lilienkamp, 2005; Munzinger et al., 2005; Nilius et al., 2000). Localized surface plasmons are collective charge density fluctuations that can be excited optically (Raether, 1988). The high concentration of electromagnetic energy into metal structures much smaller than the wavelength of the exciting radiation leads to a strong enhancement of various nonlinear optical processes such as surface-enhanced Raman scattering (Gersten and Nitzan, 1980; Kneipp et al., 1997), second-harmonic generation (Chen et al., 1981; Lamprecht et al.,

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1999), and multiphoton photoemission (Lehmann et al., 2000; Merschdorf et al., 2000; Monchicourt et al., 1997). The future prospect of plasmonic devices (Barnes et al., 2003; Ebbesen et al., 1998; van Duyne, 2004) has stimulated intense research on the fundamental nature and dynamics of surface plasmons. Many practical applications for sensing, subwavelength optics, waveguides, circuits, filters, and interferometers are within reach for the near future. LSPs, more precisely called surface plasmon polaritons or simply particle plasmons, can be induced optically in small particles due to the breaking of k-conservation (k is no good quantum number). For small metallic nanospheres with R  λ (λ, photon wavelength)—the Rayleigh limit— a dipolar surface plasmon resonance (collective mode) occurs at Re ε(ω) = −2n20 ,

(29)

where ε(ω) is the complex dielectric function of the metal sphere and n0 the index of refraction of the surrounding medium. For Ag particles in vacuum this condition is fulfilled at about hν = 3.5 eV (optical data from Hagemann et al., 1975). In (or on) a medium this value is red shifted (e.g., to 3.1 eV for n0 = 1.33). This eigenmode energy exactly matches the photon energy of the frequency-doubled Ti:sapphire laser. More precisely, for metallic spheres with 2R ≥ λ/10 (i.e., R ≥ 20 nm at our wavelength) the Mie formalism (Mie, 1908) is appropriate to describe extinction and elastic scattering. In the resonance region, the damping parameter Im ε(ω)  1 for Ag (unlike Cu or Au), that is, a large enhancement of the dielectric response occurs. For Ag nanoparticle films on SiO2 extinction curves with maxima shifting from 3.4 to 3.0 eV with increasing coverage have been measured (Hövel et al., 1993; Kreibig and Genzel, 1995). Since the resonance curves have a width of ∼0.7 eV, the photon energy of 3.1 eV is always within the region of enhanced extinction due to the vicinity of the LSP resonance. Further shifts and splittings of the resonance frequencies are expected if the particles are of spheroidal or irregular shapes (Kreibig and Genzel, 1995). Two resonances centered at 2.1 and 2.9 eV with a resonance width of ∼0.5 eV have been reported for oblate Ag spheroids with dimensions of 80 nm × 40 nm (Scharte et al., 2001). Further, the Mie plasmon frequency may be (red) shifted due to dipole and multipole interactions between neighboring particles and due to the interaction with the substrate. In continuous matter, plasmons cannot be excited optically because the energy and momentum conservation laws cannot be fulfilled simultaneously. The coupling of light into plasmon modes requires 1D or 2D nanostructures that can be metal gratings, nanoparticles, or rough metal films (Barber et al., 1983; García-Vidal and Martín-Moreno, 2002; Sarychev and Shalaev, 2000). Light can be coupled into propagating surface plasmon modes by matching of

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the phase velocity of the incoming light with that of the plasmon modes within an integer reciprocal vector of the grating. LSPs are excited when the photon frequency fits to the eigenfrequency that is determined by the condition of Eq. (29). Owing to its low imaginary part of the dielectric function, silver has proven to be an optimum material for the study and exploitation of plasmon phenomena. The resonance frequencies of LSP eigenmodes extend from the eigenenergy of the Ag bulk plasmon at 3.8 eV down to the infrared spectral range around 1.5 eV, depending on the local structure, a possible interparticle coupling, and the particle shape. LSP eigenmodes of metal spheroids have been extensively studied using optical techniques (Kreibig and Vollmer, 1992). On a surface metal spheroids can percolate and coalesce into irregularly shaped cluster composites that may resemble fractal structures (Shalaev et al., 1996). In turn, the distribution of the LSP modes broadens and extends to infrared frequencies. Even in a seemingly continuous Ag film, LSP eigenmodes can be excited at metallic protrusions, voids, and other nanoscale roughness features. The plasmon eigenmodes cause the local enhancements of the electromagnetic near field discussed in the previous section. The eigenmodes persist for typically 6 fs, the so-called dephasing time (Lehmann et al., 2000; Nilius et al., 2000). Observation of LSP modes in a phase-resolved manner requires a very high spatiotemporal resolution, which poses an enormous experimental challenge. The technique is termed interferometric time-resolved 2P-PEEM and uses a setup as shown in Figure 35. The pioneering work was recently published by Kubo et al. (2005). Figure 40(a) shows a schematic diagram of the excitation

F IGURE 40. (a) Schematic structure of the optical exitation of a silver grating sample formed by angled evaporation of silver onto a patterned quartz substrate. (b) Scanning electron micrograph of the silver grating (upper part) superimposed with the UV-PEEM image (lower part) to show correspondence in the >100 nm scale topographical contrast. (c) 2P-PEEM image at the same magnification (p-polarized, 400 nm femtosecond-laser excitation). The surface roughness features with <10 nm (root mean square) distribution in the SEM image, which is too fine to resolve with the PEEM, gives rise to excitation of the LSP modes seen as hot spots. The rectangle locates the four hot spots featured in Figure 41. (From Kubo et al., 2005.)

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process of LSP eigenmodes in a nanostructured sample by a femtosecondlaser pulse. The optimized Ti:sapphire laser oscillator provides extremely short (10 fs) pulses at 400 nm center wavelength with 100 mW average power and 90 MHz repetition frequency. A photoemission electron microscope detects the emitted electrons with a spatial resolution of typically 50 nm. In addition, a Hg UV lamp (hν = 4.9 eV) can be used for comparison. The sample was a silver grating produced by angled deposition onto a 1D array of mesa structures with a period of 780 nm photolithographically formed on a quartz substrate. The work function of the sample was ∼4.2 eV; that is, one-photon photoemission with the 3.1 eV laser photons is energetically forbidden. The SEM image in the upper part of Figure 40(b) shows the topography of the sample and reveals random <10 nm surface roughness features of the Ag film that are not visible in the UV-PEEM image, as shown in the lower part of image (b). The femtosecond-laser-excited PEEM images (c) exhibit intense hot spots, similar to the earlier experiments by Schmidt et al. (2001). Obviously, the nanoscale roughness features visible in the SEM image give rise to an excitation of LSP modes excited by the laser light. The hot spot structures visible in the PEEM image thus represent a nonlinear map of the local LSP fields excited in the sample. The 2PPE signal has an E 4 dependence on the electric field on the surface. The 400 nm laser light is resonant with only a fraction of the nano roughness features in the Ag structure (Sarychev and Shalaev, 2000). Similar to an optical interferometer, it was possible to precisely vary the delay time between the pump and probe pulses as explained in Figure 35. In the experiment of Kubo et al. (2005), the optical delay allows an extremely high precision of better than 50 attoseconds, corresponding to 1/25 of an optical cycle (1.33 fs) of the 400 nm light. A sequence of sub-femtosecond precision of 2P-PEEM images is shown in Figure 41. An LSP in a given particle is a coherent electromagnetic excitation that undergoes a spatiotemporal phase evolution comparable with a (damped) oscillator. For these measurements, the 10 fs excitation laser pulses are split into identical collinear beams by transmission through a Mach–Zehnder interferometer. Interferometric scanning of the lengths of one arm of the interferometer modulates the temporal delay between the two pulses. Kubo et al. (2005) have taken an interferometric PEEM movie with steps of 330 attoseconds per frame. The emission process responsible for the hot spots is plasmon-mediated 2PPE. This means that the observed electron signal carries the signature of the LSP oscillations excited by the first laser pulse (pump) that is observed for a certain time snapshot by the second laser pulse (probe). However, both pulses are temporally overlapping. The result can be discussed in terms

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F IGURE 41. Interferometric time-resolved 2P-PEEM micrographs of the four localized surface plasmons on the silver grating framed in Figure 40. The delay time between the pump and probe pulses is advanced from −0.33 fs to 40.7 fs corresponding to − 14 × 2π to 30 12 × 2π in terms of the optical phase of the carrier light (400 nm) with an increment step of 0.33 fs. All four dots oscillate in phase with the field during the optical excitation by the pump pulse (− 14 × 2π , 5 12 × 2π ). As the driving pulse wanes, the coherent polarization excited at each dot shifts to its own eigenfrequency. For instance, the phases of dots A, B, and D are retarded; dot C is advanced. The phase lag causes the intensity maxima to rise later (sooner) with respect to the phase of the driving field. The circled hot spots indicate the change in the intensity maxima (constructive interference) in five cycle intervals due to the phase slip of the LSP modes with respect to the driving field. (From Kubo et al., 2005.)

of a quantum interference between pump- and probe-induced polarization waves as discussed by Petek et al. (1997) and Ogawa et al. (1997). The pump pulse drives the collective electron oscillation at the frequency of the laser wave (forced mode). After the exciting pulse has passed, however, the individual eigenmode of a given nanofeature evolves according to its natural frequency (for natural modes of spheres, see Stratton, 1941) and couplings with the dephasing and dissipative degrees of freedom (Kubo et al., 2005). If the LSP eigenfrequency is larger or smaller than the laser frequency, the plasmon phase evolves out of phase with the probe field, advanced or retarded, respectively, with elapsing time. This phase lag is visible in Figure 41 at 13.34 fs (circles and arrows) and 20.01 fs (dashed ovals). It produces constructive or destructive interferences with the probe beam, which are observed as enhanced or suppressed photoemission. The sinusoidal modulation of the spectrum with a relative phase of a pulse pair is known as the optical Ramsey fringe effect (Salour and Cohen-Tannoudji, 1977). Given the sub-femtosecond precision of these experiments, even a propagating light wave or a propagating plasmon (traveling with a group velocity lower than the speed of light) can be observed in “real time” under stroboscopic illumination. The speed of light is 300 nm/fs and thus observable

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F IGURE 42. Fringes in laser-excited PEEM images due to interference of the scattered wave with the primary laser wave at an edge of a Si sample with corresponding line scan (a; from Schmidt et al., 2002) and at a Ag nanoparticle on Si (b; from Meyer zu Heringdorf, 2005).

in time-resolved PEEM. Bauer (2005) has imaged the phase propagation of a plasmon mode on extended nanoparticles. Schmidt (2000) and Meyer zu Heringdorf (2005) detected the interference fringes of the (coherently) scattered surface wave with the incoming laser wave. The two examples in Figure 42 show the interference fringes at a corner of a metal-coated Si surface (a) and at a Ag nanoparticle on Si (b). The line scan in (a) reveals a period of 3.55 µm—almost an order of magnitude larger than the photon wavelength. The reason for this finding is that the surface wave and the incoming wave form an angle of θ = 27 degrees. Hence, the interference pattern has a period of Λ = λ0 /(1 − sin θ ). For λ0 = 400 nm we thus expect fringes in a distance of 3.67 µm, in good agreement with the observed value (Schmidt, 2000).

IV. T IME - OF -F LIGHT S PECTROMICROSCOPY This section describes how a photoemission electron microscope is operated in the TOF mode. The electrons that are emitted from the sample surface with

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different energies are dispersed in a drift tube at low beam energy integrated into the imaging optics. Two methods of fast image detection have been explored: an ultrafast gated intensified CCD camera (≥300 ps gate time) and a 3D (x, y, t)-resolving DLD (time resolution <100 ps). The latter device has a lateral resolution of ∼50 µm in the image plane being equivalent to 1000 pixels along the image diagonal. An energy resolution of 150 meV has been achieved in spectroscopic imaging, which can be further improved via better time resolution. The potential of TOF photoemission spectromicroscopy is demonstrated for two different pulsed excitation sources, synchrotron radiation (in the soft X-ray range) and femtosecond lasers (in the visible and infrared spectral range). A. Time-of-Flight Versus Dispersive Energy Filters for Spectroscopic Imaging The worldwide advances in nanoscience and nanotechnology have strongly pushed the development and improvement of adequate analytical methods. In the field of microscopy there has been dramatic progress in imaging performance. Modern transmission electron microscopes (TEMs) provide atomic resolution, and aberration correction (Haider et al., 1998) paves the way to sub-Angstrom resolution in the future (Rose, 1999). Scanning tunneling microscopy (STM) and atomic force microscopy have become standard tools for imaging of conducting and insulating surfaces, respectively, with subatomic resolution. A special high-resolution mode of the latter technique recently made details of atomic orbitals visible (Hembacher et al., 2004). Less progress has been achieved in the field of nano-spectroscopy. X-ray fluorescence (EDX) or Auger microprobes in SEM reached their principal limits several years ago. Their lateral and depth resolution is limited by electron scattering processes (blooming) within the surface region of the sample. Further restrictions are set by the low X-ray fluorescence yield and the low signal-to-background ratio of electron-excited Auger spectroscopy. The spectroscopic mode of STM works well within a few electronvolts from the Fermi edge (Grandidier et al., 2000), but gives no access to core levels, being the “fingerprint” of elements and their chemical environment in a compound. Energy-filtered TEM does provide access to core levels via electron energy loss spectroscopy. The electron energy loss near-edge structure provides valuable information on the chemical bonding environment of a species (Mayer, 2002; Mayer and Plitzko, 1996). The performance of this technique is very high for specimens with good crystalline order being sufficiently thin to transmit the electron beam. 3D nanodevices can only be studied when thin samples are cut out exactly at the position of interest. For many applications in materials research and nanoscience (e.g., fast control

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during wafer and IC production, investigation of “living” electronic devices on a chip, chemical surface reactions on a catalyst, etc.), spectroscopic TEM is not suitable. Obviously, a strong need still exists for other powerful tools for nondestructive chemical nanoanalysis of surfaces of thick specimens. Looking at the problem with the eyes of a spectroscopist, we find X-rayinduced photoelectron spectroscopy the most powerful technique, termed electron spectroscopy for chemical analysis (ESCA). Established in the 1960s by Siegbahn et al. (1967), ESCA comprises X-ray photoemission spectroscopy (XPS) and X-ray-excited Auger electron spectroscopy (AES). High-performance experiments use monochromatized synchrotron radiation to excite photoelectrons and Auger electrons. Energy analysis of the electrons yields the core level binding energies. This facilitates a fingerprint-like detection of elements and their chemical states in compounds. Corresponding spectra of all elements (except H, He, and the heavier transuranium elements) and many compounds are tabulated (XPS-Database; National Institute of Standarts and Technology (USA), see http://srdata.nist.gov/xps). This makes the interpretation of spectra easy and reliable and allows for a quantitative analysis with reasonable accuracy down to 4–5 atom % (Powell and Seah, 1990; Seah, 1995). The combination of ESCA with electron microscopy provides an attractive surface analytical tool. There have been several approaches to combine ESCA with lateral resolution. A straightforward manner is to focus the X-ray beam in a small spot and scan the surface, taking spectra at each point. This concept is used in various laboratories; a good overview is provided in the special issue Spectromicroscopy (Ade, 1997), see chapters by Ade et al. (1997), Coluzza and Moberg (1997), Johansson et al. (1997), Marsi et al. (1997), Meister and Goldmann (1997), Voss (1997), Weiss et al. (1997), and Thieme et al. (1998). A commercial instrument (Quantera Scanning X-ray Microprobe; Physical Electronics, ULVAC-PHI Inc., see http://www.ulvac-phi.co.jp/english/quanteraSXM.htm) also uses this technique. The alternative method is parallel full-field image acquisition via a magnifying lens system and an imaging energy analyzer. This solution provides both a higher data acquisition rate and the possibility to take energy-filtered images at selected XPS lines and in real time. Most approaches use dispersive energy filters capable of transporting the entire image without causing significant additional aberrations. Early commercial instruments (Coxon et al., 1990; Wardell and Coxon, 1987; AXIS Ultra DLD; Kratos Analytical/Shimadzu Group Company, see http://www.kratos.com/Axis/AXISUltra.html) added an imaging lens to a hemispherical energy analyzer. Later designs (Tonner et al., 1997; Bauer et al., 1997; Bauer, 2001; Imaging Energy Analyzer; Elmitec GmbH, see http://www.elmitec.de/html/analyzer.html) started from proven electron microscopes that were complemented by energy analyzers with good imaging

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TABLE 2 C HARACTERISTICS OF P ULSED L ASERS AND L ASER -BASED S OURCES FOR T IME -R ESOLVED PEEM E XPERIMENTS Source

Repetition rate

Pulse duration

Radiation characteristics

Laser-induced plasma X-ray laser Free electron laser Ultrafast Ti:sapphire laser∗ UV laser∗∗ Pulsed electron beam MAMI

10–1000 Hz 1–1000 Hz Single spot 80 MHz

Few nanoseconds Sub-picoseconds Femtosecond range <100 fs

266 nm Up to 2 GHz

<10 ps 40 ps

Incoherent Coherent Coherent Infrared/visible range (800/400 nm) Infrared (10–100 µm) Pulsed photocathode

∗ Spectra-Physics, Newport Corporation, Irvine, CA [http://www.spectraphysics.com]. ∗∗ Lumera Laser GmbH, Kaiserslautern, Germany [http://www.lumera-laser.com].

capabilities. A good overview is given by Bauer (1998). Also, retarding-field imaging energy filters have been developed (Merkel et al., 2001). The nanoESCA (Escher et al., 2005a, 2005b) aims at a maximum transmission by correction of the leading aberration term (α 2 -term) of a hemispheric analyzer. This is achieved by using an antisymmetric tandem configuration of two hemispheres. Two fully aberration-corrected instruments are under construction and testing: the SMART project at BESSY in Berlin (Fink et al., 1997; Schmidt et al., 1998; Wichtendahl et al., 1998) and the PEEM 3-project at the ALS Berkeley (Feng et al., 2005). In view of this tremendous work on imaging dispersive energy filters, data using imaging TOF filters are sparse (Oelsner et al., 2001, 2004b; Schönhense et al., 2001; Spiecker et al., 1998). However, there are several intriguing advantages of TOF energy filtering outlined below. An important feature of TOF-PEEM is the need for pulsed photon sources with a well-defined time structure. Characteristic parameters of suitable pulsed excitation sources are listed in Table 1 for synchrotron radiation. Synchrotron sources such as BESSY II (Berlin), ESRF (Grenoble), SLS (Villigen), and ALS (Berkeley) provide tunable X-rays with pulse lengths in the range of typically ≥50 ps. Novel techniques of bunch compression have driven the limit into the region of a few picoseconds, see low-α mode of BESSY (Abo-Bakr et al., 2003; Feikes et al., 2004). In the future, the free electron lasers will provide even shorter pulses in the femtosecond range (Germany synchrotron source, Hamburg; DESY). The collection of various lasers and laser-based sources in Table 2 presents typical examples rather than a complete list. Commercial laser systems deliver intense pulsed laser radiation in the UV and visible range; these are

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excellently usable for PEEM. Excitation by femtosecond-laser radiation in the infrared or visible spectral range (∼800 nm and 400 nm for the fundamental and first harmonic of the Ti:sapphire laser, respectively) leads to intense signals in spectroscopic PEEM due to multiphoton processes, as discussed in Section IV.D. Although laboratory-based pulsed radiation in the vacuum ultraviolet (VUV) and extreme ultraviolet (EUV) range is becoming available in several laboratories, it is too early to judge its suitability for time-resolved PEEM experiments. There are several different approaches: laser-induced or pinch-plasma sources deliver (incoherent) X-rays at certain emission lines (Bergmann et al., 1999; Neff et al., 2001) in terms of intense but relatively long pulses with low repetition rate. Frequency multiplexing or mixing of laser beams provides coherent radiation (Zacharias, 2005). Such tabletop laser-based sources presently reach encouraging intensities in the photon energy range of 100 eV and slightly beyond. These sources are characterized by excellent time structures. Recently a tabletop source has been tested for its usability in PEEM (Fecher et al., 2003). A related method should be addressed that uses a pulsed polarized electron beam from a GaAs photoemitter source. The accelerator group at the Mainz Microtron (MAMI) developed a high-performance source yielding 40 ps electron pulses at high repetition rate and high intensity (average current 1 µA) (Aulenbacher et al., 1997, 1999, 2002, 2005). Such a polarized electron source can be used for time-resolved magnetic imaging exploiting spin-dependent electron diffraction in a spin-polarized low-energy electron microscope (LEEM) (Altman et al., 1991) or spin-polarized double-reflection emission electron microscope (SP-DREEM) (Grzelakowski, 1999, 2000). In the context of magnetic imaging it should be stressed that the laser-based or polarized electron-based techniques yield magnetic contrast but no element selectivity. This may be sufficient if, for example, only the micromagnetic domain structure and dynamics of the topmost magnetic layers are of interest. B. Basics of Time-of-Flight PEEM The TOF technique was originally developed for spectroscopic experiments (Becker and Shirley, 1996; Snell et al., 1999, 2001; Viefhaus et al., 1996) without spatial resolution. It makes use of the fact that the transit time τ of an electron through a drift tube of length L depends on its energy Ed within the drift space according to τ = L · (me /2Ed )1/2 .

(30)

Here me is the electron mass and Ed = Ekin + eUd with Ekin represent the initial kinetic energy on the sample and Ud the potential of the drift tube

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F IGURE 43. Energy dispersion of an electron beam after passing through a TOF spectrometer (a) in comparison to a conventional dispersive analyzer, here of 180-degree-type (b).

with respect to the sample (corrected for work function differences). If the drift tube is operated at low-pass energies (typically 50–100 eV), the energy distribution of the electrons is spatially dispersed, leading to different arrival times as in conventional TOF electron spectroscopy. Because the drift tube is part of the microscope column, the image is retained and can be recorded by a time-resolving detector. At the end of the drift tube the dependence of Eq. (30) leads to a spatiotemporal dispersion of the energy distribution of the electron beam along the electron optical axis as illustrated in Figure 43. A time-resolving detector allows observing the energy distribution along z, depicted in image (a), in a manner similar to a conventional dispersive analyzer [e.g., of hemispheric type, as depicted in image (b)]. It is near at hand that the electron optical properties of the TOF arrangement bear principal advantages compared with a common dispersive arrangement because a linear electron optical axis z is retained. The dispersion along x, perpendicular to the electron momentum direction z in image (b) requires elaborate techniques to avoid additional aberrations in imaging dispersive analyzers. Figure 44 shows the calculated TOF and energy resolution as functions of the drift energy according to Eq. (30) and the derivative dE 2 2Ed3 =− . (31) dτ L me

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F IGURE 44. Calculated energy resolution (chain curve) and TOF (full curve) versus drift energy for a TOF-PEEM; length of drift tube 433 mm. The measured energy resolution of ∼150 meV FWHM at 50 eV (circle) is in good agreement with the expected result.

At typical drift energies between 50 and 100 eV and the present time resolution of 100 ps, the energy resolution lies between 100 and 300 meV. As the retardation is done behind the first two magnifying lenses, the additional aberrations do not deteriorate the base resolution (see also Section V). For lower drift energies a resolution of <100 meV can be reached (Schönhense et al., 2001). However, there is a practical limit due to stray magnetic fields (in particular AC fields) that will finally restrict the attainable resolution. A commercial photoemission microscope (Focus GmbH, see http://www. focus-gmbh.com) was complemented by a drift tube following the projective system as depicted in Figure 45. For details of the three-lens electrostatic microscope, see Schneider and Schönhense (2002). The drift region in the column had a length of L = 433 mm. At the entrance of the drift tube the electrons are retarded from the column potential to the desired drift energy Ed . Ideally, the electron beam should be parallel within the drift tube. In the first prototype instruments, a slight beam divergence was present that was found to be tolerable. At the end of the drift tube the electrons hit a multichannelplate image intensifier. In the first approach an ultrafast CCD camera was used and the single-bunch mode of BESSY-I in Berlin was exploited (Spiecker et al., 1998). This mode delivered pulses at a repetition rate of (208 ns)−1 ≈ 5 MHz (Kleineberg et al., 1999). Behind the image intensifier the electron signal was converted into visible light by an aluminum-coated polymethylmethacrylate (PMMA) scintillator screen. Thus, the time structure of the electrons arriving at a given point of the multichannelplate reflects itself in a time structure of the luminescence light of the corresponding point on the scintillator screen.

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F IGURE 45. Schematic view of a TOF-PEEM, consisting of a state-of-the-art photoemission electron microscope complemented by a drift tube and a time-resolving image detector. The drift tube is operated at low beam energy allowing TOF microspectroscopy or energy-selective imaging.

The image was detected by a commercial CCD camera equipped with an ultrafast gated optical intensifier. By synchronization of the camera gate with the bunch marker pulse from the storage ring as a trigger, a time slice could be cut out of the time-dependent distribution of the luminescence signal from the scintillator. A variable cable delay allowed shifting the time slice along the t-axis. The decay time of the scintillator set a limit 2.1 ns to the maximum attainable time resolution that restricts the energy resolution. A second, completely different detector approach was necessary to overcome the principal limitation in time resolution imposed by the scintillator. The CCD camera was replaced by a delayline detector, which was originally developed for the study of momentum-resolved multifragment detection (Ali et al., 1999; Mooshammer et al., 1996). It was adapted to the demands of image acquisition by Oelsner et al. (2001). Figure 46 shows a photograph and a schematic view of the DLD. This detector is based on single-electron counting with position readout for every counting event. The charge cloud leaving the exit of the multichannelplate after impact of an electron passes through a crossed arrangement of two delay lines (for x and y). The delay line along y is drawn as a meander in Figure 46. Actually, the x and y delay lines are wrapped around ceramic rods in the shape of two flat coils inserted into each other, as depicted in Figure 45. The charge pulse (∼108 electrons) induces an electromagnetic pulse at the x and y delay line at the lateral position where the electron hit the channelplate. The x- and y-coils are closely spaced and nearly transparent for the electron cloud. The electromagnetic pulse travels to both ends of each delay line with its group velocity close to the speed of light for the 50 impedance line. Fast timing amplifiers at each end of the delay lines detect the arrival time t of the electromagnetic pulses

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F IGURE 46. Photograph (a) and schematic view (b) of the delayline detector. The arrangement allows 3D (x, y, t)-detection of single-electron counting events. For sake of clarity, only one of the two delay lines is shown; see text for explanation.

and determine the x- and y-position from the time delays tx and ty at the two ends of each delay line. Since the total time delay (≈60 ns) is a constant defined by the total length of the delay line (≈17 m each), a very precise determination of the two coordinates x and y is feasible using the arrival time differences. A lateral resolution of ∼50 µm has been determined (Oelsner et al., 2001). Given a typical detector diameter of 50 mm, this corresponds to 1000 image points along the image diagonal, which is also a typical value for CCD cameras. It is noteworthy that this lateral resolution in the image plane is even higher than the resolution obtained with typical multichannelplatescreen arrangements, where the lateral resolution is usually not better than 120–200 µm. The reason is that the DLD is capable of determining the center of the charge pulse very accurately by means of the constant fraction discriminators. The arrival time delay at the two ends of each delayline gives the start and stop signals of the time-to-digital converter, yielding the lateral coordinates as illustrated in Figure 47. The time coordinate t is given by the absolute time of the pulse at the multichannel plate with respect to the bunch marker of the synchrotron or the laser output serving as trigger. The anode placed in the cen-

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F IGURE 47. Operation scheme of the delayline detector. The four outputs of the x and y delay line are converted into precise timing signals by the constant fraction discriminator. These are referenced to the trigger signal (start) from the photon source and processed by the time-to-digital converter and fed into the computer via an USB 2 interface.

ter of the delayline assembly can contain a transparent fluorescent screen that allows viewing the image from the rear. State-of-the-art counting electronics and data transfer schemes allow total count rates of the order of 107 counts per second (Surface Concept GmbH, see www.surface-concept.de), yielding good SNR. The TOF spectromicroscopy mode bears an important advantage compared with the spectromicroscopy mode using a dispersive imaging energy filter because the DLD samples all time slices (corresponding to energy slices) simultaneously, at least within a certain energy interval. This is not possible with a dispersive analyzer. This picosecond time slicing technique using the DLD is very flexible and bears further advantages. The thickness of the individual time slices can be defined and optimized after image acquisition via the imaging software. In the TOF spectromicroscopy mode this thickness corresponds to the width of the energy interval of the partial image: it defines the energy resolution. In the time-resolved imaging mode it defines the time increment between subsequent snapshots and thus the time resolution (see Section II). As a third possibility, picosecond time slicing can be exploited for a new way of aberration correction as described in Section V. The DLD approach in particular allows TOF microspectroscopy (TOFµESCA), spectroscopic imaging (TOF-PEEM), as well as time-of-flight X-ray photoelectron diffraction (TOF-XPD) or Fermi surface mapping by imaging the backfocal plane of the objective lens and selecting the desired XPS line by

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its characteristic TOF. In principle, the DLD allows multifragment imaging (i.e., a detection of several emitted fragments of a single primary event). The multihit capability gives access to correlations in many-particle dynamics (e.g., in (γ , 2e) processes at surfaces). C. Spectromicroscopy Exploiting the Time Structure of Synchrotron Radiation The early TOF-PEEM experiments used a CCD camera with ultrafast gating. Figure 48 shows a typical result obtained with this setup (Spiecker et al., 1998). The PEEM image shows a region of a silicon surface partially covered by an indium overlayer. The local TOF spectra taken at two different positions on the surface reveal marked differences between positions 1 and 2 (i.e., on the In layer and on the substrate, respectively). After transformation of the spectrum from the TOF to the energy scale according to Eq. (30), a pronounced peak is identified at a kinetic energy of ∼53 eV, corresponding to the binding energy of the In 4d level. The Fermi edge appears in the spectrum as high-energy cutoff at ∼72 eV. Since the detector was a commercial CCD camera (type Picostar-HR, LaVision GmbH), this approach has proven to be a very simple means for time-resolved PEEM. However, there is one important drawback connected with the conversion of the electron signal into visible light. Although the PMMA screen used belongs to the fastest scintillators available, its decay time set a limit to the obtainable time resolution. The scintillator response

F IGURE 48. Time-of-flight PEEM microspectroscopy at a silicon surface partially covered by indium (photon energy 76 eV). The spectra have been taken at two different positions as marked in the image (with and without In present). The results have been obtained by means of the setup shown in Figure 45 using a CCD camera with ultrafast gated image intensifier.

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F IGURE 49. TOF microspectra obtained using the delayline detector attached to the TOF-PEEM. (a) Overview spectrum at hν = 800 eV for an iron sample showing the Fe 2p signal and oxygen, nitrogen, and carbon 1s lines of surface contaminations. (b) Tungsten 4f spectrum taken at hν = 120 eV.

function gave a measured width of ∼2.1 ns FWHM. This translates into a correspondingly low energy resolution according to Eq. (30) and Figure 44. Indeed, a rather large line width of the In 4d signal is observed in the spectrum in Figure 48. Moreover, the conversion efficiency of fast scintillators is very low compared with typical fluorescent screens. The DLD overcomes both drawbacks. Its time resolution is presently 100 ps and can be further improved by a factor of 2 (Surface Concept GmbH, see www.surface-concept.de); its detection efficiency is only limited by the efficiency of the channelplate. Figure 49 shows two TOF spectra taken with the DLD. The overview spectrum (at hν = 800 eV) shown in image (a) represents the entire kinetic energy range of 795 eV corresponding to a TOF

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range from 20–75 ns. Note that the energy resolution E scales nonlinearly with the experimental time resolution t, according to Eq. (31). Therefore the C 1s signal at a kinetic energy of 513 eV has a width of several 10 eV, the Fe 2p lines at 90 eV have widths of ∼1 eV, and at the low-energy cutoff the energy resolution is <0.5 eV. In this spectrum the photon signal (stray light from the sample surface) served as t = 0 reference. Figure 49(b) shows a result obtained for a tungsten surface at a photon energy of 120 eV (from Oelsner et al., 2001). At a drift energy of Ed = 43 eV the W 4f doublet is clearly resolved. Note the good signal-to-background ratio of TOF microspectroscopy. The measured energy resolution of 500 meV at Ed = 43 eV is in good agreement with the theoretical curve in Figure 44; the time resolution in these early experiments was 400 ps. This indicates that there are no significant effects that deteriorate the resolution. D. Femtosecond-Laser-Based Spectromicroscopy Quite recently, several experiments have been performed that combine TOF spectromicroscopy with multiphoton photoemission. In analogy to the previous section, these measurements exploit the time structure of a pulsed laser source. The laser yields low-energy photons in the visible (or UV) range. The technique thus provides spectroscopic information about the valence bands by detecting the laterally resolved electron signal. Cinchetti et al. (2003a, 2003b, 2004), Cinchetti (2004), and Cinchetti and Schönhense (2005) have studied the local photoemission spectra of isolated Cu hot spots and Ag nanoparticle films with varying mass thickness under femtosecond-laser irradiation. Given the precise time structure of the femtosecond-laser source, TOF-PEEM is ideally suited to gain a deeper insight into the plasmon-mediated emission process. Ag nanoparticles are particularly intriguing because their dipolar surface plasmon (Mie plasmon) resonance lies in the range of the photon energy of the frequency-doubled Ti:sapphire laser. Moreover, Ag particles have the highest dielectric response of all noble metal particles because the imaginary part of the dielectric function is very small in the resonance region. The excitation of collective modes is thus expected to be of major importance for photoemission dynamics from Ag nanoparticles. Using the same method, Gloskovskii et al. (2005) have studied valenceband photoemission from MoS2 nanotubes. These experiments revealed details of the two-photon transition. In particular, specific features could be explained by a band structure calculation giving evidence of the importance of the real intermediate state.

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F IGURE 50. Schematic representation of the sample preparation procedure. Regions 1–5 have nominal Ag film thicknesses of 0, 2, 5, 20, and 100 nm, respectively.

1. Results for Ag and Cu Nanoparticles The Ag films were deposited in UHV by electron beam evaporation onto a clean Si(111) substrate at room temperature. The sample consists of regions with different mass thicknesses, prepared by moving a mask in front of the surface during exposure to the Ag atom beam (Figure 50). The mass thickness varies from 0 to 100 nm with three intermediate steps: 2, 5, and 20 nm. The 20 µm wide stripes are labeled by numbers, with 1 corresponding to the bare Si substrate and 5 to the 100 nm thick bulklike Ag film. Assuming that the deposited particles have approximately an hemispherical shape (as observed for the 3D growth of Ag on Si(111) by Gavioli et al., 1999), their size has been estimated from AFM measurements. Stripes 2, 3, and 4 correspond to average particle radii of R ≈ 20, 25, and 40 nm, respectively. The Cu sample was prepared in a different way. A Cu polycrystal was treated by prolonged heating in UHV such that Ostwald ripening of the crystallites occurred. The micrometer-sized crystallites are visible in the UVPEEM image due to their different work functions (Dunin von Przychowski et al., 2004). The heat treatment gave rise to isolated hot spots in femtosecondlaser-excited PEEM images similar to those shown in Figure 37. The TOFPEEM was a modified commercial instrument (Focus GmbH, see http:// www.focus-gmbh.com) equipped with a shorter drift tube as in the previous section (length L = 350 mm), and a DLD. The Ti:sapphire laser system was described in Section III. Figure 51 shows two PEEM images of the same region of the stepped Ag wedge illuminated with the UV lamp (a) and the laser source (b). Step borders are indicated by arrows. In both images the brightness in a given area is proportional to the intensity of electron emission from that area. Clearly, the Ag nanoparticle film looks very different for UV and femtosecond-laser excitation. In particular, region 5 (the continuous Ag film) appears bright in the UV-PEEM image (a) but dark in the laser-excited PEEM image (b).

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F IGURE 51. PEEM images of the same region of the Ag sample for UV illumination (a) and femtosecond-laser illumination (b). Regions with different Ag coverage are labeled by 1 to 5; their borders are indicated by arrows. (c) Intensity profiles from (a) (UV illumination, dashed line) and (b) (laser illumination, continuous line) taken along line AB. The dotted vertical lines indicate the positions of the borders between regions 1 and 5.

The intensity profiles taken from these images along AB [white line in image (a)] are shown in image (c). The intensity profile for UV excitation (dashed line) shows a monotonous increase of the electron emission with increasing Ag coverage from region 1 to 4 and a weak drop toward region 5. For the rough nanoparticle film at high coverage (region 4), the effective surface and range of the momentum direction of escaping electrons are higher than for the bulk film (region 5). In addition, the surface potential barrier (connected with the work function) of the particles may decrease due to the local field around them. This assumption is proven by the TOF spectra (see below). Concerning the bare Si surface (region 1), it is known to appear very dark in UV-PEEM images because of its low density of states near EF . The bright spot in the upper left of Figures 51(a) and (b) is an artefact. The intensity profile for femtosecond-laser excitation [solid line in image (c)] looks markedly different. It reveals a nonmonotonous change of the electron emission intensity with the mass thickness (i.e., with the Ag particle

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size and areal density). The measured intensity profile exhibits steps that are clearly correlated with the stepped wedge of the Ag coverage profile. The emission intensity shows a pronounced plateaulike maximum at region 3 (i.e., at a mass thickness of 5 nm corresponding to an average particle radius of R ≈ 25 nm). The emission from the nanoparticle film 3 is more than two orders of magnitude more intense than that of the continuous Ag layer 5. The emissivity of the adjacent regions 2 and 4 (R ≈ 20 and 40 nm) is reduced by factors of 2.5 and 1.7, respectively. The continuous Ag film (region 5) and the bare Si (region 1) are characterized by very low emissivities. The nonmonotonous behavior of photoelectron emission intensity along the wedge-shaped Ag film can be explained as interplay between surface plasmon-enhanced photoexcitation and variation of the coverage (i.e., particle size and density). Absorption of laser radiation due to the excitation of collective modes followed by photoemission strongly increases when moving from a continuous film to the nanoparticles. With decreasing mass thickness of the film, however, this rise cannot persist simply because of the reduced areal density of the Ag particles (see also Leˇcko and Hrach, 1994). In order to gain further information on the emission enhancement mechanism of the Ag nanoparticle films in the case of laser illumination, the kinetic energy distribution of the emitted electrons has been investigated using the TOF-PEEM spectroscopy mode. The spectra corresponding to areas 1 to 5 marked in Figure 51(b) are shown in Figure 52(a). The delayline technique allows defining these regions of interest by setting appropriate conditions via the imaging software. The measured TOF τ directly reflects the velocity of the electrons in the microscope drift tube and is converted into kinetic energy Ekin according to Eq. (30). The kinetic energy spectra are referenced to the Fermi level EF of the sample; we term this the final state energy. This definition is free of the ambiguities of the kinetic energy scale for heterogeneous surfaces. As we observe two-photon transitions, the Fermi edge shows up at a final state energy of 2hν = 6.2 eV. All spectra have been corrected for the transmission of the PEEM objective lens (see Anders et al., 1999). The spectrum of electrons emitted by the continuous Ag film 5 reflects the well-known 2PPE spectrum of bulk Ag (Bauer and Aeschlimann, 2002). It shows the usual maximum close to the work function cutoff (left-hand side of the spectrum) and a shoulder at 5.4 eV final state energy. The Fermi edge is visible as a steplike enhancement of the intensity within a small energy interval. Note that the intensity scale of spectrum 5 has been expanded by a factor of 20. The nanoparticle spectra 1–4 exhibit distinct differences. The low-energy part has a strongly enhanced intensity (for region 3 it is 36 times higher than for the continuous layer), and its low-energy cutoff is shifted to lower energies reflecting a lower local vacuum level. The Fermi edge appears slightly shifted and broadened.

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F IGURE 52. (a) TOF spectra plotted as function of the electron final-state energy above EF for the square areas 1–5 marked in Figure 51 taken with femtosecond-laser illumination at hν = 3.1 eV. Since the intensity from the continuous Ag layer (region 5) is very small, the corresponding spectrum was scaled by a factor of 20 (a factor 8 in the inset). (b) TOF spectra taken in an isolated hot spot (curve 1) and in a homogeneous region (curve 2, spectrum scaled by a factor of 20; by a factor 4 in the inset) on a polycrystalline copper surface. The microregions 1 and 2 are marked in the TOF-PEEM image Figure 37(g) by a circle and a square, respectively. The Fermi edge is marked by the arrow.

The same general behavior is visible in the TOF spectra of the Cu sample, shown in Figure 52(b). The spectrum of the hot spot [spectrum 1, area marked by a circle in Figure 37(g)] appears with much higher intensity at

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low energies and a shifted low-energy cutoff compared with the spectrum taken at a homogeneous crystallite [spectrum 2, area marked by a rectangle in Figure 37(g)]. Also for Cu, the Fermi edge is slightly shifted and broadened in the hot spot spectrum. It should be stressed that all spectra in Figure 52(a) and (b) have been extracted from one measurement, that is, the full 3D (x, y, t) data set of the corresponding images, taken by the delayline detector. This ensures that the absolute intensity scale, energy positions, and resolution are perfectly identical in all spectra. The total yield [i.e., the area under the curves in Figure 52(a)] is a factor of almost 40 higher for the nanoparticle film in region 3 than for the continuous layer. In addition, the area coverage of the substrate surface is a factor of 4 lower in region 3 compared with regions 5. Thus, a nanoparticle in region 3 emits on the average about 160 times more electrons than a region of the continuous layer with equal lateral size. For region 3 the intensity step at EF is a factor of 8 higher than for the continuous film [see inset in Figure 52(a)]. Scaled with the coverage ratio this corresponds to a factor of 32 for the Fermi edge signal of a particle in region 3 compared to that of an area with equal lateral size in the continuous layer. The enhancement in the region of the Fermi edge is significantly less than the factor of 160 for the total intensity enhancement because the shape of the spectra is different. To understand shape and features of the kinetic energy spectra, we must consider the photoelectron excitation process in more detail. In contrast to Mie scattering, where the far-field scattering cross section is important, photoemission is governed by the near-field behavior. Due to the boundary conditions at the particle surface, the near-field strongly deviates from the incoming plane wave, both in magnitude and in angular character. Aers and Inglesfield (1983) and Messinger et al. (1981) have calculated the relevant quantities for Ag, Cu, and Au nanospheres both in the Rayleigh limit and in the Mie regime. For the photoemission process the absorption cross section is important, that is, the difference between the total extinction and (far-field) scattering cross sections. For large particles (R = 100 nm) the absorption cross section maximum is 0.8 (in units of the particle cross section π R 2 ); that is, in the maximum of the Mie resonance the particle absorbs 80% of the photons from the incoming plane wave that intersect the area π R 2 . In the Mie regime the extinction results mainly from far-field scattering rather than absorption. Hence, the situation becomes even more favorable toward the Rayleigh limit. For particles with R = 22 nm (corresponding approximately to our regions 2 and 3) the absorption cross section is almost half of the scattering cross section and reaches a value of 6.5. The distortion of the plane wave by the boundary conditions thus results in the absorption of all photons out of an increased “effective” particle cross section, in the calculation of

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Messinger et al. (1981) with Reff ≈ 2.5R. When resonantly exciting the LSP, a Ag particle with optimum size (R = 18 nm) absorbs an order of magnitude more photons per unit area than a larger particle in the Mie regime. The electric field enhancement at the edge of an oblate Pt spheroid particle 200 nm wide and 10 nm high was derived by Dürr et al. (2001) and was found to be two to three orders of magnitude in the maximum of the Mie resonance. Indeed, their PEEM images of 200 nm dots of a CoPt multilayer on Si showed more pronounced edges of the dots when excited resonantly. For the laser fluence used by Cinchetti et al. (2004) (6.4 µJ/cm2 ) the calculation by Messinger et al. (1981) predicts about 103 photons per laser pulse to be absorbed by a free Ag nanosphere with R = 22 nm. For our hemispheroids on the Si surface there will be quantitative differences. However, the basic behavior should persist. The Mie resonance frequency depends rather weakly on the particle size, and the resonance curves have widths of the order of 0.7 eV. It thus can be expected that many of the particles in the film will experience an enhanced optical response to the laser field. As optical excitation of surface plasmons is impossible at a smooth surface, the continuous film absorbs many fewer photons. The Fermi edges in the nanoparticle and hot spot spectra (insets of Figure 52) appear broadened and slightly shifted (∼0.1 eV) toward lower final state energies in comparison with the Fermi edge of the continuous regions. The shape of the Fermi edge in photoemission spectra of small particles can be influenced by the dynamics of the thermalization process. Thermalization of excited electrons has previously been studied in a pump-probe experiment without spatial resolution by Fann et al. (1992b). They observe a smearing of the Fermi edge that can be fitted by a slightly heated electron gas (625 ◦ K at maximum). Moreover, for pump-probe delays up to 600–800 fs a clear discrepancy from the Fermi–Dirac function is found in the range from 0–0.5 eV above EF (termed “hot tail”) that is obviously not in thermal equilibrium with the Fermi liquid. This phenomenon has been theoretically treated in detail by Rethfeld et al. (2002). The energy resolution of about 150 meV of the experiment by Cinchetti et al. (2004) does not allow reliable conclusions on the temperature of the electron gas. The width of the Fermi edge is 4kT ≈ 100 meV at room temperature. Both the shift and broadening would be in accordance with a gradually increasing number of holes generated during the laser pulse. The holes relax toward EF so that a depletion zone closely below EF can occur. Thus a broadening and shift of the edge could occur. There is, however, another possible contribution to the shift, described by the final-state cluster charge model of Wertheim et al. (1983) and Wertheim and DiCenzo (1988). During the photoemission process a unit positive charge

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can remain localized on a nanoparticle supported by a poorly conducting substrate like carbon or a semiconductor. In this case, charge neutralization happens on a time scale longer than the intrinsic time scale of photoemission (∼1 fs) but long before the next photoemission process from the given particle (>12 ns). On the given conditions a nanoparticle cannot emit more than one photoelectron per laser pulse as is evident from the total intensity values. Thus there is no long-term charge buildup as on insulators. However, a transient state with one positive charge located on the surface of the particle exists. The Coulomb energy of this transient, nonneutralized state of the particle leads to a corresponding reduction of the final state energy of the outgoing photoelectron, fulfilling the energy balance equation of photoemission. The resulting material-independent shift of the Fermi edge, the core level positions in the spectra (as well as the low-energy cutoff) is simply e2 /2R for free spherical metal clusters. It is reduced for supported clusters by about a factor of 2 because of image charge screening by the substrate. It is likely that the final-state cluster charge model—one positive unit charge residing on the particle surface for more than 1 fs—contributes to the observed shift (∼0.1 eV) of the Fermi edge. This mechanism also contributes to the shift of the low-energy cutoff in the nanoparticle spectra. The photovoltage effect as observed by Alonso et al. (1990) would yield a shift toward higher final-state energies (on a p-doped semiconductor) and can thus be ruled out in the present case. Obviously, the cluster charge exists in the hot spot on the Cu surface, too [Figure 52(b)]. This means that even a metallic protrusion can experience a localized hole on the time scale of 1 fs. The additional shift at the low-energy cutoff is most likely connected with the reduced mirror charge experienced by the escaping electron in a nanoparticle or small protrusion in comparison with a smooth metallic surface. The different overall shape of the nanoparticle spectra in comparison with the bulk spectrum is presumably connected with how the collective oscillation transfers energy to the photoelectron in the 2PPE transition. In this mode the material excitations are coherent (i.e., synchronous) with the incoming plane wave. As discussed in Section III.D it is a forced mode driven by the laser field in the vicinity of the natural mode of the Mie resonance. The radiative decay channel plays only a minor role for small particles. Electron scattering at surfaces and surface defects gains importance with decreasing particle radius below 10 nm (Voisin et al., 2001). This causes dephasing (i.e., a loss of the macroscopic phase relation within the collective motion of the electron ensemble). Dephasing can also result from inhomogeneous phase velocities in the surface region. In the jellium model the centroid of the charge oscillation of the surface plasmon is located 0.08 nm above the surface (Liebsch, 1993): in the electron spill-out region. Finally, a transfer of energy into single-electron excitations (i.e., electron–hole pairs) (Kawabata

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and Kubo, 1966) is the decay channel of utmost importance for 2PPE. Energy dissipation into the phonon system happens on a picosecond time scale (i.e., much longer than the laser pulse). The first transition (see Figure 34) populates the intermediate state |i of the 2PPE process. It extends from EF up to a maximum final state energy of 3.1 eV (i.e., the photon energy). Breaking of k-conservation in the particle can cause indirect (i.e., nonvertical) transitions (Shalaev et al., 1996); these are not possible in bulk photoemission. On a smooth surface no direct (i.e., vertical) transitions are possible because no real intermediate states exist, thus demanding a 2PPE transition with simultaneous absorption of two photons. Relaxation of the intermediate-state electrons yields a characteristic electron population in a wide energy band up to 3.1 eV above EF . According to Fermi liquid theory (Pines and Nozières, 1966) the single-particle lifetime above EF scales as (E − EF )−2 . Bauer and Aeschlimann (2002) have measured relaxation times at energies several electrovolts above EF with very high time resolution and found values between 20 and about 3 fs for energies ranging from 1.0–2.7 eV above EF in bulk Ag. Note that the term population refers to the statistical average of many single-electron excitations and not to an ensemble in one particle. Given the estimated photoabsorption rate of the order of 100 to 1000 photons per laser pulse, a collective mode in a given single particle is excited within a short time of the order of 1 fs. The electron in the intermediate state can therefore absorb a second photon out of the near-zone field so that the final state energy then extends up to 2hν above EF (see spectra in Figure 52). We can conclude that the second step of the cascade transition can happen on a timescale of a few femtosecond after the first step— during thermalization of the intermediate-state electron distribution. The steep increase toward lower energies very likely reflects the hot-electron lifetime behavior. This regime could be termed thermally assisted photoemission because the photon operator of the second transition acts on a transient hotelectron state. This phenomenon becomes even more dominant for lower photon energies (Gloskovskii, 2006). Without being enhanced by plasmon excitations, the intensity at the Fermi edge in the nanoparticle spectrum would be a factor of 4 (the fraction of coverage of the film in region 3) lower than that of the bulklike spectrum region 5. Instead, it is a factor of 8 higher. The plasmon-enhanced field obviously acts comparable to an incoming plane wave with a higher intensity (high concentration of electromagnetic energy into the nanoparticle). A similar conclusion has been drawn concerning the optically induced demagnetization investigated by Dürr et al. (2001). The plasmon lifetime (dephasing time of 4–6 fs) along with the estimated photoabsorption rate (see above) gives a hint on the excitation of multiple plasmon excitations in one particle. The above-

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mentioned difference between the integral intensity gain (factor 160) and the gain at the Fermi edge (factor 20) is most likely due to the different relaxation contributions in a simultaneous and a cascade transition. Recent studies (Gloskovskii, 2006) addressed the question at which conditions a heating of the electron gas can lead to thermionic emission. Such a contribution to the emissivity has been observed and explained by Fedorovich et al. (2000) for higher laser fluences but lower photon energies in the infrared spectral range. Thermionic emission of hot electrons is expected to contribute at high peak power (i.e., short laser pulses) and for small particles. The TOFPEEM technique is capable of distinguishing between the two processes: 2PPE is characterized by a visible Fermi edge at an energy of 2hν, whereas hot-electron emission gives rise to a Boltzmann-type of energy distribution. In practice, relaxation proceeds gradually (Rethfeld et al., 2002). Thus, there is a continuous transition between both regimes. At 1.6 eV photon energy, Gloskovskii (2006) found evidence of 3PPE, thermally assisted 2PPE (leading to a fractional exponent in the laser-power dependence of the electron yield), and also most likely for optical field emission (exhibiting a linear power dependence) at maximum photon flux. 2. Results for MoS2 Nanotubes The same technique has been used for the study of nanotubes. MoS2 nanotubes were synthesized using silica nanotubes as template. Diammonium thiomolybdate in dimethyl formamide was heated with the templates under constant stirring, dried, and reduced in a H2 /N2 gas stream at 450 ◦ C. Finally, the template was dissolved in HF. A TEM image of one of the MoS2 nanotubes is shown in the inset of Figure 53(a). An ensemble of MoS2 nanotubes was deposited on the smooth surface of a Si-wafer covered by native oxide (SiOx surface). The coverage was chosen to be low enough that individual nanotubes could be identified and localized in the PEEM image. The nanotubes appear very bright on a dark background if excited with 3.1 eV femtosecond-laser radiation; an example is shown in Figure 53(a). The high-intensity contrast between nanotubes and Si substrate was a very positive result and was not anticipated after the nanotubes appeared dark with VUV excitation. It is explained by the nature of the phototransition induced by the femtosecond-laser. The work function of the deposited nanotubes is higher than the photon energy. Hence, one-photon photoemission is energetically impossible. An important factor for the high intensity is the high density of states in the intermediate state of the two-photon transition. This, in turn, leads to an enhancement of the matrix element of the two-photon transition. The electron signal forming the image in Figure 53(a) thus reflects the nature of the two-photon transition proceeding through a real intermediate state at the given photon energy of hν = 3.1 eV.

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F IGURE 53. (a) PEEM image of a group of MoS2 nanotubes on SiOx excited by femtosecond-laser radiation with 3.1 eV photon energy. Inset: TEM image of a nanotube. (b) Local spectra of selected nanotubes (A, B denote the corresponding regions in a) and the Si substrate (region C). Spectrum A after background correction is shown in D. The probability for direct transitions (E) at the excitation with 3.1eV quanta was derived from the calculated density of states.

Figure 53(b) shows spectra extracted for different regions of the sample as marked in image (a). The energy scale is referenced to the top of the valence band becoming visible at an energy of about 6.2 eV (i.e., 2hν). The local work function of the micro areas is directly visible as low-energy cutoff of the spectra. The work function of the nanotubes (spectra A, B) is reduced

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by φ = 0.3 eV compared with the substrate (spectrum C). The nanotube spectra show a width of 2.5 eV, thus giving access to the topmost region of the valence states. Because there is a background of photoelectrons from the Si substrate contained in the nanotube spectra, the Si-spectrum C (weighted with an empirical intensity factor) has been subtracted from spectrum A. The result is shown as spectrum D. Electronic structure calculations were performed to explain the peculiarities of the spectra. The limiting case of a nanotube with infinite radius is a single slab, so slab calculations should be a reasonable estimate of the electronic structure of the nanotube. This assumption is supported by calculations for TiS2 (Ivanovskaya and Seifert, 2004; Ivanovskaya et al., 2005) showing that the density of states in various nanotubes is very similar to that of the slab. Bulk MoS2 already exhibits a layer-type structure and it showed that the difference in the density of states between slabs and bulk material is also not very pronounced. The full potential WIEN2k code (Blaha et al., 2001) was used to perform the slab calculations. The generalized gradient approximation was used for the parameterization of the exchange-correlation potential, as it accounts better for correlation compared to the pure localdensity approximation (LDA) potentials, in particular if dealing with semiconducting materials. The calculations were performed for P-3m1 symmetry and the separation between the slabs was set to 4 nm. It was tested carefully by varying the separation that the slabs are decoupled from each other. A 49 × 49 × 3 mesh, leading to 650 irreducible points in the Brillouin zone, was used for the final k-space integration. The results of the calculation are shown in Figure 54. The band structure for bulk material (not shown here) agrees with the one obtained by Coehoorn et al. (1987). The calculation reveals the slabs to be semi-conducting with a band gap of ∼1 eV, comparable to bulk material. The band structure may not be directly comparable to a nanotube as this has 1D symmetry, whereas the slab has 2D symmetry. In the limit of large-diameter tubes, however, the density of states should be comparable. The density of states may be better for comparison with the observed spectra, as it is already an integrated quantity. One possible two-photon transition at 3.1 eV is indicated in Figure 54 by arrows. The density of states exhibits a pronounced maximum at ∼1.3 eV below the valence band maximum (EVB-max ) that may serve as an initial state for the photo excitation. In that case, the maximum in the unoccupied density of states at ∼1.8 eV will serve as a very effective intermediate state for the two-photon process such that a coherent excitation is possible. This leads to much higher intensities compared to two-photon transitions through virtual intermediate states as often observed in metals with a large gap in the unoccupied part of their bandstructure (e.g., Cu, Ag, or Pt).

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F IGURE 54. Calculated bandstructure (a) and density of states (b) of a MoS2 slab. The arrows denote one possible two-photon transition induced by femtosecond-laser radiation of 3.1 eV. The shaded areas assign the ranges that are energetically allowed to take part in the two-photon excitation.

Due to the gap in the intermediate density, there are no direct transitions possible into states below 4.2 eV final-state energy. The gap in the finalstate density prevents direct transitions into states between 4.7 eV and 5.2 eV; in particular, the expected direct, high intense transition between initial and intermediate states at 5 eV would be in the final-state gap. The probability for direct transitions may be estimated from a multiplication of the density of states in the initial, intermediate, and final state and neglecting the transition matrix elements. The result is shown as spectrum E in Figure 53(b). From this probability it is seen that high intensities are expected at final-state energies of 4.5 eV and in the range of 5.2–5.4 eV. The high density in the intermediate states (1.8–2.3 eV above EVB-max ) may also serve very effectively as a base for high intense indirect transitions ending at a final-state energy ∼5.4 eV. The measured spectra reproduce the calculated probability of the direct transitions reasonably well. The energy positions of the maxima at 5.25 and 5.75 eV are slightly shifted toward the high-energy cutoff, what may arise from the influence of the substrate on the nanotube, compared with a free single nanotube. The SiOx substrate background spectrum exhibits no structures at these energies; thus the observed features originate from the nanotubes. The nanotubes in regions A and B have different sizes and their spectra, in particular the height of the low-energy peak, are different. This

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peak contains the contribution of inelastic electrons but also transitions to a low-energy peak (4.5 eV) of the calculated probability of the direct transitions. E. Time-Resolved Spin-Polarization Spectromicroscopy As long as we are interested in field-pulse induced magnetization changes, the total time resolution is limited by the characteristics of the electric pulse generator providing a maximum rise time in the order of several 10 ps. The demagnetization of magnetic materials by intense laser pulses occurs on a shorter time scale. Early experiments in the group of F. Meier at Swiss Federal Institute of Technology Zurich (ETH Zürich) showed the demagnetization on optical heating with an excimer laser (Bona et al., 1986) but did not give access to the relevant picosecond time scale. The fundamental processes that govern spin excitation dynamics happen on a femtosecond time scale. This regime is accessible by ultrashort laser pulses in a pump-probe arrangement as described in Section III.C. Magnetic sensitivity is obtained by analyzing the spin polarization of the emitted photoelectrons in the PEEM. The pioneering experiment combining magnetic sensitivity with nanometer spatial and femtosecond time resolution has been performed by Dürr et al. (2001). Figure 55 shows the first spin-polarized PEEM, a customer-modified combination of a commercial microscope and a spin-polarization detector (Focus GmbH, see http://www.focus-gmbh.com). An adjustable field aperture

F IGURE 55. Spin-polarized PEEM used for the study of femtosecond spin dynamics in ferromagnetic nanostructures. The region of interest is selected by the variable field aperture (iris). The beam is electrostatically deflected by 90 degrees and focused into a spin-polarization analyzer that detects the in-plane component of the magnetization. The out-of-plane component is measured by a second pair of detectors rotated by 90 degrees (not shown). With the 90-degrees deflector being switched off and the field aperture fully opened the investigated nanostructures can be observed in a CCD camera. The right panel shows an image of 200 nm × 200 nm squares of a CoPt multilayer taken using a Ti:sapphire laser. (From Dürr et al., 2001.)

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mounted in the first intermediate image plane allows selection of the desired micro area for spin analysis. After the micro area is defined in the image, the photoelectron beam is electrostatically deflected into the spin polarization analyzer. Spin-dependent electron diffraction from a W(100) single-crystal surface is used for polarization analysis. The scattering asymmetry in detectors 1 and 2 is proportional to the photoelectron spin polarization P that is a measure of the sample magnetization. Photoelectrons were excited using a Ti:sapphire laser system delivering pulses of 150 fs width at a repetition rate of 76 MHz and a photon energy of 3 eV (second harmonic). A typical PEEM image taken with laser radiation is shown in Figure 55 (right panel). An array of a nanostructured CoPt multilayer (200 nm×200 nm squares, separated by 100 nm wide and 200 nm deep troughs) is visible with good contrast. Although the photon energy is smaller than the work function of the sample, intense photoemission is observed due to two-photon processes. Electron emission is assisted by excitation of LSPs that are here preferably excited by s-polarized light (i.e., with the electric vector oriented parallel to the surface). The first pump-probe experiments studied the reduction of the sample magnetization upon optical heating. The measurements revealed a marked laser-induced demagnetization increasing almost linearly in the range of 0.2– 0.6 nJ pulse energy. These experiments gave first evidence of a lateral energy transport mechanism that leads to a nonlocal reduction of the magnetization: the magnetization drops in regions where the local laser intensity is strongly reduced. The novel technique allows studying the underlying process of phonon–magnon coupling with high spatial and time resolution. In conclusion, an imaging TOF electron analyzer has been implemented into the column of a PEEM. Since this type of imaging analyzer retains the linear electron optical axis, it is highly attractive in terms of minimizing aberrations. The 3D (x, y, t)-resolving delayline electron image detector yielded a time resolution of presently 100 ps that can be principally further improved. This will facilitate an energy resolution of less than 50 meV in spectroscopic full-field imaging. Its point resolution is ∼50 µm in the image plane (typical diameter 50 mm) and is thus comparable with a CCD camera. Synchrotron-radiation-excited microspectra indicate that the signalto-background ratio is very high because the background signal is very effectively suppressed by the TOF analysis. The same approach has also been applied to femtosecond-laser-induced 2PPE from nanoparticles and nanotubes. The spin-polarization analysis implemented into a PEEM can also be combined with TOF spectroscopy. The presented results for inhomogeneous films, Ag and Cu nanoparticles, and MoS2 nanotubes demonstrate that the novel TOF-based spectromicroscopic method has a high potential for the study of nano-scale materials.

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V. T OWARD A BERRATION C ORRECTION BY T IME -R ESOLVED D ETECTION AND / OR T IME -D EPENDENT F IELDS As the TOF scales with E −1/2 it offers various possibilities to increase the lateral resolution. Gated detection is equivalent to energy filtering and can improve the resolution considerably. Going one step further, a novel theoretical ansatz for correction of the chromatic and spherical aberration of round-lens systems in PEEM and LEEM is based on TOF. The method uses fast switching of electrical acceleration fields or lens fields. It exploits the highly precise time structure of pulsed photon sources such as electron storage rings for synchrotron radiation or pulsed lasers, as well as pulsed photocathodes of a LEEM. First results indicate that the new approach is a promising alternative to the implementation of multipole or mirror correctors into the electron optical column of a microscope. A. Basic Considerations: Early Approaches of High-Frequency Lenses The chromatic and spherical aberrations of round lenses are the main factors limiting resolution in electron microscopy. Astigmatism may result from misalignment or from limitations in manufacturing tolerance (e.g., a slight ellipticity of the anode bore in a tetrode objective lens) and can be compensated by electric or magnetic stigmators. Coma and field distortion are often of minor importance. In contrast to light optics the chromatic and spherical aberrations cannot be corrected by lens combinations. Independent of type and geometry of a round lens, the spherical aberration coefficient cs and the chromatic aberration coefficient cc are always positive. This fundamental property of all electron-optical round lenses is referred to as Scherzer’s theorem (Scherzer, 1936). As a consequence, the ray paths in electron microscopes are restricted by very small aperture diaphragms. Scherzer himself searched for possible ways out of this dilemma and discussed various possibilities for the correction of cs and cc (Scherzer, 1947). This subject was treated in a number of papers; for a review, see Hawkes and Kasper (1996). The preconditions for the validity of Scherzer’s theorem are as follows: round lenses, real images, static fields, no space charge, and the potential and its derivative are continuous. This list opens the way for different possibilities to circumvent the theorem. Despite numerous attempts based on different methods, only the use of multipole correctors in high-resolution TEM and in SEM was successful up until now (e.g., Haider et al., 1998). Table 3 summarizes the different methods of aberration correction in electron microscopes. In addition to multipole or mirror elements, there are other ways of circumventing the preconditions. One approach used potential

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SCHÖNHENSE ET AL . TABLE 3 P OSSIBLE A PPROACHES OF A BERRATION C ORRECTION IN E LECTRON M ICROSCOPES

Method

Correction

Precondition broken

Reference

Multipole elements

cs

Haider et al. (1998)

Electron mirrors

cc + c s

Deviation from cylindrical symmetry Virtual images

Microwave-excited lens system Grids and foils

cc + c s

Time-dependent fields

cc + c s

Potential jumps

cc

Time-dependent fields and/or detection

cs

Same

Pulsed sources, fast potential switching, inversion of energy distribution Diverging round lens

Rempfer and Mauck (1992); Rose and Preikszas (1992) e.g., Oldfield (1976); Dietrich et al. (1975) e.g., Hibino and Maruse (1976) This work

This work

The third column denotes the broken precondition of Scherzer’s theorem.

jumps induced by grids or foils in the electron path (see, e.g., Hibino and Maruse, 1976). Another possibility exists in the application of time-dependent lens fields. Several authors (e.g., Dietrich et al., 1975), discussed the approach of so-called high-frequency lenses (i.e., lenses excited by a microwave and acting as resonator). Figure 56 shows the arrangements proposed by Oldfield (1976), Scherzer (1947), and Zworykin and Hiller (1944) for spherical aberration correction. The necessary phase condition (relation between phase of the microwave and phase of the electron bunch when entering the resonator) and the transit time through the resonator play a crucial role. None of the proposals in connection with high-frequency lenses or grids or foils could be experimentally realized successfully. In third-order theory, the contributions of the axial chromatic aberration, the spherical aberration, and the diffraction term to the total resolution of a round lens are given by δc = cc αE/E,

(32)

δs = c s α 3 ,

(33)

δd = 0.61λ/α.

(34)

Here δc denotes the aberration disk of the chromatic aberration (subscripts “s” and “d” denote the spherical and diffraction terms, respectively). cc and cs are

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F IGURE 56. Old approaches of spherical aberration correction with time-dependent fields. High-frequency lenses by Scherzer (a) and Oldfield (b) and patent for dynamic correction by Zworykin (c). (From Oldfield, 1976; Scherzer, 1947; Zworykin and Hiller, 1944.)

the (axial) chromatic and spherical aberration coefficients, respectively, that depend on lens geometry and energy. The beam pencil angle α accepted by the electron-optical system is usually defined by the size of a contrast aperture in the backfocal plane of the objective lens (or a conjugate plane). As these contributions increase with α and α 3 , respectively, resolution increases with decreasing starting angle. However, at small starting angles the diffraction of the electron waves at the contrast aperture sets in, leading to a α −1 -like increase of the resolution curve toward small angles. E is the width of the electron energy distribution being centered around E; that is, E/E is the relative energy spread of the electrons passing the lens and λ is their wavelength. The resolution of cathode-lens microscopes in particular has been derived by several authors (see Chmelik et al., 1989, and Veneklasen, 1992). It is limited by the chromatic and spherical aberration of the acceleration field between sample and first electrode (extractor) and of the subsequent converging lens of the objective. Figure 57 shows the contributions of chromatic and spherical aberrations and the diffraction term for an optimized electrostatic

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F IGURE 57. (a) Lens geometry defined by sample S, extractor E, focus F, and column electrodes C. (b) Total resolution limit of an optimized electrostatic cathode lens (full curve) and its different contributions. Chromatic and spherical aberrations of the extractor field and lens are denoted by “c-ex,” “s-ex,” “c-le,” and “s-le,” respectively; the diffraction contribution is denoted by “d.” Extractor voltage 30 kV, starting energy 1.5 eV, width ±0.7 eV FWHM. (Courtesy M. Escher, Focus GmbH, see http://www.focus-gmbh.com)

tetrode cathode lens. This lens reaches a high lateral resolution despite a very low starting energy of the electrons via a high electrostatic extractor field in front of a planar sample surface (cathode). Results are given separately for the extractor field “-ex” and for the lens “-le.” The results have been obtained using a simulation program (Simion 6.0, see http://www.simion.com) for the geometry of a commercial instrument (Focus GmbH, see http://www. focus-gmbh.com). For details on this fully electrostatic emission electron microscope with low column energy being ideally suited for the concepts discussed here, see Schönhense (2001) and Schneider and Schönhense (2002).

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First, the whole tetrode lens has been simulated, then the analytically known (Bauer, 1985) contribution of the acceleration field has been subtracted to separate both contributions. The lens includes the demagnifying aperture lens given by the bore in the extractor electrode (anode). The abscissa denotes the true starting angle on the real sample surface. It corresponds to the radius of the contrast aperture plotted as the top abscissa for a starting energy of 1.5 eV. The energy width was assumed to be ±0.7 eV FWHM being typical for X-PEEM. The full curve shows the root of the squared sum of the three terms. Obviously, the leading terms limiting the resolution are the chromatic aberrations of extractor field “c-ex” and lens “c-le.” Due to the steep increase of these terms the instrument’s resolution limit of 14 nm demands a very small contrast aperture. Practically, a best resolution of about 50 nm has been reached in X-PEEM using the lens of Figure 57 and a small contrast aperture of 10 µm radius. The simple means of resolution optimization via reduction of the starting angle α to the minimum of the full curve is paid for: the intensity drops like α 2 with decreasing starting angle. The maximum starting angle at the resolution limit is only about 3 degrees, leading to a strong reduction in intensity as discussed by Anders et al. (1999). It is clear from Figure 57 that more common aperture sizes in the 40–80 µm range (which often must be used for intensity reasons) can principally yield only moderate resolutions above 100 nm. Moreover, for such large apertures the width of the electron energy distribution is usually considerably higher than ±0.7 eV, thus resulting in an additional increase of the chromatic aberration terms. In threshold excitation the energy width can be smaller, thus driving the theoretical resolution limit below 10 nm. Practically, a resolution of ≤20 nm has been reached by several groups using UV-PEEM. Let us now consider the usefulness of aberration correction for such an emission microscope, in particular for X-PEEM. This is the most popular application of cathode lens microscopy widely in use at synchrotron radiation facilities worldwide because it gives access to both chemical and magnetic contrast. The X-ray absorption near-edge structure (XANES) can be exploited as chemical fingerprint in imaging as introduced by Tonner and Harp (1988). In favorable cases, XANES-PEEM can even reveal the bonding nature of certain elements (Ziethen, 1999; Ziethen et al., 2000, 2002). XMCD provides a large magnetic contrast and gives access to the micromagnetic structure (see Section II) as well as the spin and orbital moments of ferromagnetic materials. XANES- and XMCD-PEEM require photons in the soft X-ray range, typically between 600 and 800 eV for 3d-elements. At such high photon energies the electron intensity distribution is strongly dominated by the intense signal of the low-energy secondary electrons used for image formation. Their width is typically 4–5 eV if not restricted by a contrast aperture.

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SCHÖNHENSE ET AL . TABLE 4 A BERRATION -C ORRECTED C ATHODE L ENS E LECTRON M ICROSCOPES B EING U NDER C ONSTRUCTION

Instrument

Corrector

Special features

Reference

PEEM (Arizona State University, Tempe) PEEM (University of Mainz) PEEM III (ALS, Berkeley) SMART (BESSY, Berlin) LEEM (Delong Instruments a.s., Brno) Picosecond PEEM (University of Mainz)

Electron mirror

First test operation

Rempfer et al. (1997)

Corrected multipole Wien filter Electron mirror

Linear column

Marx et al. (1997)

Synchrotron-based

Electron mirror and omega filter Electron mirror

Same, ultimate resolution 2 nm Laboratory-based

See http://www.lbl.gov Rose and Preikszas (1995) See http: //www.dicomps.com

Time-dependent lens/accelerator fields

Linear column, pulsed excitation

See this work

The spherical aberration contributions “s-ex” and “s-le” can obviously be neglected for this starting energy of 1.5 eV up to relatively large starting angles of about 20 degrees. At higher starting energies this angle reduces because the k-vector component parallel to the surface increases. This component is the relevant quantity for the abscissa of Figure 57. It is worth mentioning that even for threshold photoemission widths of the electron, energy distribution of the order of 1 eV are often met (Merkel et al., 2001), depending on work function and the spectral distribution of the mercury lamp. Hence, chromatic correction will also improve the performance of UV-PEEM. For cathode-lens microscopes electron-mirror correctors as tested by Rempfer and Mauck (1992) and Rempfer et al. (1997) are just ready to prove their capability of correcting chromatic and spherical aberrations (Rose and Preikszas, 1992, 1995). Technically, this method is very demanding. Another possibility is an imaging multipole Wien filter, the development of which was started in the Mainz group years ago (Marx et al., 1997) but was discontinued due to its complexity. Table 4 provides an overview of attempts aiming at aberration correction for cathode-lens electron microscopes. What can be expected from a chromatic correction of an X-PEEM? A complete chromatic correction would drive the theoretical resolution limit down to about 4 nm (see the full circle at 20 degrees in Figure 57). This is an improvement of a factor of 3.5 in resolution and, simultaneously, a factor of 20 in intensity. If we aim at the same resolution limit as the uncorrected instrument, we can open the angle up to almost 40 degrees (open circle) and thus gain more than a factor of 100 in image intensity. Chromatic correction

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will be particularly useful in synchrotron-radiation-excited PEEM because of the width of the secondary electron distribution. This comes along with the fact that synchrotron radiation also is naturally pulsed in the standard multibunch mode. TOF chromatic aberration correction does not require special single- or few-bunch modes. The early attempts to use high-frequency lenses for aberration correction failed because of timing problems. The crucial phase condition between the microwave-excited lens and the entry and transit time of the bunched electron beam could not be fulfilled. We present a novel theoretical ansatz exploiting time-dependent fields. The method is capable of both cc and cs correction in photoemission or low-energy electron microscopy (PEEM/LEEM) making use of the highly precise time structure of pulsed photon sources such as electron storage rings for synchrotron radiation or pulsed lasers (e.g., driving the photocathode of an LEEM; refer to Tables 1 and 2). The characteristics of state-of-the-art electronic pulsers will set a practical limit to the performance of the novel method. The developments for TEM and SEM target an ultimate resolution in the sub-Angstrom range for TEM (Rose, 1999) and 1 nm for SEM (Haider et al., 1998). The LEEM/PEEM correctors rather aim at a substantial enhancement of the imaging performance at moderate resolution in the range of a few nanometers. B. Time-of-Flight Energy Filtering The technique of time-resolved image detection is illustrated in Figure 58 for the case of X-PEEM. The TOF-spectrum (shown in image a; note the logarithmic scale) shows the typical XPS features of the microstructured FeCo sample. The right cutoff represents the Fermi edge; the high peak on the lefthand side is the secondary electron signal with the low-energy cutoff reflecting the vacuum level. The DLD acquires the 3D (x, y, t) data set simultaneously. By setting a time condition, the individual time slices can be displayed [see the image series in (b)]. The contrast aperture was fully open so that the entire energy band of 775 eV width could pass the microscope column. This leads to a dramatic change in magnification, including even a crossover. In nonenergy-filtered X-PEEM the intense signal of the secondary electrons is used for imaging. The width of the secondary electron distribution (typically 4–5 eV) can be strongly reduced by orders of magnitude if a small contrast aperture limits the angular acceptance. This aperture cuts out high-energy electrons with large k-vector components parallel to the surface. Such electrons are distributed over a large disk in the backfocal plane of the objective lens, whereas low-energy electrons exhibit small k-vector components and thus form a smaller disk. However, this low-pass filtering

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F IGURE 58. Time-resolved image detection in X-PEEM; a FeCo microstructure has been illuminated with photons of hν = 780 eV yielding electrons with a TOF (i.e., kinetic energy) distribution of 775 eV width (a). This wide energy distribution is connected with a broad TOF range. The series of time slices (b), taken at fully opened contrast aperture, reveals that this broad energy range gives rise to striking differences in magnification in the low-energy microscope (drift energy 50 eV, L = 433 mm).

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substantially reduces the image intensity because the dominating part of the energy distribution is cut off when a small aperture of radius 20 µm or less is used. This drawback is overcome by TOF energy filtering (Oelsner et al., 2004a, 2005). The individual time slices in Figure 58(b), in particular around 80 ns, exhibit a better contrast and resolution than the unfiltered sum image. A quantitative example is shown in Figure 59. At the given settings the width

F IGURE 59. Improvement of lateral resolution by time-of-flight energy filtering. The full electron energy distribution (a) leads to a rather blurred image (b), whereas the time-of-flight filtering strongly enhances contrast and resolution by cutting a narrow time slice out of the energy distribution, shown for t = 375 (c) and 150 ps (d).

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of the secondary electron peak in the spectrum (a) is 4 ns (corresponding to 4.3 eV). Here the time interval can be set right in the center of the electron energy distribution. The gray vertical bar in the spectrum denotes an interval of 150 ps (corresponding to 185 meV); the dashed lines mark 375 ps (corresponding to 400 meV). The TOF filtered images and line scans (c) and (d) reveal a substantially improved resolution and signal-to-background ratio compared with the unfiltered image (b). As shown by Nepijko et al. (2004), the lateral resolution in the TOF-PEEM can be as good as several nanometers (2–3 nm). C. Novel Concepts of Aberration Correction The time structure of pulsed photon sources such as electron storage rings or pulsed lasers is characterized by ultimate precision in terms of deviations from periodicity (jitter). Pulse widths can be as low as a few picoseconds for synchrotron radiation and several 10 fs for laser sources. When a pulsed excitation source is used in a PEEM, the photon time structure translates into corresponding parameters of the electron beam. This opens up new technical possibilities far beyond the microwave-modulated electron beam of the early days of high-frequency lenses. We describe three methods of chromatic aberration correction; they have no analog in light optics. The approach toward spherical correction resembles an optical achromat. 1. Chromatic Correction by Time-Resolved Image Detection (Picosecond Time Slicing) Similar to light optics we distinguish between the axial (or longitudinal) chromatic aberration and the lateral chromatic aberration (Hecht, 1987), also referred to as chromatic aberration of magnification (Hawkes and Kasper, 1996, p. 414), with its coefficient often denoted as ccM . The former quantifies the axial distance between two focal points corresponding to different energies; the latter quantifies the energy dependence of the transverse magnification. We cite the important conclusion: “A chromatically aberrant lens . . . will fill a volume of space with a continuum of more or less overlapping images, varying in size and colour” (Hecht, 1987). In our case, color would be replaced by electron energy or TOF; this offers fascinating ways of chromatic correction of an electron lens. A first straightforward way uses time-dependent image detection and is illustrated in Figure 60. The electron ensemble is dispersed in the low-energy drift space such that at the end of the drift space the fastest electrons travel at the front and the slowest at the end of the bunch. We take advantage of the fact that, unlike light optics where this effect is extremely small in transparent

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F IGURE 60. Chromatic aberration correction using picosecond time slicing in connection with time-dependent lens fields (a). The electron velocity distribution is dispersed in a low-energy drift tube. A time-resolving image detector divides the total image into time slices (b) that can be corrected by lateral rescaling and/or rapid lens refocusing. The series of partial images corresponding to different time slices (c) reveals a substantial lateral chromatic aberration that is visible in a blurred sum image, but disappears in the corrected sum image (i.e., the sum of the rescaled partial images). The width of the vertical bar is 5 µm.

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matter, the images corresponding to different electron energies show up at different arrival times in the sequence from fastest to slowest electrons as shown in Figure 58. At the end of the drift space the temporal dispersion t of an ensemble with drift energies between E0 − E and E0 is given by  −1/2 t = L · (me /2)1/2 (E0 − E)−1/2 − E0 . (35) The images corresponding to different electron energies can be separately collected (e.g., by a delayline detector). A fast-gated CCD camera as used in the first TOF-PEEM experiments (Spiecker et al., 1998) or other gated devices are not suited for this mode of cc correction. Here, true 3D time- and space-resolving image acquisition is mandatory. The temporal spread of the electron signal due to the finite pulse length of the excitation sources is ∼40 ps and 100 fs for the synchrotron and Ti:sapphire laser radiation, respectively. This spread is negligible compared with the relevant values of the temporal dispersion t. For typical settings and an assumed energy width of the secondary electron distribution of E = 5 eV, we obtain t ≈ 10 ns [see also the example in Figure 60(b)]. The image series of a NiFe frame shown in Figure 60 illustrates this time-slicing technique. The microstructure fabricated on a silicon substrate was imaged using X-PEEM at the Fe L3 line using the DLD counting all single-electron events into a 3D (x, y, t) memory. After finishing data acquisition, time conditions are set in the image-processing software; that is, the desired absolute arrival times with respect to the synchrotron clock and the width of the time interval (thickness of the time slices) are chosen as illustrated in Figure 60(b). At this stage, free choice of both parameters acting on the given (x, y, t) data set allows optimization of the result. We thus obtain partial images corresponding to different time of flight (i.e., to different electron energies). An example set of partial images taken at 1 ns time difference is shown in Figure 60(c) (same data set as Figure 58). Due to the lateral chromatic aberration the magnification varies with energy, in the given example by about a factor of 2 between the −2 ns and +3 ns images. To demonstrate the effect more pronounced, the lens system was operated purposely at a rather large ccM value. The sum image of all detection times is identical to the image observed by a simple fluorescent screen. Using the imaging software, each partial image is now individually scaled by the corresponding magnification factor. Finally, the rescaled images are summed again. The result is shown in the bottom right image. Clearly, resolution and contrast are markedly enhanced compared with the uncorrected sum image (Schönhense and Spiecker, 2002). This result is further quantified by extracting a series of intensity line scans across the vertical bar visible in the sequence in Figure 60(c). Narrow stripes

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F IGURE 61. Series of intensity line scans across the vertical bar in Figure 60(c) without correction (a) and after linear rescaling (b). The horizontal stripes correspond to different time slices.

across this bar are plotted for all time slices in Figure 61. Before correction [image (a)] the bar appears in the different partial images with different magnifications. However, after rescaling the differences in the width of the bar have almost disappeared (b). In this example, relatively thick (1 ns) time slices have been defined for sake of clarity. For an optimum result the individual time slices would be chosen close to the resolution limit (e.g., 100 ps). In addition, nonlinear scaling will account for the specific lens characteristics. In the example shown in Figure 60, the electron optics of the microscope was kept static during image acquisition. Consequently, the images corresponding to energies away from the center energy (0 ns image) are not exactly in focus. This is a consequence of the axial chromatic aberration (Hecht, 1987, p. 233). At higher magnification this effect becomes more pronounced. This approach of cc correction can thus be substantially improved by actively varying the excitation of part of the lens system [e.g., of a projector lens; see Figure 60(a)] synchronized with the actual energy of the electrons arriving at the lens after having passed the low-energy drift space. A timedependent lens voltage U (t) is applied to one or several lenses behind the drift space. The lens field is varied synchronously with the pulsed signal such that for all electrons of different energies, arriving one after the other, the image remains in focus. Thus, all different time slices of the total image signal experience their individual optimized lens settings. If a single-lens potential is varied, the partial images exhibit the chromatic aberration of magnification (i.e., an energy-dependent magnification). Using the DLD allows the same type of correction as described above. The partial images corresponding to different arrival times can be individually rescaled after image acquisition and can finally be summed. Using pulsed zoom optics, where several lens potentials are varied, even the magnification can be kept constant. In this case, no time-resolved detection is needed. In the same way, an energydependent image shift or rotation (e.g., resulting from magnetic lenses) can be compensated by the image-processing software. Because all partial images are summed, picosecond time slicing is a true correction method that exceeds the imaging TOF filter that selects just one

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time slice as described in the previous section. It should be mentioned that the gain in image quality in the example image shown in Figure 60 is solely due to the software-assisted rescaling of partial images after 3D (x, y, t)-resolved image detection and time slicing. Generally the lens voltages must be varied nonlinearly with time. Proper focusing for all electron energies (arriving one after the other) is achieved by matching with the temporal dispersion of the electron ensemble in the drift space. In order to correct for both the axial and transversal chromatic aberration, several lens voltages must be varied synchronously with a nonlinear slope; this approach is rather demanding but technically possible. Nevertheless, it seems worthwhile to explore a different, easier approach as described in the next section. 2. Inversion of Electron Energy Distribution Owing to the charge of the electrons it is possible to manipulate their energy distribution by means of a pulsed electric field. In particular, it is possible to invert the electron energy distribution by means of a suitable pulsed accelerator (Schönhense and Spiecker, 2002, 2004). Electrons arriving with the smallest kinetic energy at the entrance of the pulsed accelerator will end up with the highest energy after inversion. Obviously, there is no light-optical analog of this approach. An electron-optical realization of this type of chromatic corrector is schematically sketched in Figure 62(a). The electrons starting from the sample pass a lens system 1, a low-energy drift space, the accelerator, a lens system 2, and finally are focused on the image detector. A pulsed acceleration field Facc (t) is applied to the electron ensemble after spatial dispersion in the drift tube. The energy gain of each electron in the accelerator depends on its position when switching on the field. A parabolic acceleration field then leads to an inversion of the electron energy distribution behind the accelerator. Schematic TOF spectra of the imaged electrons at low kinetic energies before (Iin ) and after inversion (Iout ) are shown in image (b). The formerly slowest electrons have now become the fastest electrons. The second lens system acts on the inverted ensemble and thus apparently has a negative cc [refer to Eq. (32)]. This lens system must be designed such that its chromatic aberration compensates the aberration of the first lens system. The temporal action on an ensemble with initial energies between E1 > E2 is shown in images (c–e). The voltage is switched on when the ensemble lies completely in the accelerator (d). Behind the accelerator the ensemble is inverted; that is, E1 > E3 (e). The operation of this device can be illustrated best in terms of an energyversus-z diagram (z is the path along the optical axis) as shown in Figure 63.

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F IGURE 62. Chromatic correction based on inversion of the electron energy distribution. (a) Schematic cross section of the electron-optical system. The radial beam size is strongly exaggerated; only α-rays are shown. (b) Electron energy distributions (schematic) before and after passing the accelerator, denoted by Iin and Iout , respectively. (c–e) Snapshots of an electron ensemble traveling through the accelerator. The initial distribution (c) is changed by fast switching of the accelerating voltage U (t) when the ensemble has entered the accelerator (d). This rises the energy E2 < E1 of the formerly slowest electrons to E3 < E1 (e).

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F IGURE 63. Electron energy distribution as a function of the optical path z. Ekin denotes the actual kinetic energy of the electron ensemble. The Ekin -versus-z distributions before and after passing the pulsed acceleration field are denoted by in and out, respectively.

Owing to the pulsed excitation the electron ensemble (denoted by the black area) starts at the sample surface with a certain energy Es and width E and a certain distribution along z determined by the pulse duration and initial velocity. The strong homogeneous extractor field and lens optics of the objective accelerates and transports the ensemble without significantly changing its shape. When passing the drift space, however, the distribution is expanded along z in the way that the fastest electrons (energy E0 ) gain distance from the slower electrons. This expansion is linear in electron velocity (i.e., parabolic in electron energy). When the ensemble has entered the accelerator (distribution denoted “in”), the energy distribution E is reflected by a corresponding spatial distribution z given by 1/2   , (36) z = L · 1 − (E0 − E)/E0 with L representing the total length of the drift space. When the fastest electrons (energy E0 ) reach the exit electrode of the accelerator, the electric acceleration field Facc is switched on rapidly. The slowest electrons (energy E0 − E) at a distance of z behind experience the action of Facc during their way through the accelerator. Their energy gain is eFacc z. In the example drawn in Figure 63, they gain 2E (which is no necessary condition), so that their final energy after passing the accelerator is E0 + E. Analogously, all other electrons experience an energy gain that is defined by their local potential at the moment when Facc is switched on. If Facc increases linearly (i.e., the local potential of the acceleration field increases quadratically along z), the energy distribution is inverted after all electrons have passed the accelerator (new distribution denoted by “out”).

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Such a parabolic potential can be defined by suitable fringe-field electrodes. Numerical simulation revealed that under typical conditions (drift energy E0 = 100 eV, width E = 5 eV) a linear potential increase is a very good approximation. The curvature in this short parabola section causes a deviation of only less than 1% if 10 equally spaced fringe-field electrodes are used. In the schematic view of Figure 62(a) the electron beam is almost parallel to the electron-optical axis it passes the drift space. However, in practice, deviations from this idealized geometry occur and could even be advantageous. In addition, the spatial structure of the acceleration field could be designed in a special way to achieve an additional lens action or beam shaping. Instead of a rapid rise of Facc , the field could be increased with a welldefined nonlinear slope to achieve the desired action on electron energy and momentum distribution. Finally, lens system 2 focuses the electron ensemble onto the image detector (e.g., a fluorescent screen). This lens system has a chromatic aberration of the usual way: slower electrons are focused more strongly. However, this aberration now acts on the inverted energy distribution as indicated by the solid and dashed rays in Figure 62(a) denoting the fastest and slowest electrons, respectively. Electrons corresponding to E0 are underfocused by lens system 1 but overfocused by lens system 2 since they are the slowest electrons after the inversion. Thus, the second lens system in combination with the pulsed accelerator can be considered to have a negative cc with respect to the initial energy distribution. Given an ideal matching of the quantitative chromatic aberrations of both lens systems and the slope induced in the E-versus-z diagram by the acceleration field, the total chromatic aberration [being linear in E; see Eq. (32)] can be completely compensated. With the accelerator switched off, lens system 2 would again overfocus the slowest electrons. This would result in a total axial chromatic aberration, as shown by the dotted trajectories in Figure 62(a). Trajectory calculations revealed that a cc -corrected cathode-lens microscope is technically feasible. Figure 64 shows two preferred operation modes. Lens system 1 was modeled as an electrostatic tetrode objective lens Ob (magnification only M = 20 in the first intermediate image I1 ), followed by an immersion lens (asymmetric einzel lens) operated as transfer lens T1 forming the parallel beam at low energy (typically 80 eV) that is injected into the drift space D, at the end of which the accelerator A is located. Lens system 2 consists of a second, almost identical transfer lens T2 with reversed order of the lens potentials. This lens forms the second intermediate image I2 . Subsequently, a projector lens P1 (or several lenses) yield the final magnification and facilitate the compensation of field aberrations in the final image I3 . One important question was: To what extent do the low-energy drift region and its adjacent optics deteriorate the spherical aberration of

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F IGURE 64. Electron trajectories calculated for two different settings of a pulsed accelerator and its entrance and exit optics, simulation with the Simion 6.0 program (SIMION). The crossover lies either in the center of the accelerator (a, symmetric geometry with minimum aberrations) or at the end of the accelerator (b, asymmetric geometry with smallest angular divergence). Radial beam size is strongly exaggerated.

the total system? One fact is known from Gaussian dioptrics. A completely symmetric arrangement (i.e., a telescopic beam between two identical lenses) causes practically no additional cs contribution owing to symmetry. This rule obviously also holds for immersion lenses, as we have confirmed in the simulation. The spherical aberration disk of the first intermediate image was exactly reproduced in the second intermediate image in case (a). However, another aspect is important for the aberration-free operation of the pulsed accelerator. The above condition holds for the case of a parallel beam of the α-rays—rays starting on the axis at an angle α such as those shown in Figure 62(a). In the geometry of Figure 64(a) the field-rays (πrays) starting off-axis with α = 0 pass the drift section at an angle defined by their initial off-axis distance and the focal length of the first immersion lens. For large FOV this angle becomes significantly large so that the π trajectories could be distorted by the accelerator field. A better solution than a parallel bundle of α-rays in the drift region would be a weakly divergent α-bundle. This, in turn, reduces the maximum angle of the π -rays. In the “optimized angle case” (b) the angles of α- and π -rays with respect to the optical axis are both less than 10−3 (for 20 µm FOV). This is sufficiently small to avoid additional aberrations caused by the pulsed accelerator. The

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above-mentioned condition for cs does not hold for this asymmetric case and consequently the total spherical aberration somewhat increases. For a starting energy of 1.5 eV and as much as ±20-degree acceptance angle we derive an increase of the spherical aberration disk from 10.6 nm in the first intermediate image to 12.1 nm in the second intermediate image (both values referring to sample coordinates, i.e., M = 1). The pulsed accelerator causes no detectable aberrations up to more than 20 V accelerating voltage (i.e., much more than necessary). For the case of X-PEEM, a perfect cc -correction would improve the total resolution by about one order of magnitude at these settings. Note that typical energy widths in X-PEEM exceed the value of ±0.7 eV assumed in Figure 57. It should be mentioned that the proposed device is a true chromatic corrector: it retains the full electron energy distribution for image formation. This is in contrast to the TOF filter described in Section V.B where only part of the energy distribution is selected via time slicing. In view of the strong intensity decrease imposed by the small contrast apertures necessary for standard high-resolution PEEM, we expect a very high gain in intensity when operating the corrector. Provided an ideal field arrangement and timing, cc can be completely compensated and the resolution limit thus driven into the range of a few nanometers at acceptance angles as high as 20-degrees (see remaining spherical contributions “s-ex” and “s-le” and open circle in Figure 57). 3. Correction of Spherical Aberration by Diverging Round Lenses with Negative cs This method of aberration correction resembles the approach used in light optics—combining converging and diverging round lenses with different signs of cs (and cc ). The operation principle of the spherical corrector is illustrated in Figure 65. The basic idea can be demonstrated already for a simple two-element lens, although in practice more flexible lens designs would be used. Regardless of its operation in the accelerating or retarding mode, a static round lens is always converging and cs is always positive in accordance with Scherzer’s theorem. The electron trajectories for the retarding case are illustrated in Figure 65(a). The converging action can be easily understood if the radial force component is plotted as function of z [lower part of image (a)]. Owing to symmetry, the force is antisymmetric with respect to the center plane. However, since the electron velocity is smaller on the right-hand side, the electrons stay longer in this region with negative radial force and thus they are deflected toward the electron-optical axis. The spherical aberration causes the outer rays to be overfocused compared with the paraxial rays, yielding a spherically aberrant image with positive cs .

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F IGURE 65. Diverging round lens with negative spherical aberration coefficient cs ; trajectories are simulated, radial beam size is strongly exaggerated; only α-rays are shown. (a) Static action of a retarding two-element lens with corresponding radial force component versus z. (b) Diverging round lens realized by instantaneous switching of the second element when the electron ensemble has reached plane M. The radial force distribution experienced by the electron ensemble when passing through the lens is purely positive (i.e., diverging).

A diverging action can be realized when the lens field is switched off instantaneously when the electron ensemble reaches the symmetry plane M. The resulting trajectories and corresponding radial force are shown in Figure 65(b). Since the converging part of the radial force now is switched off, only the diverging part remains. Completely analogous to light optics the lens generates a virtual image and the outer rays are deflected too strongly, resulting in a negative cs . Very short switching times are mandatory for this type of corrector. For rapidly switched electrostatic lenses an additional lens action arises as a consequence of the induced magnetic ring field. We have quantitatively derived this influence on the basis of Maxwell’s equation curl B = dE/dt. For typical switching times with voltage gradients ∼1000 V/ns and typical lens geometries this lens action can be neglected in comparison with the electrostatic lens action. As the electrons travel in the lens field when the voltage is switched, the finite rise time or a jitter of the pulser and a temporal spread of the electron signal can cause an undesired energy broadening. This, in turn, increases the chromatic aberration of the subsequent electron lenses. Simulations revealed that other types of lenses may be superior to the simple two-element lens shown in Figure 65. One possibility is to switch to an aperture lens, which is divergent even in the static case (see Hawkes and Kasper, 1996, section 35.2.1). The field strength in the symmetry plane of the lens is the crucial parameter that quantifies the energy broadening. This parameter can be minimized for specially designed einzel lenses (consisting of three elements). Of course, an easy way is to increase the physical dimensions of the lens,

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F IGURE 66. Schematic example of a spherical-aberration-corrected three-element lens with switched central element. In the pulsed operation mode the spherical aberration is corrected, whereas the static lens is strongly aberrant.

but there are limitations for an electron microscope. The negative aberration coefficient of the corrector lens must compensate the positive coefficients of all other lenses. Hence, it requires a rather large cs value because the terms in the equation for the total spherical aberration are weighted by the factor M −4 (see example in the following Section). Of note, unlike multipole correctors, this approach is capable of correcting higher-order aberrations. Consequently, it can work up to very high filling factors of the lens. In addition to electron microscopy, this may be an important advantage also for other purposes such as electron and ion projection systems or general transport optics for charged particles. Furthermore, the switched lens field also inverts cc in the same way as an optical achromat. Quantitative optimizations based on computer simulations are desirable. A possible realization of a corrected three-element lens (asymmetric einzel lens) is shown in Figure 66 (trajectories schematic). In this example, the first two elements act as a retarding lens as in Figure 65. At the moment when the electron ensemble reaches plane M, the center element is instantaneously switched to a smaller (i.e., more negative) potential. This results in an acceleration of the electrons when they enter element 3 and, in turn, in a diverging force action. Provided instantaneous switching, correct timing, and a negligible distribution z of the electron ensemble along z, all electrons can be exactly focused to the image plane (denoted as corrected image in Figure 66). Without correction the spherical aberration blurs the image as indicated schematically by the dashed trajectories intersecting the optical axis in different planes (indicated as static image). 4. Quantitative Estimations Two practical cases are presented in this Section to estimate the conditions for cs -correction reached with state-of-the-art electrical pulsers. Synchrotron radiation is characterized by a repetition rate of 5–500 MHz depending on

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operation mode, and a pulse duration τ of typically 40 ps (3 ps in the special low-α mode). Ti:sapphire laser radiation is characterized by 80 MHz and a τ of typically 100 fs. When voltages must be switched rapidly the pulser also needs to be operated at this frequency. The sources deliver trigger signals for the synchronization with the electrical pulsers. Fine adjustment is facilitated by means of variable delays with picosecond precision. The high repetition rates in the megahertz region guarantee that space charge effect similar to the Boersch effect (Boersch, 1942) can be completely neglected because at typical conditions only 1–100 electrons are emitted per photon pulse in the entire FOV. Present-day pulsers are limited in voltage to a few 10 V for rise times down to 80 ps and higher voltages up to several 100 V for rise times of the order of 500 ps. Due to these limiting voltage amplitudes the corrector elements must be operated at beam energies of the order of 1 keV or less. The limitation of pulse height and rise time is essentially due to the very high peak currents resulting from the capacitance of the switched element and its electrical leads and connectors. In the future, there is potential for further improvement of the performance of pulsers. The spread of the electron ensemble along z depends on the pulse duration τ and the actual kinetic energy Ekin according to z = τ · (2Ekin /me )1/2 .

(37)

For an injection into the corrector at Ekin = 1 keV we find a spread of the ensemble of z = 0.76 mm in normal mode (60 µm in low-α mode) or z = 1.9 µm for excitation with synchrotron radiation or the Ti:sapphire laser, respectively. For 100 eV injection energy these quantities reduce to z = 0.24 mm (16 µm) or 0.6 µm, respectively. As the electrons travel in the lens field when the voltage is switched, this spread along z will produce an undesired energy broadening of the beam. This, in turn, increases the chromatic aberration of the subsequent electron lenses. For a realistic corrector lens the latter values translate into an additional energy spread of E(z) = 10.1 eV (0.1 eV) or 0.03 eV, respectively. The value for synchrotron radiation in normal operation mode seems critical because it is higher than the initial energy width. It must be remembered, however, that the chromatic aberration contribution of each lens is weighted with M −2 with M being the magnification of the preceding optics. Assuming a rise time of 100 ps of the electric pulser, the electron path length during the rise time is 1.9 mm (0.6 mm) at 1 keV (100 eV). In the limit of vanishing initial spread z = 0 the field change during this path length acts on all electrons of the ensemble in the same way. So the rise time does not increase the energy width as long as there is negligible jitter. In practice, the jitter can be reduced to a few picoseconds. For the operation of the chromatic corrector this path length during rise time is also of minor importance, because

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the rising speed and temporal profile of the pulsed voltage acts on all electrons of the ensemble in the same way. Small lens energies are advantageous 1/2 because the path length decreases with Ekin . However, very low energies may cause troublesome influences such as sensitivity to stray magnetic fields. As a realistic example we consider the correction of the spherical aberration of the cathode lens of an emission microscope. For an optimized geometry the spherical aberration coefficient of such an objective lens is of the order of csob = 250 mm. Taking into account the magnification Mob of the objective lens, the total spherical aberration is determined by the coefficient ges

cs

4 = csob + csK /Mob ,

(38)

where csK is the spherical aberration coefficient of the corrector lens and Mob is the lateral magnification of the objective lens, typically between 10 and 40. ges 4 . For a twoThe total coefficient cs disappears, if csK = −250 mm · Mob element lens as shown in Figure 65 we obtain for a given potential ratio of V2 /V1 = 2.6 an aberration coefficient of csK = 3.4 × 105 mm, according to Harting and Read (1976). With these given parameters the spherical aberration is corrected when we additionally fulfill the condition of a total magnification of objective and corrector of Mtot = 12.2 as a reasonable value for emission microscopes. The quality of the electrical pulser required must be very high (i.e., a very fast rise time and a small jitter in the range of a few picoseconds). It is advantageous if cs - and cc -correction can be performed by subsequent, independent optimization steps. The cs -corrector lens must be located immediately behind the objective lens to retain the minimum spatial and temporal dispersion. The cc -corrector requires TOF dispersion; it therefore must be placed behind the drift space. Thus, both correctors can be optimized largely independent of each other. When excitation sources with repetition rates in the range of several megahertz are used, space-charge effects can be neglected because the average number of photoelectrons per photon pulse is less than one up to a few hundred in the entire FOV. Space charge can lead to serious image blur for sources with low repetition rates as we have found in PEEM using a laserinduced plasma-based EUV source. Because of their lower velocity, ion beams can be corrected much easier and at higher drift energies. The spatial resolution in ion probes and ion imaging and projection systems is usually chromatically limited. Thus, the described methods of aberration correction are expected to be very effective for ion1/2 beam optics. Since the temporal dispersion scales with me [see Eq. (35)], the timing is much less critical for ion beams. A spherical corrector for imaging of pulsed ion beams, ion projector systems, or ion microprobes is thus feasible using state-of-the-art pulsers.

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Although not all technical difficulties of both methods have been encountered yet, we can compare the approach outlined above with the mirror corrector. Both approaches are capable of spherical and chromatic correction and are particularly useful for low-energy microscopes (i.e., PEEM and LEEM). The main advantage of the mirror corrector is that it is fixed. The optical setup is quite complex because it requires a magnetic sector field as beam separator. This results in a nonlinear optical axis. The necessary static power supplies are state of the art. The main advantage of the timevarying potential method is that the optics itself is very simple and retains a linear column. However, the demands on the voltage pulsers (rise time, jitter) are very stringent. For the design of an “optimum” spherical corrector they probably exceed the performance of the best present-day pulsers. The electron beam needs to be pulsed, which is always the case in synchrotron- and laserexcited PEEM but not in LEEM, where a pulsed photocathode (like those used in spin-polarized LEEM) would be required. For practical use the number of adjustable parameters is an important issue. A tetrode mirror corrector has four adjustable potentials plus two for the sector field (one for the sector itself and one for the fringe-field correction; Rose and Preikszas, 1992). The electron-optical system may require further correction elements. Pulsed spherical and chromatic correction require (at least) two pulsers, each characterized by its amplitude and phase (i.e., switching time with respect to the beam clock). This makes a total of four parameters plus the (standard) linear optics. Both aberrations can be adjusted independently provided the cc -corrector causes only a small additional cs (depending on the field of view) and the additional energy spread induced by the cs -corrector is negligible. Once pulsers with the required performance become available, this method seems to be less demanding with respect to adjustment as long as we aim at a resolution limit of several nanometers.

VI. C ONCLUSIONS AND O UTLOOK Time-resolved PEEM has a broad range of applications from real-time observation of dynamic phenomena at surfaces and transient states to TOF spectromicroscopy and even aberration correction by opening a way to circumvent one of the preconditions of Scherzer’s theorem. Among the first category are magnetic switching phenomena in the sub-nanosecond range, which is attractive for advanced magnetic memory elements or future spin logic devices. On an even shorter time scale effects of spin dynamics and various transient electronic states down to the femtosecond range are accessible. In addition, the dynamics of photochemistry and other photoninduced processes can be studied. For example, the observation of laserinduced surface melting and recrystallization has recently been observed. This

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review has provided examples from areas as different as the femtosecond carrier dynamics in semiconductors and metals, the spatiotemporal nature of resonant plasmon excitations in nanoscale metal objects, or the subnanosecond dynamics of ultrafast remagnetization processes. Section II reviewed recent experiments on magnetization dynamics using time-resolved photoelectron X-ray photoelectron microscopy. Typical devices such as magnetic random access memories, magnetic sensors, or spintronic elements pose a high challenge on simultaneous spatial resolution and time resolution. We showed by several experimental examples that PEEM is capable of fulfilling these requirements. Experimental techniques specific to the PEEM approach are explained in detail. In a typical experiment dynamic series of domain patterns with variable delay between field pulse and photon pulse (synchrotron radiation) were taken using stroboscopic XMCD-PEEM. In this mode only periodic magnetization processes can be probed easily, while irreversible effects lead to homogeneous blurring of the images. The angular momentum related to the magnetic moment leads to a precessional torque on the magnetization when it is exposed to fast changes of the external field. This in turn causes unexpected dynamic response phenomena. The response on fast magnetic field pulses leads to the excitation of magnetic eigenmodes and to short-lived domain patterns that do not occur in quasi-static magnetization reversal. Such transient spatiotemporal patterns and particular detail features in the patterns are discussed. Examples are presented for ferromagnetic platelets of various shapes and sizes. An important feature is the action of the demagnetizing field that develops via the damped precessional motion of the magnetization on the nanosecond time scale. The typical lengths of 50–100 ps of the standard synchrotron modes proved sufficient to answer many important questions. More recently, time resolution of these experiments could be dramatically improved to below 20 ps. Very short probe-pulses down to a length of t ≈ 3 ps (root mean square) were achieved in the novel low-α operation mode at BESSY in Berlin. Using synchrotron radiation as high-speed probe, fast magnetization processes such as domain wall oscillation in the frequency range of several gigahertz have been observed. Snapshots of the dynamic response of the magnetic domain structure as a function of delay time with increments of a few picoseconds became possible. In addition to gigahertz oscillations of domains we observed rapid switching with wall speeds of several 1000 m/s, coherent and incoherent magnetization rotation, as well as the fast formation of striped domain patterns. The topical experimental results reviewed here represent the first steps into a new understanding of magnetodynamic processes. Several problems accessible to time-resolved XMCD-PEEM questions have not yet been addressed.

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Element selectivity is most easily obtained exploiting the fingerprint-like X-ray absorption edges. The XANES yields information on the chemical state of the elements. The low-energy electrons provide a probing depth that can exceed 10 nm, depending on the material. Thus, the magnetic layer buried underneath a protective coating several nanometers, thickness can be studied with high lateral resolution and good SNR. Magnetic sensitivity is obtained via XMCD and XMLD giving access to ferromagnetic and antiferromagnetic structures, respectively. The method is therefore ideally suited for the investigation novel materials for spintronics applications such as the Heusler compounds (Elmers et al., 2003; Felser et al., 2003). The fundamental spin dynamics happens on the femtosecond time scale. This time domain is accessible using pulsed lasers (e.g., the Ti:sapphire laser capable at photon pulses below 100 fs width). A novel approach by Dürr et al. (2001) combines a femtosecond-laser-excited PEEM with an electron spin polarization detector in a customer-modified commercial instrument. In the first experiments 200 nm × 200 nm dots of a CoPt multilayer have been studied using the spin-polarization signal as magnetic probe. The pioneering experiment shows the potential of the method for probing electronic and spinrelaxation and transport processes in magnetic materials. For a microscopic understanding of the energy transfer between electrons, spins, phonons, and magnons a very high time resolution is mandatory because the nonequilibrium electron distribution assumes thermal equilibrium within several 100 fs. The main limitation of present-day instruments is the lateral resolution, which is restricted to typically 100 nm in synchrotron-radiation based experiments due to the chromatic aberration of the microscope optics. The base resolution below 20 nm can only be reached in threshold excitation (UVPEEM) owing to the narrow energy distribution. There are a few concepts of aberration correction in photoemission electron microscopes driving the resolution to a few nanometers. A novel approach was outlined in Section V that uses the highly precise time structure of synchrotron radiation. To overcome the limited beamtime and experimental effort for synchrotronbased experiments we propose the use of LEEM (Bauer et al., 2002) providing an even better spatial resolution of <10 nm. For magnetic contrast the magnetization dependence of the backscattering cross section of spin-polarized low-energy electrons is exploited. At low energy the reflectivity of electrons is very high (up to 50%). The spin-dependent part of the reflectivity is proportional to the relative orientation of spin polarization and magnetization. The asymmetry can be quite large (i.e., 30% and more for Co/W(110); Duden and Bauer, 1996). Spin-polarized LEEM is a favorable method to detect relations between microcrystalline and micromagnetic structures (Duden et al., 2001) since one can easily switch between imaging and diffractional mode. Time resolution is implemented by a pulsed electron beam. A GaAs photoemitter

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is used as an electron source for a pulsed and spin-polarized electron beam. Novel strained-layer photocathodes show an increased polarization of up to 80% of the emitted electrons (Aulenbacher et al., 1997, 1999, 2002, 2005) and a pulse width as short as <20 ps. The remaining part of the experiment is similar to the method described in Section II.B. Single-crystalline thin films of Co(0001) on Mo(110) microstrip lines have been successfully prepared (Valdaitsev et al., 2005). Section III discussed recent experiments that probed short-lived electronic states using time-resolved PEEM. In single-shot experiments using a pulsed Nd:YAG laser for excitation and an excimer laser for probing, structural transitions such as surface melting or the dynamics of thermionic electron emission could be observed by Bostanjoglo et al. (2000) and Schäfer et al. (1994). In a pioneering experiment by Sedov and Zlobin (1974) the propagation of electrical pulses in a p–n junction could be detected combining PEEM with a streak camera-like device. The optical near fields of LSPs could be visualized using femtosecond-laser radiation exploiting 2PPE in PEEM. A two-photon pump-probe arrangement was used to obtain electron lifetime contrast in the femtosecond range. Interferometric time-resolved PEEM in a similar arrangement allowed observation of the phase lag of the plasmon eigenoscillation in relation to the phase of the exciting light wave. The latter experiment set a milestone in time precision: the all-optical approach by Petek and coworkers (Kubo et al., 2005) is characterized by a time precision of 50 attoseconds. It must be kept in mind, however, that this value is the interferometric resolution. In phase-averaged experiments the time resolution is of the order of the pulse length, that is, ≥10 fs (Schmidt et al., 2002). In Section IV we demonstrated the performance of an imaging TOF electron energy analyzer implemented into the column of a PEEM. Since this type of analyzer retains the linear electron optical axis, it is highly attractive in terms of minimizing aberrations. Two different ways of time-resolved detection have been explored—the first uses an ultrafast CCD camera and the second uses a 3D (x, y, t)-resolving single-electron counting detector (e.g., DLD). The time resolution of the first approach was limited to ∼2 ns due to the decay time of the scintillator screen. The DLD yielded a time resolution of presently 100 ps that can be principally further improved. This will facilitate an energy resolution of less than 50 meV in spectroscopic full-field imaging (150 meV has been reached). Its point resolution is ∼50 µm in the image plane (typical diameter 50 mm) and is thus comparable with a CCD camera. Measurements with synchrotron radiation proved the spectromicroscopic possibilities of TOF-PEEM, although no systematic studies exist up until now. The first results indicate that the signal-to-background ratio in the microspectra is very high because the background signal is very effectively suppressed by the TOF analysis. The same approach has also been very

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successfully applied to femtosecond-laser-induced electron emission from Ag nanoparticle films, from hot spots (i.e., spots of very high electron emission yield) on Cu and from single, size-selected MoS2 nanotubes. In these experiments the phototransition was induced using a frequency-doubled Ti:sapphire laser at a photon energy of 3.1 eV. The formation of granular metal films (cluster films) led to an enormous enhancement of the electron emission yield. TOF (i.e., kinetic) energy distributions of the electrons emitted from such films have been registered using the delayline detector. In particular for Ag films, essential differences between the spectrum corresponding to 2PPE from a continuous film (being well-known from literature) and the spectra obtained from the Ag nanoparticle films have been found. The results reveal details of the electron emission dynamics from nanoparticles, in particular when LSPs are excited. The nanotube spectra reveal an unexpected high intensity compared with the Si substrate surface, whereas they looked dark on VUV excitation using a He lamp. The enhancement is caused by a 2PPE transition via a real intermediate state as revealed by a bandstructure calculation. The presented results for inhomogeneous films, Ag and Cu nanoparticles, and MoS2 nanotubes demonstrate that the novel TOF-based spectromicroscopic method (TOF-PEEM) has a high potential for the study of nano-scale materials. A particular challenge will be the study of transient electronic states in pump-probe experiments. Two full-field imaging pumpprobe experiments (without energy filtering) have recently been successfully performed as described in Section III. In the near future it will be possible to combine this optical pump-and-probe approach with TOF energy analysis. This combination will facilitate spectroscopic investigations in the context of adsorption and desorption kinetics (Dunin von Przychowski et al., 2003, 2004), chemical reaction fronts (Mundschau et al., 1990) or the ferroelectric electron emission (Klais et al., 2004, 2005) and its intrinsic time structure. The spin-polarization analysis implemented into a PEEM can also be combined with TOF spectroscopy. Trajectory calculations have shown that the scattering process in the spin detector does not limit the time resolution. In a gasphase experiment, a TOF-based spin-polarization detector (without spatial resolution) has been operated successfully (Snell et al., 1999, 2001). Section V presented novel approaches toward “old” ideas of chromatic and spherical aberration correction of round-lens systems in electron microscopes that require pulsed electron beams. The methods are based on fast switching of electrical acceleration or lens fields and/or time-resolved image detection. The cs -corrector exploits the TOF of electrons with different energies in a drift space. The spatial and temporal dispersions at the end of the drift space facilitate three correction methods. The straightforward way is to actively vary the excitation of the lens system behind the drift space synchronized with the

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photon source such that for all electron energies (arriving one after the other) proper focusing is achieved. As a second technique, time-resolved image detection in connection with numerical image processing can compensate energy-dependent image magnification (i.e., the lateral chromatic aberration), as well as image rotation or shift. A first experimental example has been shown. The third method is to introduce a switchable acceleration field behind the drift space that inverts the energy distribution of the electrons forming the image. As the chromatic aberration is proportional to E, this effect directly inverts the chromatic aberration of the subsequent lens system. Proper design of accelerator and lens parameters can thus lead to a cancellation of the positive and negative cc values corresponding to the lens optics before and behind the accelerator, respectively. Previously, TOF energy filtering has demonstrated to gain a substantial increase of resolution and contrast in synchrotron-based PEEM. Unlike these methods of cc -correction that have no analog in photon optics, the cs -corrector resembles an optical achromat. It makes use of the fact that time-dependent fields open ways of realizing a diverging lens with an inverted cs (and also an inverted cc ) in its virtual image. One possibility is to rapidly switch off the lens field as soon as the electrons enter the region with negative radial force component (i.e., the converging part of the field). Experimentally, this requires a very fast rise time of the switch because otherwise the energy distribution will be broadened and, in turn, chromatic aberration increases. Quantitative estimations of realistic examples on the basis of state-of-theart electronic pulsers reveal that cc -correction is feasible today. However, cs -correction is a challenge for the capability of electric pulsers which presently are limited in rise time to about 80 ps. Especially in synchrotronradiation-excited X-PEEM, which is used by many groups worldwide, the chromatic aberration of the extractor field and objective lens are the dominating contributions limiting lateral resolution. Thus cc -correction by pulsed electric fields synchronized with the photon pulses of the synchrotron is expected to yield a considerable gain in intensity and lateral resolution, especially in X-PEEM in the near future. The electron-optical simulation and construction of a chromatically corrected PEEM is in progress. TOF-based aberration correction is also of interest for imaging of pulsed ion beams. Ion optics is currently attracting much interest in the context of ion projector systems for lithography, ion microprobes, and ion milling. These systems are chromatically resolution limited, so especially cc -correction would be very effective. Because of their lower velocities the TOF handling of ion beams is much easier compared with electrons. Therefore, even cs -correction is technically feasible with present fast pulsers provided a sufficiently good time structure of the ion beam.

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For electron-beam projection lithography and for future mask- and waferinspection systems based on cathode-lens-type instruments, the desired fieldof-illumination (or FOV) is very large. This may cause significant field aberrations that must be carefully avoided in lithography. An investigation of the question of whether such aberrations such as image curvature and pincushion- or barrel-type distortions can be corrected by the pulsed-potential method would be highly desirable.

ACKNOWLEDGMENTS We thank A. Oelsner (Surface Concept GmbH), A. Krasyuk, F. Wegelin, D. Neeb, M. Cinchetti, A. Gloskovskii, D. Valdaitsev, Ch. Ziethen, and G.H. Fecher (University of Mainz), and A. Kuksov and D. Bedau (Forschungszentrum Jülich) for their participation in the experiments. Special thanks are due to H. Dürr (BESSY, Berlin) for providing the data in Section IV.E; to H. Petek (Pittsburg) for providing the data in Section III.E; to J. Raabe (SLS, Villigen) and A. Scholl (ALS, Berkeley) for providing the data in Sections II.C.2 and II.C.5; and to M. Escher (Focus GmbH) for providing the data for Figure 57. G.S. would like to thank H. Rose (University of Darmstadt) and R. Tromp (IBM, Yorktown Hights) for fruitful discussions on aberration correction and H. Spiecker (LaVision Biotec) for his important contributions during the early phase of the TOF-PEEM development. We are grateful to the staffs of BESSY (Berlin) and ESRF (Grenoble) for excellent support of our experiments. The various projects were funded by BMBF (Fkz 05 KS1 UM 1/5, 05 SL 8 UM 10, 13 N 7675/2, 13 N 7759, and “Center for Multifunctional Materials and Miniaturized Functional Units” Fkz 03 N 6500), DFG-Schwerpunktprogramm “Ultraschnelle Magnetisierungsprozesse,” Sonderforschungsbereich 625 (TP P9), and Stiftung Rheinland Pfalz für Innovation (Project 535).

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