Spin-dependent electronic structure at magnetic surfaces: The low-Miller-index surfaces of nickel

surface science reports Surface Science Reports 20 (1994) 251-316

Spin-dependent electronic structure at magnetic surfaces: the low-Miller-index surfaces of nickel Markus Donath Max-Planck-Institut fir Plasmaphysik, EURA TOM Association, D-85740 Garching bei Miinchen, Germany

(Manuscript received in final form 10 November 1993)

Abstract

The understanding, on a microscopic level, of magnetic phenomena at surfaces and interfaces hinges on a detailed knowledge of the spin-dependent electronic structure, particularly close to the Fermi level. Experimentally, the most direct access to the spin-dependent electronic states is given by angle-resolved photoemission and inverse photoemission with spin resolution for the emitted and incident electrons, respectively. This report reviews spin-resolved inverse photoemission results on empty electronic states at the low-Miller-index surfaces of nickel as a prototype of a ferromagnetic 3d transition metal. Examples cover bulk-like electronic states, different kinds of surface states, and adsorbate-induced modifications of the surface electronic structure. The data are discussed along with photoemission results on the occupied states. A variety of results is presented which demonstrate how surface magnetic properties are reflected in the spin-dependent electronic structure.

1. Introduction

Surface, interface, and thin-film magnetism is a research area in which industrial laboratories and laboratories dedicated to basic research are highly active [l]. The discovery of novel physical effects in artificially made, ordered systems of magnetic materials has stimulated much research activity worldwide [2,3]. The magnetic recording industry with its demand for even smaller and faster devices for information storage and retrieval is paying special attention to these developments [4,5]. Ferromagnetism, the phenomenon of spontaneous collective magnetic order in solids below a critical temperature called the Curie temperature T,, has already been studied as a three-dimensional (3D) effect for a long time [6]. The achievement of ultra-high vacuum conditions in surface-science equipment about two decades ago opened the way to studying

0167-5729/94/$26.00 0 1994 Elsevier Science B.V. All rights reserved SSDZ 0167-5729(93)E0024-T

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clean surfaces as well as thin-film structures prepared in a defined way by molecular beam epitaxy. The dimension of these systems is reduced compared with the bulk, which means lower symmetry and a smaller coordination number of the atoms. Interesting questions arise when studying the surface of a 3D ferromagnet, ultra-thin films as realizations of two-dimensional (2D) systems, the transition from 2D to 3D behaviour with increasing film thickness, or the magnetic coupling in layered structures of different materials. Novel magnetic properties are observed concerning, for example, the magnitude of magnetic moments, the magnetic phase transition, the sign and strength of exchange coupling at surfaces and between layers, or magnetoresistance effects. A large variety of experimental techniques have been developed to prepare surfaces and thin-film structures in a defined way and characterize them chemically, structurally, and magnetically [7-111. How are the classical primary magnetic quantities reflected in the electronic structure? In a microscopic picture the magnetic moments in 3d itinerant ferromagnets result from the different number of electrons with spin magnetic moment parallel and antiparallel to a given direction. The energy levels of these two subsets of electrons, called majority and minority electrons, respectively, are separated from each other by an energy-, momentum-, and possibly temperature-dependent exchange splitting A E,. Of particular interest are electronic states that are located with their wave functions at the surface of a 3D ferromagnet or at an interface where two different materials meet. They serve as a local probe where modified magnetic properties may occur. Studying the electronic states and their energy versus momentum relation E(k) as a function of the quantum number spin provides valuable contributions to a microscopic description of ferromagnetic phenomena. This is a challenge to experimental as well as theoretical approaches [1,12] to investigating and explaining the spin-dependent electronic structure. Nickel, a 3d transition metal, is probably the ferromagnetic system most studied in the literature with respect to its electronic structure. The ferromagnetic properties of nickel are carried mostly by the uppermost d-band. At zero temperature the majority d-bands are completely occupied, while the uppermost d-bands are partially empty in their minority parts. Nickel is called a strong ferromagnet because it has no majority d-holes in the ground state. The spin-dependent electronic structure of the low-Miller-index surfaces of nickel has been studied in detail by spin- and angle-resolved photoemission (PE) for the occupied states [13-161 and, in recent years, also by spin- and angle-resolved inverse photoemission (IPE) for the empty states [17-191. The two techniques complement each other in studying the partially occupied bands, which carry the magnetization. Actually, it had been argued that the proper study of the magnetism in nickel lies in the hole states, which are in a sense the “active ingredients” of the magnetism [20]. This report reviews spin-resolved IPE results on the electronic structure of Ni(OOl), (llO), and (111). The data are discussed along with PE results with regard to an improved understanding of surface magnetic properties. The review is organized as follows. Chapter 2 describes briefly some experimental aspects: the detection and generation of spin-polarized electrons, the techniques of PE and IPE for studying the electronic structure, experimental requirements concerning the sample magnetization, and details of the IPE experiment. Chapter 3 gives an interpretation of bulk electronic states at low temperatures, well below T,, and at higher temperatures, where the magnetic phase transition occurs. Chapter 4 presents results on different kinds of surface electronic

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states: crystal-induced as well as image-potential-induced surface states and modifications of the surface electronic structure upon adsorption of adatoms. A summary is given in Chapter 5.

2. Experimental

aspects

2.1. Spin-polarized electrons Experiments using spin-polarized electrons provide direct access to surface magnetic properties by separately probing the exchange-split majority and minority electronic states in ferromagnets. A detailed description of the intrinsic electron spin angular momentum and its associated spin magnetic moment as well as examples of the importance of spin-polarized electrons in various fields of physics are given in Refs. [21,22]. The vector of the spin polarization P is defined as

(1) where ( ai) are expectation values of the spin direction along the three coordinates. Choosing the quantization axis parallel to the magnetization direction of the ferromagnetic sample means that only one component P has to be considered. The application of spin-polarized electrons in solid-state physics was mainly pioneered and has been continuously influenced by Siegmann and co-workers at the Swiss Federal Institute of Technology [23-25,9]. Since in ferromagnets more electron spins are oriented in one direction along the magnetization axis than in the other, magnetic information can be obtained by probing the net spin density. This can be done in two ways, either by detecting the spin polarization p=

(N, -q/p,

+NJ)

of N = N, + N, emitted electrons, or by measuring the spin asymmetry

A = (‘t -z&(zt

+I,)

of an emitted signal Z excited by spin-polarized electrons. T ( J) gives the direction of the spin magnetic moments of the emitted or incident electrons as parallel (antiparallel) to the magnetization direction of the sample. Experiments with spin-polarized electrons require a spin-polarization detector and/or source of spin-polarized electrons. Scattering of polarized electrons from high-Z materials results in a left-right scattering asymmetry due to the spin-orbit interaction. Many of the spin-polarization detectors currently used are based on this principle, called Mott scattering [21,26-281. The efficiency or figure of merit is defined as E =

( Z/Zo)S2,

(4)

where I, is the current entering the polarimeter, Z the total scattered current measured by the left and right detectors, and S the asymmetry function or analyzing power of the polarimeter. Depending on the experimental parameters (electron energy, target material, scattering angle or diffuse scattering,. . . >, E varies from lo-’ to 10m4 and S ranges from 0.1 to 0.4. Alternative ways to detect P with similar values for E are spin-polarized low-energy electron diffraction or

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measurements of the absorbed current, again on high-2 materials [26,27]. An efficient polarimeter using the exchange interaction in ferromagnets was recently introduced [29]. The spin-dependent reflection of low-energy electrons from a ferromagnetic surface works as a spin-polarization detector with E = 3.5 x 10p3. A variety of ways have been tried to produce a spin-polarized electron beam [21,26,27]. Photoemitted electrons from negative-electron-affinity (NEA) GaAs excited by circularly polarized light have turned out to be the most efficient way by now to get high currents with considerable spin polarization Ps [30,31]. It takes advantage of the selection rules for circularly polarized light for spin-selective pumping of electrons from the spin-orbit-split valence-band maximum to the conduction-band minimum. NEA is achieved by adsorption of Cs and 0, thereby lowering the work function. Ps is limited to 50% in this experiment due to the valence-band degeneracy of the heavy-hole and light-hole bands at the r-point in GaAs. Experimental values for Ps reported in the literature range from 24% to 43%. Removing the degeneracy of the heavy- and light-hole bands promises an enhancement of P, to values of up to 100%. Experiments with strained GaAs layers or AlGaAs-GaAs superlattices have succeeded in removing the degeneracy, reaching a polarization of over 70% [32,33]. Recently, even values of up to 90% were obtained from strained layers [34,35]. Future investigations will have to show how reproducibly these artificial structures can be prepared and activated without losing the strain and, as a consequence, the high polarization values. At present, experiments dependent on an electron beam with stable and reproducible spin-polarization conditions still use the conventional GaAs source with Ps = 30%. The figure of merit of the spin-polarized electron source is better than that of the spin-polarization detector because there is no intensity loss compared with non-spin-polarized thermal electron emitters, i.e. Z/Z, = 1. The efficiency is only determined by Ps, the quantity corresponding to S. In other words, experiments for detecting spin-polarized electrons suffer from a considerable intensity loss compared with spin-integrated measurements, while experiments using spin-polarized electrons in the exciting channel do not. The fact that S and Ps are not 100% is not a fundamental limitation of the experiment. Provided the actual value for S or Ps in the experiment is known, the measured data can easily be resealed to S or P, = 100%. The case in which the quantization axis for the electron spin polarization and the direction of the sample magnetization are at an angle 4 can also be taken into account. Then Eqs. (2) and (3) are modified to P=

A=

N,-N,

1

N,+lv,

scosc)’

I, -I,

1

I, + I, P, cos c#J.

(5)

(6)

The statistics, however, suffers from the incomplete analyzing power or source polarization, which makes longer data acquisition times necessary. Spin-resolved electron spectroscopies are widely used in the field of surface and thin-film magnetism. Magnetometry with spin-polarized secondary electrons gives information on the magnetization as a function of the field and temperature as well as on the exchange coupling at

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a ferromagnetic surface or between ultra-thin magnetic films [36-401. Spin-polarized secondary-electron emission performed in a scanning mode is known as SEMPA (scanning electron microscopy with polarization analysis) [41-441. It is used to image magnetic microstructures at surfaces with a lateral resolution of better than 40 nm. Spin-resolved Auger electron spectroscopy [45,46] as well as appearance potential spectroscopy [47,48] provide element-specific magnetic information because core levels are involved in the excitation process. This is of great importance in the study of layered structures of different materials [49]. The spin dependence of elastic (low-energy electron diffraction [50,51]) and inelastic low-energy electron scattering (electron-energy-loss spectroscopy [52,53]) can be used as magnetization detector, but, more important, helps to understand electron scattering in more detail. The spin-resolved version of the low-energy electron microscope (LEEM) makes real-time imaging of magnetic structures possible [54]. Spin-polarized-electron tunneling for use in scanning tunneling microscopy is still the subject of current research [55,56]. Spin-polarized electron capture spectroscopy is an extremely surface-sensitive technique that probes exclusively the outermost atomic layer [57]. The most direct access to the spin-dependent electronic states in the vicinity of the Fermi level is provided by spin-resolved photoemission and inverse photoemission, which will be discussed in more detail in the following subsection. Finally, it should be noted that time-resolved photoemission studies with spin resolution have added to our knowledge on spin-lattice relaxation times [58]. The information depth for low-energy electrons is determined by the electron inelastic mean free path in the solid. According to the “universal” curve the electron attenuation length is smallest ( N 5 A) for kinetic energies around 50 eV and increases for higher and lower energies [59]. There is, however, experimental evidence [60-621 that in materials with high density of states around the Fermi energy the electron attenuation length for kinetic energies lower than 50 eV is smaller than theoretically expected [63] and slightly spin-dependent. Remarkably, overlayer experiments which were performed in different laboratories with different deposition techniques on various substrates exhibited equivalent results (e.g. Refs. [39,64]). A linear relationship between the inverse mean free path and the number of empty d-states was found to describe the experimental data of a variety of materials well [9]. This finding proves the relevance of empty d-states as final states for inelastic scattering processes. It turns out that the information depth for low-energy electrons in ferromagnetic 3d materials is about 2 to 3 layers only. This result makes spin-resolved low-energy electron spectroscopies especially attractive for surface and thin-film studies. However, the access to buried interfaces is limited. In spectroscopies which probe specific electronic states, one additional aspect comes into play. The spatial origin of spectral intensities in (I)PE depends on the wave functions of the electronic states that are responsible for the observed features. The information depth discussed above influences, however, the relative intensities of spectral features originating from different kinds of electronic states, e.g. bulk and surface states. 2.2. Photoemission - inverse photoemission Angle-resolved photoemission (PE) [65-701 and inverse photoemission (IPE) [71-761 are electron spectroscopies which provide detailed information on electronic states of solids and their surfaces by observing radiative transitions between these states. Electronic states of

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crystalline solids are characterized by their energy versus momentum relation E(k). In the case of ferromagnetic materials, the spin degeneracy of the states is removed and each band appears in the magnetic state as a twin of bands separated in energy. The exchange splitting

between minority and majority spin band has not a constant value, rather it depends on the band character, the energy, the wave vector, and possibly the temperature. A comprehensive description of electronic states in ferromagnetic crystalline solids therefore requires resolution of the energy, momentum, and spin of the emitted or incident electrons in PE or IPE, respectively. Symmetry information on the states involved in the transitions requires polarization analysis of the incident or emitted light. The kinematics of transitions is defined by conservation of energy and momentum: E fT,l

=EiT,J

kf - ki =

*ho,

(9)

G f 4.

f and i denote the final and initial states, G is a reciprocal lattice vector, and 4 is the momentum of the incident (emitted) photon. + (-) describes absorption (emission) of a photon in the PE (IPE) process. For photons in the ultraviolet spectral range the momentum 4 is small compared with the size of the Brillouin zone. Due to the fact that 4 is also small compared with the experimental resolution, it can be neglected in the momentum balance. This implies that the angle of photon incidence (emission) cx does not influence the kinematics of the experiment. Describing transitions in the reduced-zone scheme, which already includes the exchange of reciprocal lattice vectors G, leads to the direct transition concept ki = k,.

(10)

Fig. 1 shows schematic diagrams for spin-resolved PE and IPE for photon energies in the ultraviolet. Radiative transitions show up as vertical arrows between bands in the reduced-zone scheme. In PE, electrons from initially occupied states Ei T,* below the Fermi level E, are excited by absorption of photons to empty final states E, T,L above the vacuum level E,. The electrons emitted into vacuum are analyzed with respect to their energy E and momentum k. With monochromatic light being used, the PE spectrum gives the intensity distribution XPE( El of the emitted electrons as a function of their kinetic energy. For separately probing minority and majority states in ferromagnets, in addition, a spin-polarization detector is needed. This reduces the speed of the experiment by up to four orders of magnitude owing to the low efficiency of the spin-polarization detector. Two energy distribution curves are obtained, one for the majority electrons Yp(E) and a second one for the minority electrons .YF(E): y,p:JE)

=3’“(E)

[l H’(E)]/2,

(11)

where P(E) is the spin polarization of the emitted electrons at a given energy and YPE(E) = +Yy( E). Over the last ten years, angle- and spin-resolved PE work has significantly improved our understanding of ferromagnetic solids. For a recent review, see Ref. [77]. In spin-resolved IPE, low-energy spin-polarized electrons, usually emitted from a GaAs photocathode, impinge on a remanently magnetized sample. They may occupy empty initial

Y?(E)

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PE

k

IPE

k Fig. 1. Schematic diagrams for spin-resolved photoemission energy ranges are accessible to the techniques.

(PE) and inverse photoemission

(IPE). The nonhatched

states Ei t, I above Ev and then undergo radiative transitions to lower-lying empty final states of energy E, t L. The emitted photons are detected either at a fixed energy in an energy-selective Geiger-l&ller counter or at variable energy in a monochromator. For intensity reasons, spin-resolved IPE measurements have hitherto been taken exclusively in the isochromat mode. In this mode spectra are recorded by varying the kinetic energy of the incoming electrons, with the angle of electron incidence 0, the detection angle of the photons cr, and the electron spin polarization as parameters. A spin-integrated IPE spectrum displays the intensity distribution YIPE(E) of emitted photons with energy Ao as a function of the kinetic energy of the incident electrons. In the case of spin-resolved measurements, the partial spin spectra are given by s:::(E)

=YIPE(E)

[1*45)]/2,

(2)

with A being the spin asymmetry as defined in Section 2.1. The energy scale is usually referred to the Fermi energy of the sample. Spin-resolved IPE was first proposed in 1980 as a technique to study magnetism by probing hole states [78]. Since its first application in 1982 [17] a variety of results on ferromagnetic solids and their surfaces have been obtained [79,80,18,19]. PE provides information on the states below E, and above Ev, while IPE probes the empty

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states above E, (nonhatched energy ranges in Fig. l>, especially the states between E, and Ev, which are inaccessible to PE. With respect to magnetic properties, completely empty as well as occupied electronic states carry magnetic information by hybridization effects, but they do not contribute directly to the magnetic moment in ferromagnets. Therefore, the partially occupied/empty states close to the Fermi level, called magnetic states, are of particular interest. PE and IPE complement each other in this important energy range, from which the magnetic moments originate. The schematic E(k) of Fig. 1 describes a ferromagnetic material with a partially empty, spin-split band which contributes to the magnetic moment of the material. For a given quantum energy defined by the length of the vertical arrow, an IPE transition between minority states is possible, while majority electrons do not find empty final states close to E,. Qualitatively, this situation is realized in nickel, where the uppermost d-band is partially occupied and is responsible for the ferromagnetism. It was the first application of spin-resolved IPE that proved the minority character of the empty d-states in nickel [ 171. One more aspect can be seen from Fig. 1. The spin splitting observed experimentally, i.e. the J - t -peak separation, does not necessarily represent the exchange splitting AE,, of the initial or final band. Considering IPE, the measured spin splitting is identical to AE,, of the final state only in the case of a final band with zero group velocity. In all other cases, the measured spin splitting is not only influenced by the exchange splitting AE,, of the final band, but also by its slope and by A E,, and the slope of the initial band. For a fixed quantum energy, the transitions generally occur at slightly different k for majority and minority electrons. This has to be taken into account when deducing values for exchange splittings from the experimentally observed spin splittings. Usually, the ability to resolve energetically split spectral features is limited by the experimental energy resolution and the intrinsic linewidths of the observed features. By using the electron spin polarization as an additional experimental parameter, however, the detection of spin splittings is not limited by them, because the two partial spin spectra are recorded separately. The effective resolution for the detection of spin splittings is significantly enhanced by experimentally defining the electron spin polarization [81]. As a consequence, spin-resolved (1)PE is not only able to assign spectral features unambiguously to majority and minority spin states, it also makes it possible to deduce spin splittings that are considerably smaller than lifetime broadening and/or experimental energy resolution. Recently, this was impressively demonstrated by detecting an exchange splitting a factor of 5 smaller than the intrinsic linewidth and a factor of 20 smaller than the experimental energy resolution [82]. While PE and IPE seem to be completely equivalent, there is one significant difference. Since the wavelength of photons in the ultraviolet spectral range is much larger than that of electrons with comparable energy, the number of states per energy interval in phase space is much smaller for photons than for electrons. A detailed analysis shows that, as a consequence, the cross section for the IPE process is reduced by a factor of (Y*= 5 X lop5 compared with PE, where cy is Sommerfeld’s fine-structure constant [78,201. Hence, the quantum yield for IPE is only about lo-’ photons per electron. IPE in a spin-resolved mode, however, does not suffer from additional intensity loss, because it is possible to produce spin-polarized electron beams equivalent in intensity to non-spin-polarized beams. This fact, in principle, makes spin-resolved IPE comparable to spin-resolved PE in respect of measuring time. In practice, the use of

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high-intensity synchrotron light makes data recording considerably faster for spin-resolved PE than for IPE. In any case, in PE as well as in IPE, one has to accumulate data a lot longer in the spin-resolved mode to get the same statistics as in the spin-integrated mode. This comes from the analyzing power S and source polarization Ps being smaller than one. With a typical value of 0.3 for S or Ps,the measuring time to get the same statistical error in spin-resolved spectra is about 10 times longer under otherwise identical conditions. 2.3. Sample magnetization To get reliable and quantitative results from spin-resolved measurements on ferromagnets, an essential requirement has to be met. The angle between the directions of the electron spin polarization and sample magnetization has to be well defined. The geometry of the electron spin polarimeter or the spin-polarized electron source defines the preferred direction in the experiment. But, how about the sample magnetization? Note that spin-polarized low-energy electrons are disturbed with respect to the wave vector k and spin polarization P even by small external magnetic fields. In the early days of spin-resolved experiments, the samples were always magnetically saturated perpendicularly to the surface by a high external field applied during the measurements, limiting them to normal electron incidence or emission [83-851. Angle-resolved measurements, however, call for samples which are remanently magnetized parallel to the surface plane. The concept of a closed magnetic circuit minimizes stray fields in the so-called transverse geometry. This was realized by clamping a single crystal onto a small horseshoe electromagnet to perform spin-polarized low-energy electron diffraction experiments [50]. The first experiment detecting low-energy photoelectrons in the transverse geometry used a long single-crystal plate that was magnetized before the PE measurement [86,871. An elegant way of getting a closed magnetic circuit is to cut a single crystal along the main crystallographic directions into a picture-frame shape. This magnetic single-crystal circuit can be magnetized by a current pulse through a self-supporting coil wound around one side of the frame. It was assumed that the directions of the resulting remanent magnetization are parallel to the sides of the frame [88]. This assumption is, however, not necessarily true, as will be shown below. In addition, it should be noted that for the study of magnetic glasses continuous loops of the material were successfully used to get in-plane surface magnetization [89]. One further aspect is of importance in choosing a sample geometry: the existence of directions of hard and easy magnetization caused by the magneto-crystalline anisotropy, which may give rise to magnetic domain structures in remanence other than single-domain, depending on how the crystal is cut. With increasing temperature the anisotropy constants usually decrease and become zero even before the Curie temperature is reached [6]. Measurements on surfaces with no direction of easy magnetization in the plane of the magnetic circuit or, even more complicated, in the surface plane may, therefore, only be possible at elevated temperature such that the magneto-crystalline anisotropy is sufficiently reduced. Moreover, shape- and strain-induced anisotropy can influence the domain structure. The situation is somewhat different with ultra-thin films in view of their considerably smaller stray fields and their modified anisotropy conditions. In many cases, the as-grown state shows a single-domain configuration [43]. Monolayer films often exhibit out-of-plane anisotropy changing to in-plane anisotropy with increasing film thickness [421. Even a reversible transition from perpendicular

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to in-plane magnetization as a function of the temperature has been observed for certain thicknesses [go]. In general, a way of magnetic sample preparation has to be found for each individual sample to get a defined magnetic domain structure in remanence, monitored by, for example, Kerr microscopy [91,92]. The probing depth of the magneto-optic Kerr effect (MOKE) is given by the penetration depth of the light, typically of the order of 100 A. Although this is much larger than the probing depth of low-energy electrons, MOKE probes the magnetic microstructure also relevant to electron spectroscopic studies. The length scale of magnetic microstructures is even much larger than the prvbing depth of MOKE if one considers, e.g., a typical domain wall width of the order of 1000 A. In nickel, the body diagonal of the cubic unit cell, the (111) direction, is the direction of easy magnetization at room temperature [93]. The (001) direction is the hard, the (110) direction the medium axis. As usual, the anisotropy constants of nickel decrease with increasing temperature, while the quantitative agreement between different measurements is only poor [94]. It is not clear whether the strength of the anisotropy simply decreases monotonically or whether the axis of easy magnetization changes from (111) to (001) or (110) at elevated temperatures. Considering the low-Miller-index surfaces of nickel (1101, (0011, and (1111, it turns out that only the (110) surface contains axes of easy magnetization in the surface plane. Sample geometries for the (110) surface which are magnetized along an easy (111) direction are expected to exhibit a single-domain configuration in remanence [50,86,95,96]. Samples with a (110) surface magnetized in-plane along a (110) direction contain two easy (111) directions in the surface plane. A number of studies on this sample geometry observed a plate-like domain structure with domains in (111) directions, separated by 71” walls [97-1021. Consequently, the directions of the applied field and the magnetization direction in remanence form an angle of 35.3“. This domain structure is consistent with threshold photoemission results on a plate-like (110) sample magnetized in a (110) direction [87]. More recent studies used a rectangular picture-frame single crystal with its sides oriented along (110) directions and a (001) direction perpendicular to the rectangle plane, as shown in Fig. 2a. No evidence was found for the

(a) 10

(bl

(cl

mm

4frt9 (1111

LOI

I1101

LOI

[OOll

/JQol [llll

Fig. 2 (left). Sample geometries of nickel picture-frame single crystals used for spin-resolved low-Miller-index surfaces (110) (a), (001) (b) and (111) (c).

(1)PE studies of the

M. Donath /Surface

-10

-06

-0.6

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-0A

-02

0

02

0.L

0.6

06

263

10

l(A) Fig. 3 (right). the high spin magnetization Fig. 2a (from

Hysteresis curve of the NifllO) surface obtained with spin-resolved IPE (hw = 9.6 eV) by measuring asymmetry in the centre of the d-band transition 0.3 eV above the Fermi level as a function of the current. Inset: Schematic domain structure of the (110) surface of the nickel picture-frame crystal of Ref. [109]).

plate-like magnetic domain structure, rather a single-domain state in remanence was assumed [103-1061. The multi-domain structure described above was even found to be inconsistent with the spin polarization values obtained [107]. On the other hand, investigations with Kerr microscopy on a crystal of the same type exhibited unambiguously the plate-like domain structure. Even with this multi-domain structure, the (110) surface showed an almost square hysteresis loop, which is shown in Fig. 3. The high spin asymmetry of an IPE transition into empty d-states in nickel was used as magnetization detector [108,109]. Interestingly, after repeated mechanical polishing of the surface, the multi-domain structure in remanence was observed to be different from the previous one. The width of the plates was smaller by a factor of roughly 10 and was dependent on the magnitude of the current pulse. These somewhat controversial results on the domain structure of (110) surfaces magnetized along (110) directions lead to the following, not at all novel, conclusion. There are more factors than the magneto-crystalline anisotropy that influence the domain structure in remanence: geometry of the individual crystal, external or internal strain, induced by, e.g., the crystal holder or mechanical polishing of the surface, history of the sample concerning, e.g., temperature treatments, strength of the applied external field pulse, and maybe other factors. The (001) surface of nickel does not contain any axis of easy magnetization. A complex closure domain structure is expected in remanence independently of the direction of the external magnetic field used to magnetize the sample [102]. Spin-polarized low-energy electron diffraction experiments did not suffer from this situation, because they were performed at temperatures close to the Curie temperature, where the anisotropy constants are known to vanish [88]. In a spin-resolved PE study of Ni(0011, the possible influence of a multi-domain structure on the spin asymmetry was not considered [llO]. The data were taken at room temperature and the Ni(001) surface was magnetized by an external field in a (110) direction.

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Remanence (MOKE )

l

Ni(O0 1)

-

I

I

I

I

Science Reports 20 (1994) 251-316

Bulk Saturation ( Weiss Theory )

I

I

I

1

I

300 400 500 600 700

T W Fig. 4. Temperature dependence of the average surface magnetization Fig. 2b, obtained by magneto-optic Kerr effect (left panel). Arrows loops of the right panel were taken (from Ref. [112]).

1 b-W in remanence of the Ni(001) surface shown in indicate temperatures at which the hysteresis

A spin-resolved IPE study on Ni(OOl), magnetized in a (001) direction, was hindered by ill-defined surface magnetization conditions [ill]. A re-investigation carefully dealt with the sample magnetization [112]. A picture-frame single crystal (as shown in Fig. 2b) was used, magnetized in a (110) direction. Fig. 4 shows the average surface magnetization following the bulk magnetization for temperatures above 440 K. Below 440 K the surface magnetization decreases drastically and vanishes at 330 K. At room temperature it is even antiparallel to the bulk magnetization, nicely demonstrated by hysteresis loops, also shown in Fig. 4. Consequently, meaningful spin-resolved (1)PE measurements on this particular sample are only possible for temperatures above 440 K. It should be noted that measurements of the bulk magnetization of the same sample leg exhibit high remanence even at room temperature. Thus, the problem of low average magnetization in remanence below 440 K is limited to the surface region and caused by closure domains. The only spin-resolved (1)PE measurements of a Nit1111 surface with transverse magnetization geometry were performed on one and the same crystal, schematically shown in Fig. 2c [113,82,114]. The sample is a nickel single crystal cut into a hexagonal picture-frame shape with its sides oriented along ( 110) directions and the [ill] direction perpendicular to the hexagon plane. No axes of easy magnetization lie in the plane of the sample. Surprisingly, even at room temperature, a remanently magnetized sample in a one-domain state, as proved by magnetooptic Kerr microscopy, was obtained by applying a high current pulse through a magnetization coil wound around one leg of the crystal [82]. This one-domain state was found to be metastable. Small external fields are able to destroy it and produce a complex closure domain structure. The geometry and individual history of this sample may be responsible for this

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26.5

behaviour, which is desirable for (1)PE studies. With no external fields around, successful spin-resolved (1)PE studies could be performed on this Ni(ll1) sample in a single-domain magnetic state in remanence. A knowledge of the magnetic state of the sample is essential for any data analysis from spin-resolved electron spectroscopies. Since the surface domain structure is influenced by a number of factors, a way of magnetic sample preparation has to be found for each individual sample to get a defined magnetic domain structure in remanence. In addition to the structural and chemical sample characterization usually done in surface science, the sample has to be characterized magnetically with respect to investigations of its magnetic properties. For this reason, an in situ Kerr microscope is a highly desirable tool. The spin-resolved IPE results on the low-Miller-index surfaces of nickel presented in this report were obtained from picture-frame single crystals, whose geometries are given in Fig. 2. In analyzing the data of Ni(ll0) the angle of 35.3” between the directions of the remanent surface magnetization and electron spin polarization was taken into account [109]. The measurements on Ni(001) were performed at elevated temperatures, where an almost singledomain magnetic state exists [112]. The Ni(ll1) surface was magnetized by a high current pulse through the magnetization coil to get a single-domain magnetic state in remanence [82]. All surfaces were magnetically characterized by extra situm Kerr microscopy. 2.4. Details of the inverse-photoemission experiment Descriptions of the pioneering spin-resolved IPE experiments on nickel [17] and iron [115,116] are published in the literature. In this subsection, some details of the experimental set-up will be discussed that was used to obtain the data presented in this report [117,118]. A schematic of the apparatus for angle- and spin-resolved IPE is displayed in Fig. 5. The upper part shows the spin-polarized electron source, the lower part the IPE experiment. Both parts of the two-chamber ultra-high vacuum (UHV) system are connected by an electron-transfer optics. Compensation of the earth’s magnetic field by Helmholtz coils, screening of remaining magnetic stray fields by lining the vessels with CONETIC, and the exclusive use of truly nonmagnetic materials in the surroundings of the electron beam make sure that the disturbing influence of magnetic stray fields is reduced to a minimum. In the source chamber, spin-polarized electrons are photoemitted from GaAs(001) by circularly polarized light with a wavelength of 830 nm from a 25 mW GaAlAs laser diode. Adsorption of Cs and 0 onto the GaAs(001) surface provides for the negative-electron affinity of the photocathode. The photosensitivity of the freshly activated cathode is typically lo-20 pA/mW, and the lifetime is several days until the sensitivity is reduced to about 10% of its initial value. The electron spin polarization is parallel to the emission direction, the axial direction of the circular polarization of the light being the quantization axis. A 90” spherical electrostatic deflector transforms it into transverse polarization, which is most suitable for normal electron incidence on a ferromagnetic sample magnetized in the plane of the surface. Up to 80% of the emitted electrons impinge on the sample, with a divergence of less than 2” and kinetic energies of typically 7 to 20 eV. The angle of electron incidence 0 with respect to the surface normal is experimentally defined with an accuracy of better than 2”. The diameter of the electron beam on the sample is about 3 to 4 mm and may be reduced for small samples

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electrostatic deflection p t electron

electron beam with polarization

P’

t

transfer opt its

ferromagnetic sample

Fig. 5. Schematic of the apparatus for angle- and spin-resolved IPE (from Ref. [llS]).

by apertures within the electron optics at the cost of transmitted current. The width of the energy distribution of the electrons was found to be below 300 meV for emission currents of 5 to 10 ,uA, with the sample being used as a simple retarding-field analyzer. The value of the electron spin polarization was determined as 33% + 3% [118], with the exclusive minority character of nickel d-holes being used as polarization detector. A recent re-analysis of temperature-dependent IPE measurements of a transition into empty d-states by the maximum-entropy method found maximum evidence for an electron spin polarization of Ps = 32% [119], in perfect agreement with the previous result. The effective spin polarization is influenced by the angle of electron incidence 0 and the direction of the remanent magnetization M of the sample. In the case of a sample magnetization that is not collinear to the spin polarization for normal electron incidence onto the surface, the factor cos $J of Eq. (6) is modified to cos 4 = cos 0 cos y,

(13)

with y being the angle between Ps and M at normal electron incidence. The photons emitted from the sample are detected by two iodine-filled Geiger-Miiller counters at 37“ and 90” with respect to the electron beam [120], providing two different photon collection angles. In case the crystal mounting is such that positive and negative angles of electron incidence correspond to equivalent momentum directions in the target crystal, a third nonequivalent photon detection angle is available by changing from +O to -0. Only the photon counter close to the electron beam is active in this geometry [llS]. The photon detection energy is 9.6 eV for CaF, and 9.4 eV for SrF, as entrance windows at the counters, with a variance of the optical resolution function of (240 meVj2 and (113 meVj2, respectively [121]. This results in the latter case in an overall apparatus function with full-width at half-maximum of about 400 to 450 meV [119].

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The nickel surfaces were prepared using standard procedures of sputtering and annealing. Low-energy electron diffraction was used to characterize the crystallographic order. The cleanliness of the surfaces was initially checked by Auger electron spectroscopy and - after reducing the contamination levels of S, 0, and C to below the detection limit of our retarding field analyzer - by the intensity of surface states observed by IPE. The determination of the E(k) relation for the electrons in the solid is somewhat hindered by the influence of the crystal surface. In vacuum, the vector k’“” of the electrons is defined by their kinetic energy Ekin and the angle of incidence 0. When they enter the crystal, the component perpendicular to the surface is increased by the crystal potential: k,>k’,““.

(14)

k,,, however, is conserved apart from the exchange of reciprocal lattice vectors of the surface due to the periodicity of the crystal potential parallel to the surface: k,,=k;;““+G,,.

(15)

Surface umklapp processes, i.e. G,, # 0, mean diffraction limited for energetic reasons:

Ik;;“kG,,IsIk/.

at the surface. These effects are

(16)

With no surface umklapp involved, i.e. G,, = 0, the three-dimensional problem of k localization is reduced to a one-dimensional one, confined along the k I line. k,, is directly accessible to the experiment:

(17) where Ekin denotes the kinetic energy of the electrons and Qs the work function of the sample. k ,_ can be estimated by making assumptions on the inner crystal potential, but absolute experimental determination of k is only possible by a second measurement of the same electronic state from a different surface. In this case, the intersection of the two k,, gives the location in k space [122]. In the usual case of results from one surface only, the data are summarized in E(k,,) plots. For comparison with theoretical results, the three-dimensional band structure is projected onto the surface, i.e. the energy values for all nonequivalent k I corresponding to one k,, are assigned to this k,,. This way of comparing experimental data with theoretical results is used in this report. To get reliable IPE results on spin splittings, a number of experimental details have to be under control. Aging of the photocathode results in a work-function change. The Fermi level onset of the IPE spectrum, however, depends directly on the work function ac of the cathode. It is given by the equation eU, = Aw - Qc, with U, being the acceleration and sample, which corresponds the work-function change was artificial spin splitting as a

voltage, i.e. the potential to the Fermi level onset. found to be smaller than result of this, the two

(18) difference between the photocathode In the described experimental set-up, 20 meV within 3 days. To avoid any partial spin spectra were measured

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I c t I”” 3 ’ I “‘I”“‘,“‘, Gaussian Function

FWHM = 0.6 eV

Gaussian Function FWHM = 0.6 eV

AE [meVI -20 S

02

Difference

.O.l % z

E -10

0: k? 0.1 LL E

g I 5

0.2 0 1

-1 E-EOok”I

-1

1 E-

~ob2vI

Fig. 6. Simulation of spin-split spectral features and their difference spectra normalized to maximum peak intensity (left panel). Simulation of spin-split spectral features, sitting on a spin-dependent linear background, and corresponding asymmetry functions (right panel). As parameter the energetic splitting AE is varied.

quasi-simultaneously by reversing the spin polarization about every 5 s for each value of the energy sweep, with the magnetization kept fixed. To get good statistics, many single spectra were recorded and accumulated after each single spectrum had been checked for any intensity change or energy shift. When measuring a sequence of single spectra, the work-function change, if necessary, was compensated by an offset to the acceleration voltage, such that the spectra could be added channel by channel. Furthermore, the “spin asymmetry” of the apparatus, i.e. the nonequivalence of spectra recorded with reversed spin polarization and sample magnetization, was tested. The difference between the exchange splittings obtained from the two data sets was detected to be less than 5 meV [82]. To eliminate even this small effect, in most cases, half of the spectra were recorded with reversed sample magnetization. Spin-resolved IPE results can be presented as four data sets: the spin-integrated spectrum YIPE, the spin asymmetry A, and the two partial spin spectra YF and SFE. Since the IPE intensity contains contributions from direct transitions as well as background intensity due to inelastic processes, asymmetry data have to be interpreted with caution. The left panel of Fig. 6 presents simulated spectra “N, L” with no background intensity together with their difference spectra normalized to the maximum peak intensity. An IPE spectral feature is simulated by a Gaussian function with a full-width at half-maximum (FWHM) of 0.6 eV. As parameter the energetic splitting A E is varied. The difference spectra clearly reveal the splitting by a - / +

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feature. The real situation is more complicated because spectral features sit on a spin-dependent background. The high spin asymmetry of the density of states in nickel above the Fermi level serving as final states for inelastic processes is responsible for the spin-dependence of the background intensity. The right part of Fig. 6 displays a simulation for a spin-split feature sitting on a spin-dependent linear background. Even for zero spin splitting the asymmetry function shows a dip centred at the energy of the unpolarized peak. With increasing spin splitting a - / + feature is superimposed. The examples show that asymmetry data are able to indicate a spin splitting, but the size of the splitting cannot be directly deduced from them. In addition, in the real case the determination of spin splittings is hindered by a possibly spin-dependent linewidth or even line shape. Furthermore, the background intensity does not necessarily increase linearly with energy nor change its spin asymmetry linearly. At least in small energy intervals the linearity was found to be a good approximation [123,82]. In any case, excellent stability of the apparatus is required for accumulation of data with good statistics, which is necessary for unambiguous detection of spin splittings that may be smaller than experimental resolution and/or intrinsic linewidths.

3. Bulk electronic states 3.1. Low-temperature results Angle-resolved PE and IPE are spectroscopies involving low-energy electrons, and so they probe electronic states at the surface of solids to an information depth of a few atomic layers only. On the other hand, the electronic structure in metals two or three layers deep already exhibits bulk-like character. The influence of the surface on the electronic states is limited to the outermost layers. Consequently, spectral features observed in (1)PE contain mixed information of bulk as well as surface effects. The advantage of gaining comprehensive information on both has to be paid for by the disadvantage of more difficult interpretation of the data. In this section, spectral contributions will be discussed which can be described by bulk band structure calculations. The bulk electronic structure of the ferromagnetic ground state of nickel has already been extensively studied both theoretically and experimentally. The noninteger value of the bulk magnetic moment per atom of N 0.6 pn (p a: Bohr’s magneton) [124] proves that nickel is a band ferromagnet. At zero temperature the majority d-bands are fully occupied, while the associated minority states extend to energies slightly above E,. Calculating the ground-state energy of a material on the basis of density-functional theory yields one-particle energies as Lagrange parameters, which, in principle, have no physical meaning. Nevertheless, (IlPE results for many materials have been successfully explained in terms of transitions between these calculated single-particle energies. The calculations for nickel, however, yield values for the magnetic exchange splitting and the occupied d-bandwidth which are up to twice as large as the experimental values [125,126]. Fig. 7 displays a state-of-the-art spin-dependent band structure calculation along certain high-symmetry lines that shows a quite realistic exchange splitting of about 0.39 eV in the d-band region [127]. The exchange splitting is not at all a rigid shift, rather it depends on the energy, the wave vector, and the symmetry of the band. The energy range of

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Ni --- maj. -

min.

Fig. 7. Section of the nickel band structure along certain high-symmetry lines (after Ref. [127]).

about 5 eV below the Fermi level is dominated by the d-bands, which exhibit the largest exchange splitting. They show little dispersion, which means low group velocity and hence rather high degree of localization compared with the delocalized sp bands above and below in energy. Correlation effects between the nickel 3d electrons have to be taken into account to describe quantitatively the small exchange splittings and the d-band narrowing of the quasi-particle states observed in experiment [128-1301. While the cited investigations are restricted to the ferromagnetic ground state, a recent many-body calculation gives the full temperature dependence of the quasi-particle properties [131,132]. Experimentally, several PE studies without spin analysis have investigated the occupied electronic states of nickel [133-1391. The lack of spin resolution is a severe shortcoming for studying ferromagnets because the spin character of a band cannot be identified directly. The assignment to different spin states is guided by theoretical results [140]. Resolving exchange splittings in nickel is limited to d-states in the vicinity of the Fermi level, where the lifetime broadening is small enough. In addition, the determination of AE, is dependent on line-shape analyses, which are difficult and doubtful in the case of nickel with its small exchange splitting of a few hundred meV. Nevertheless, AE,, of the uppermost d-band could be determined at different k points: . II2 + A, + L,: 310 + 30 meV [134,135], . L + A: 258 f 50 meV [136],

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. halfway along W, + Z, +X,: 281 f 50 meV [136], . K, + S, + X, close to X: 330 meV [137], . K, + S, + X, close to X: 170 meV [137]. The substantially lower AE, in the last case is ascribed to correlations between the d-electrons, whose influence depends on the symmetry of the states. They affect e&I’,,)-type states more strongly than t,,(I’,,,)-type states [141,128,142,130]. Calculations found AE,, for tzg states to be N 370 meV, for eB states N 210 meV [128]. As another experimental result, the minority d-bands at L, and X, are observed to be located above E,. Spin resolution not only increases the effective energy resolution, which helps to identify the origin of spectral features, it also opens the way to determining unambiguously their spin character. For example, a structure close to E, observed by ordinary PE from Ni(001) was ascribed to a majority-spin surface state [143]. In contradiction to this interpretation, spin-resolved measurements demonstrated that this structure has minority-spin character and is mainly due to off-normal emission from a bulk band [llO]. Two spin-resolved PE studies dealt with the exchange splitting of the d-bands in nickel. The first one on Ni(ll0) determined three critical point energies: X, t = - 0.10 eV, X, ,, = - 0.06 eV, X, T = -0.24 eV [103]. This results in an exchange splitting of 180 + 20 meV for the S, band at the X-point of the Brillouin zone in good agreement with earlier spin-integrated results [137] as well as spin-dependent calculations within the one-step model of PE [144]. The wave-vector dependence of the exchange splitting of nickel was the subject of the second spin-resolved PE study [113]. Normal emission from Ni(ll1) excited with three different quantum energies provided three AE,, measurements along the uppermost d-band of A, symmetry at k = $,+,tI’L: 160 f 20, 214 f 20, and 245 + 20 meV. A value of 310 + 30 meV deduced from spin-integrated measurements was reported for k = ZIL [134,135]. The increase of AE,, from I to L can be understood by the symmetry change from II2 with pure eg symmetry to L, with a symmetry mixture of t&e, = 3/2 [145]. Extrapolating the results to states with pure eg and tzg symmetry gives AE,,(e,) = 160 f 30 meV and A E,,(t 2g) = 330 f 30 meV. To date, no spin-resolved PE experiment on A E,, of sp bands has come to the author’s attention. The measurement of unoccupied states above the Fermi level E, is the domain of IPE. Numerous angle-resolved IPE studies on the low-Miller-index nickel surfaces revealed d, sp, as well as different kinds of surface states [146-1541. The data were analyzed by the one-step model of IPE [155,156] and by an empirical band structure combined with a phase-analysis model for describing surface states [157]. The comprehensive IPE data base provides a detailed knowledge of the empty electronic states of nickel surfaces. A considerably smaller number of spin-resolved IPE studies dealt with the spin character of the empty states. As shown in Fig. 7, the d-holes of nickel at zero temperature are exclusively minority states, which was proved by the first spin-resolved IPE experiment [17]. This pioneering work was followed by several studies dealing with d-bands, sp bands and surface states [111,118,158-161,82,114]. The electronic states which have been investigated by spin-resolved IPE, most of them at room temperature, are summarized&r Fig. 8. It shows E(k,,) plots for Ni(llO), (OOl), and (111). -In each case, k,, was varied in the [llO] direction, which corresponds to IX for Ni(llO), (001) and TK for Nit1111 in terms of the surface Brillouin zone. Thick solid lines show spin-averaged final-state dispersions for transitions observed in experiment (Ni(ll0) [118], Ni(001) [160,161], Ni(ll1) [114,162]). The actual data points are given in the cited references. A calculated bulk

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-,

M

63 -1

r

4

A

R

i4

Ni (110)

Ni (001)

k,, W)

-)

tiiol

Ni (111)

k,, W)

--R

- ciiol

-Fig. 8. Electronic states investigated by spin-resolved IPE summarized in E(k,,) plots for Ni(llO)-rX [118], Ni(OOl>-~~ [160,161] and Ni(lll)-fK [114,162]. Nonhatched areas denote gap regions of the projected bulk band structure. The corresponding surface Brillouin zones are shown above.

band structure has been projected onto the three surfaces. It was calculated by means of a combined interpolation scheme based on the E(k) relation of Fig. 7 at the high-symmetry points I, X, L, K, and W. Hatched areas denote energy regions where bulk states exist. From Fig. 7 it is obvious that along selected directions no bulk states are available. Along I-A-X there exists an sp-band gap between X,, and X, and along I-A-L between L,, and L,, which is traversed by the uppermost d-band of L, symmetry. The two gaps are responsible for the gaps of the projected bulk band structures shown as nonhatched areas in Fig. 8. Thin solid and dashed lines denote majority and minority band-gap boundaries, respectively. Electronic states labeled SS and IS appear mostly inside these gaps and will be discussed in Chapter 4 about surface states. Final-state energies which are identified with bulk electronic states are named B, and B,, according to their band character. Transitions into empty d-states are expected to show minority character at low temperatures. Room-temperature data (T/7’, = 0.48) are regarded as low-temperature data because the magnetization is only slightly reduced compared with the

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273

ii&i% l5w = 9.4 eV

oa

in

I+

10

0 1 E-E,

(eV)

0

1 2

0

1

2

3

L

E-E,(eV)

Fig. 9 (left). IPE spectra for the d-band region of Ni(ll0) in the Fx azimuth, both spin-averaged as a function of the electron angle of incidence 0 (from Ref. [llS]).

and spin-resolved

Fig. 10 (right). Spin splitting of a bulk transition B,, for an sp-like final band. Spin-averaged data and the asymmetry function are shown in the upper part, spin-resolved spectra in the lower part (from Ref. [llS]).

zero-temperature value. For all three surfaces, transitions into d-states are observed over the whole k,, range investigated. Owing to the high density of d-holes close to E,, indirect non-k-conserving transitions are observed in addition to direct ones. Fig. 9 displays spin-re-solved IPE data of Ni(ll0) in the TX direction in the d-band region. For small and large angles of electron incidence 0 no direct transition into empty d-states is possible for reasons of energy conservation as well as selection rules. Nevertheless, indirect transitions cause a spectral feature just above E,. In between, for 0 = 25”, a direct transition Z, + Z, (marked in Fig. 7) into the uppermost d-band is observed with high intensity. For all angles 0, the emission B, close to E, has almost exclusive minority character. The small majority peak seen in, for example, the 0 = 25” spectrum is attributed to the combined effect of Fermi-energy broadening and slightly reduced magnetization at room temperature. The majority d-state approaches E, sufficiently closely at this specific k point to appear in the room-temperature IPE spectrum. The weak structure B,, in Fig. 9 stems from transitions between sp bands accessible via surface umklapp [118]. A look at sp bands in Fig. 7 makes it clear that one expects considerable exchange splittings depending on their wave vector and degree of hybridization with d-states. IPE was the first to

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resolve this experimentally. All branches B,, shown in Fig. 8 exhibit -- spin splittings between 80 and 280 meV. An example from the upper B,, branch of Ni(llO)-I’X is shown in Fig. 10. The spin splitting of the transition expected for a measurement at fixed angle of electron incidence is about 150 meV. The experimental result is 140 + 20 meV [118]. This transition takes place close to the A high-symmetry line, which is also accessible with normal electron incidence on Ni(001) (marked by an arrow in Fig. 7). No spin splitting was detected by the first spin-resolved experiment on Ni(OOl), which was hindered by ill-defined surface magnetization conditions [ill]. A more recent study on Ni(001) determined the exchange splitting of B,, for 0 = 0 as 80 f 20 meV [158], which is a lower bound with regard to the influence of closure domains as well as to the elevated temperature of the measurement [112]. The observed 1 -t-peak separation is affected by Alex of the initial and final states as well as the slope of both bands because the measurement was taken at constant transition energy. The transition occurs close to the X point where X, exhibits strong s-d hybridization, while X,, is p-like. As a consequence, the initial-state splitting at T = 0 is predicted to be 160 meV, the final-state splitting only 80 meV [127,163]. Owing to the opposite slopes of the initial and final bands, the observed splitting of the transition is expected to be between the two values in agreement with experiment. The exchange splitting of the upper band edge Xi has been determined by measuring the absorbed target current as a function of the energy of the incoming electrons for spin parallel and antiparallel to the magnetization direction of the sample. The band edge is observed as a spin-dependent onset in the target current, split by 230 + 70 meV [160]. The experiment is in good agreement with calculations for the transmission coefficients [161]. The considerable exchange splitting of X, demonstrates the strong hybridization of this highly excited band more than 9 eV above E, with the magnetic d-states. While for Ni(ll0) and Ni(001) the transitions into d-states as well as between sp-like states are well separated in energy for ho = 9.4 eV, the E(k,,) results for Ni(ll1) show a different situation (see Fig. 8). Distinguishing between the surface state SS, sp band Bsp, and d-band B, was only made possible by analyzing the spin character. Fig. 11 displays a series of IPE spectra, spin-averaged and spin-resolved, for Ni(ll1) in the TK azimuth [114,162]. As always for nickel, the data exhibit a peak just above E,, usually interpreted as a result of direct and/or indirect transitions into the uppermost minority d-band with its high density of states [150,152]. Inspection of the electronic states along the A line in Fig. 7 shows that direct transitions into the minority A, band cannot contribute to the data for the transition energy of 9.4 eV, which was used in the experiment. While the spin-averaged emission intensity close to E, for normal electron incidence looks almost the same as for Ni(ll0) (see data for 0 = 25” in Fig. 91, the spin-resolved data exhibit a considerably smaller spin asymmetry. A detailed analysis shows that the spectral feature stems predominantly from a surface state, becoming a surface resonance for off-normal electron incidence [114]. With increasing k,,, SS disperses to higher energy while losing intensity and broadening the more it overlaps with bulk states. Moreover, the spin-resolved data reveal an sp band crossing the Fermi level from below, first with its minority part (see spectrum for 0 = lo”), then with its majority part (see spectrum for 0 = 14”). The crossing process can be nicely followed by looking at the changing ratio between the minority and majority intensities with increasing 0. The spin asymmetry in the vicinity of E, is the key to interpreting the spectra. Starting with a small negative value at 0 = O”, it becomes

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0

E-E,

1

Science Reports 20 (1994) 251-316

2

(eV)

3

0 E-E,

1

2

275

3

(ev)

Fig. 11. Series of IPE spectra (ho = 9.4 eV) of Ni(ll1) in the rI( azimuth, both spin-averaged function of the electron angle of incidence (from Ref. [162]).

and spin-resolved as a

more negative at 0 = lo”, where the majority part of SS shifts away from E,, while the minority part of B,, already starts to cross E, from below. Between 0 = 14” and 0 = 20” the asymmetry changes sign due to the majority part of B, crossing the Fermi level. For 0 = 30” and higher, the asymmetry again becomes negative because B, has shifted away from E, to higher energies, while indirect transitions into minority d-states now dominate the spin asymmetry. Finally, at 0 = 40”, the spectra exhibit indirect transitions into minority d-holes well separated from the sp-band transition, spin-split by about 280 meV. Even the longer lifetime of the majority compared with the minority state due to the high density of minority hole states serving as decay channels is reflected in the different linewidths. Obviously, it would not have been possible to arrive at these clear-cut conclusions from the spin-averaged measurements with their broad structures. The data of Ni(ll1) impressively illustrate how helpful spin resolution is for identifying the origin of spectral features. In conclusion, spin-resolved PE and IPE provide a comprehensive data base of bulk electronic states of nickel. The exchange splittings of d- and sp-bands have been determined and have helped to develop a quantitative theoretical description of the spin-dependent band structure, describing the ferromagnetic ground-state of nickel.

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3.2. Magnetic phase transition

The discussion of low-temperature results already made it clear that correlation effects between the neither strictly localized nor itinerant d-electrons in nickel are critical for describing its electronic structure. This is even more true of the ferromagnetic properties at finite temperatures. The Heisenberg model is not adequate, because it assumes localized magnetic moments. In nickel, however, the d-electrons, which carry the magnetization, are also responsible for, e.g., the electrical conductivity, proving their delocalization. The itinerant character is also reflected in the noninteger value for the magnetic moment per atom. On the other hand, the Stoner model, which is essentially a mean-field approximation to the Hubbard model, describes the behaviour of strictly itinerant electrons. The prediction of a rigid band shift between majority and minority bands is at variance with experiment. The most serious deficiency of the Stoner model is the predicted Curie temperature, which is more than an order of magnitude higher than the experimental value. Within the model, the finite-temperature magnetic properties are described by a temperature-dependent exchange splitting AE,,( T) proportional to. the macroscopic magnetization. In particular, AE,,(T) goes to zero as T approaches the Curie temperature TC. No local magnetic moments are left above T,. This is, however, in contrast to neutron scattering experiments, which found that the spin waves change very little in character even at 80 K above the Curie point [164]. Spin-polarized electronenergy-loss spectroscopy studied the temperature dependence of the spectrum of Stoner excitations [165,53]. Since the shape of the spectrum remained unaltered for 0.48 I T/T, I 0.97, it was concluded that the exchange splitting in nickel is essentially independent of temperature up to T,. The same conclusion was drawn from measurements of the two-dimensional angular correlation of polarized positron annihilation radiation. The Fermi surface topology of nickel was found to be essentially unchanged between 4.2 and 600 K, while a slight reduction of AE,, of about 28% could not be excluded [166]. In contrast to these results, indirect evidence for a significant change of the Fermi surface across the magnetic phase transition was provided by measurements of the pressure coefficient of the electrical resistivity [167]. Probing the temperature dependence of the magnetization of Ni(ll1) with respect to long-range versus short-range magnetic order was the subject of an electron capture spectroscopy experiment [168]. According to this study, the long-range surface magnetic order decreases almost linearly with temperature, while the short-range surface magnetic order is temperature-independent and is detected far above T,. Fluctuating mean-field theories of itinerant magnetism are extensions of the Stoner theory to account for magnetic behaviour in the paramagnetic state [169-1711. A local mean field whose direction may vary in space and time is assumed. At and above T, the long-range magnetic order disappears, but local magnetization may still exist. One approach, the disordered local moments (DLM) theories [172,173], describes the finite-temperature behaviour by uncorrelated longitudinal and transverse spin fluctuations. Another approach, the local band theories (LBT) [169,174-1761, assumes short-range magnetic order even above T,. Correlated transverse fluctuations lead to a local band structure. A third approach is small-to-moderate short-range magnetic order models, which should, in particular, apply to nickel with its small magnetic moment [177,178]. Within this approach, cluster calculations for regular spin configurations

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with variable degree of short-range magnetic order have been performed to model PE results [179,180]. An alternative proposal uses a generalized Hubbard model combined with a many-body approach to investigate the influence of electron correlations on the temperature dependence of the quasi-particle properties of ferromagnetic nickel [131,132]. Since it uses translational symmetry from the very beginning, it cannot be directly compared with the fluctuating mean-field theories. Nevertheless, it reproduces the localized aspects in the band ferromagnetism of nickel. The local spin magnitude as well as the degree of effective moment localization change only little with temperature. Macroscopic properties such as the Curie temperature at 631 K, the Brillouin-type magnetization curve, or the Curie-Weiss behaviour of the paramagnetic susceptibility are quantitatively described by the model. Furthermore, microscopic quantities such as the spin-dependent quasi-particle band structure with a realistic k-dependent exchange splitting of the d-bands in the range from 0.23 to 0.36 eV at T = 0 are derived as well [181]. It is the first model that provides a spin- and temperature-dependent quasi-particle band structure for nickel. On the basis of the results of this model, temperaturedependent spin-resolved (1)PE spectra were calculated within the one-step model of (1)PE. They are in good agreement with experiment [182-1841. From the experimentalist’s point of view the following question is essential: What kind of measurements are capable of distinguishing between the proposed models? So far, the experimental work with (IlPE has concentrated on the temperature behaviour of the exchange splitting A&,. This is because LBT, which appears to be the most popular model, predicts the local exchange splitting to be almost independent of temperature due to short-range magnetic order even at and above T, [174,175], in striking contrast to the Stoner model with its temperature-dependent exchange splitting. As a consequence, observed spin-up and spin-down spectral features originating from bands with low group velocity, equivalent to flat dispersion, are not expected to collapse with increasing temperature. They are subject to depolarization due to a mixing of spin-up and spin-down states resulting in “extraordinary” features at the energy of the other spin direction. The measurement averages over many domains of short-range magnetic order, hence the experimental spin polarization vanishes at T, with the breakdown of the long-range magnetic order. The local band structure, however, is still spin-split, which is reflected in double-peak structures in the spectra even at and above T,.The validity of the model is supported by spin-resolved (IlPE experiments on Fe [185,116]. Fe exhibits an exchange splitting of about 2 eV, which is considerably larger than in nickel. The scenario described so far is valid for substantial short-range magnetic order and for bands with low group velocity, equivalent to flat dispersion. Spectra from bands with high group velocity are subject to “motional narrowing” reflecting the average magnetization, which leads to collapsing band behaviour even within the LBT picture. The so-called fast approximation is valid for “light” bands, while the slow approximation should be reasonable for “heavy” bands. One more critical parameter is the magnitude of the exchange splitting, favouring the fast approximation in the case of a small AE,. Model spectra for nickel predict collapsing band behaviour for light bands and noncollapsing behaviour for heavy bands [176]. The low-velocity states, which are partially occupied and hence carry the magnetization, are expected to remain split [175]. It should be noted that the DLM picture assumes a priori the fast approximation. Model calculations for realistic bands have not been worked out so far. The generalized Hubbard

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model [131,132] predicts a temperature-dependent exchange splitting vanishing at T, for all bands, even the truly magnetic ones. Angle-resolved PE measurements without spin resolution depend on line-shape analyses for separating spin-up and spin-down states. Temperature-dependent measurements on Ni(ll1) indicated a reduction of AE,, of about 40% on approaching T, by using a two-peak analysis with temperature-independent linewidths [134]. Further data of Ni(ll1) were analyzed by assuming two magnetic peaks and one nonmagnetic peak in between. The nonvanishing magnetic peaks at T, were taken as evidence of short-range magnetic order [186]. Actually, the three-peak analysis was based on an incorrect interpretation of a calculation within the LBT model [175]. A third study was dedicated to distinguishing between the influence of lattice and spin disorder on the temperature-dependent modifications of PE spectra [187,188]. Superimposed on lattice disorder effects, known from a study on Cu(llO), the PE line shapes observed for NKllO) exhibited a complicated temperature dependence of magnetic origin. From the data which werz analyzed according to a model of spin spirals [179] a short-range magnetic order of about 10 A at T, was deduced. In all cases described, the data exhibit an obvious narrowing of the d-band structure from a clearly resolved two-peak to a broad one-peak structure with increasing temperature. This can also be interpreted as a substantial reduction of the exchange splitting combined with a broadening of the partial spin intensities. The first spin-resolved PE study on the temperature dependence of d-band intensities from nickel was reported for the band of S, symmetry close to the X, point [104,14]. The data for normal electron emission from Ni(ll0) were recorded in the temperature range 0.5 I T/T, I 0.94. The spin-resolved spectral features were observed to approach each other with increasing temperature while becoming broader. This result, which seemed to be at variance with the LBT because of the vanishing AE,, at T,, was interpreted by the LBT as a motional narrowing effect due to the nonzero group velocity combined with the small AE,, in nickel [175]. The LBT model calculations were done on the assumption of the existence of short-range magnetic order on a scale of about 20 A above T,. It should be noted that collapsing band behaviour is naturally also predicted by the DLM model. The pure Stoner model, however, fails to describe the data owing to the changing line shapes with increasing temperature. Calculations within a generalized Hubbard model are in qualitative and quantitative agreement with experiment [182,184]. A further spin-resolved PE experiment dealt with the A3 band observed for normal electron emission from Ni( 111) [113]. Upon approaching T, collapsing band behaviour similar to the result for the S, band was found for k = +lYL. Plotting the t - 5 -peak separation as a function of temperature reveals a slightly faster decrease with increasing temperature compared with the bulk magnetization in both experiments. This result was interpreted as a consequence of the high surface sensitivity of the PE experiment. No clear-cut conclusions could be drawn from the data for k = i,ilYL. Asymmetric broadening of the spin-up and spin-down peaks was observed with increasing temperature, possibly originating from barely resolved extraordinary intensities at the binding energy of the opposite spin direction expected in the case of a temperature-independent A E,,. In contrast to experiment, calculations within a correlated-local-moment cluster theory expect the merging-peak behaviour to be less pronounced for k = +lYL [145]. The finite angular resolution of the PE experiment was identified as a possible reason for the experimentally observed large linewidths that hinder the experimental distinc-

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tion between collapsing and noncollapsing band behaviour. Calculations for off-normal electron emission revealed a splitting of the bands due to the break-up of the degeneracy away from the A high-symmetry line. As a consequence of the large linewidths, no quantitative result for the amount of short-range magnetic order could be deduced. Calculations within a generalized Hubbard model taking into account off-normal contributions describe the data quite well, but not as well as for the S, band [183,184]. In particular, no experimental evidence for the predicted reversed exchange splitting was found, although the complicated experimental line shapes exclude unambiguous conclusions. Worth mentioning are model calculations for the A line about halfway between I and L with the size of the exchange splitting A.&, and the amount of short-range magnetic order A as parameters [145]. For the nickel case with AE, = 0.25 eV, noncollapsi~g band behaviour can be expected only for substantial short-range magnetic order of A > 10 A. Only for large AE, and A do the extraordinary peaks clearly appear at the energy of the other spin direction. In all other cases, complicated line shapes have to be expected. In nickel, therefore, the experimental detection of extraordinary peaks suffers from lifetime broadening of the peaks comparable in size to AE,. So far, all described spin-integrated as well as spin-resolved temperature-dependent PE measurements have dealt with completely occupied d-bands polarized by the magnetic bands, but not carrying the magnetization. LBT predicts for the low-velocity states, which carry the magnetization, that they remain split, allowing substantial magnetization in the paramagnetic state [175]. The experimental information on the truly magnetic bands by PE or IPE, however, is incomplete per se, because the Fermi level cut-off veils part of the band. A complete experiment, a combined effort of PE and IPE studying a partially occupied/empty d-band at the same point in k space at the Fermi level, has not yet been reported. However, the temperature dependence of the empty part of the magnetic d-band of Z, symmetry has been studied by spin-resolved IPE [189,18]. Inspection of the band structure shows that the band has close-to-zero dispersion and a maximum value for the exchange splitting in nickel. According to a ground-state calculation [127], the X, L point lies 0.33 eV above, the X,, p oint 0.06 eV below E,. Along the Z line the dispersion of this band is very flat. The majority band reaches W,, t at - 0.05 eV. The experimental condition -- applying for the Z, + Z, transition, marked by an arrow in Fig. 7, is an angle of 25” in the TX azimuth on the Ni(ll0) surface. The room-temperature data have already been presented in Fig. 9. Fig. 12 displays IPE spectra for the Z, + Z, transition for different temperatures. The spin-integrated intensities shown in the left panel exhibit a peak shift towards the Fermi energy of less than 150 meV upon approaching T,. No further shift has been measured above T,. The line shape is dominated by the apparatus function, and the integrated intensity does not change significantly with temperature. The small intensity increase above T, is not understood at present. While the spin-integrated intensities are not very elucidating, the partial spin spectra (middle panel of Fig. 9) contain detailed information. With increasing temperature the minority-peak intensity decreases and the peak shifts by as much as 150 meV to lower energy. By contrast, the intensity of the majority peak increases in conjunction with a peculiar change of its energetic position. The initial shift tends to the Fermi level, while above T/T, = 0.82 this trend reverses. Remarkably, the majority peak gains intensity at energies different from those where the minority intensity loss occurs. Actually, the spin asymmetry just below E, becomes positive

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0

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1

E - E,(eVl

E-EF (eV1

Fig. 12. Spin-averaged (left panel) and spin-resolved (middle panel) IPE spectra for transitions into the magnetic d-band of symmetry Z, for different temperatures. Simulation of IPE spectra for a Lorentzian line L crossing the Fermi level (right panel) (from Ref. [189]).

with increasing temperature. This is completely incompatible with depolarization of energetically stationary bands, i.e. the appearance of extraordinary peaks expected for a temperatureindependent A E,. The peculiar majority peak shift has to be interpreted with caution. Apparent peak positions close to E, may differ considerably from their “true” values [190,191]. This is due to a combined effect of the temperature-dependent Fermi function, the intrinsic linewidth, the inelastic background, and the experimental energy resolution. In order to demonstrate this effect, a simulation has been performed. A Lorentzian L at energy E = E, with linewidth 0.1 eV FWHM on top of a constant background U was multiplied by the Fermi function f at T = 300 K and subsequently convoluted by a Gaussian A of 0.4 eV FWHM representative of the experimental energy broadening. The resulting series of spectra with E, as parameter is shown in the right panel of Fig. 12. It demonstrates in a convincing way that an emission peak above but close to E, may well originate - at sufficiently high temperature from a band which is fully occupied at T = 0.In particular, the behaviour exhibited at constant temperature as a function of E, is suspiciously similar to that of the majority peak as a function of temperature. The combined observation of the obvious movement of the minority peak towards E, and the peculiar behaviour of the majority peak, indicative of a peak crossing the Fermi level from below, is fully compatible with the assumption of a temperature-dependent AE,, approaching zero at T,.Even the residual majority peak in the room-temperature data fits into this picture as a residue of the Z, majority band, which is incompletely occupied at finite temperature. It gives evidence of a slightly reduced spontaneous magnetization at room temperature as compared with saturation at T = 0. The foregoing discussion gives qualitative arguments for collapsing emission features upon approaching T,.No quantitative conclusions on actual majority- and minority-peak positions as a function of temperature could be drawn, because the experimental information is distorted by Fermi distribution and apparatus function. To recover the quasi-particle spectral density

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281

I

I

I

I

I

0.3Cl z

0.2-

f

Mbulk

-w

’

.A

X Q) %

\

0.1 -

P

9

0

-Y0

E-E,(eV)

E-E,

(eV1

0.2

0.4

I 0.6

I 0.8

I 1.0

TIT,

Fig. 13 (left). Spin-dependent quasi-particle spectral densities (a, c) and experimental spin-resolved IPE spectra (from Fig. 12) of the Z, -+ Z, transition in nickel for two temperatures T/T, = 0.72 (a, b) and 0.82 (c, d) (from Ref. [1191). Fig. 14 (right). Exchange splitting A E, of the Z, band in nickel as a function of temperature (solid circles with error bars) obtained by using the maximum-entropy regularization to deconvolute spin-resolved IPE spectra [119]. Open squares present theoretical results [181]. The full line is the experimental bulk magnetization of nickel resealed to fit the AE,, data [193].

constitutes an ill-posed inversion problem. Recently, the maximum-entropy regularization 11921 was invoked to deconvolute the IPE spectra [119]. The effective energy resolution is hereby enhanced to 40 meV. Fig. 13 shows recovered quasi-particle spectral densities (a, cl in comparison with the original IPE spectra from Fig. 12 (b, d) for two different temperatures. The spectral densities clearly reveal a pair of spin-split bands which collapse on approaching the Curie temperature, confirming the qualitative interpretation given above. Moreover, no evidence is found for the development of complex line shapes with increasing temperature at this specific point in k space. This result is in accord with calculations of the temperature-dependent quasi-particle band structure [181]. There is no significant indication of extraordinary peaks at any energy for all temperatures. In addition, AE,, was determined as a function of temperature as shown in Fig. 14. The data follow nicely the resealed experimental bulk magnetization curve [193] and are in perfect agreement with the theoretical results of the generalized Hubbard model [181]. The theory predicts a ground-state splitting of 252 meV for the magnetic Z, band, while the extrapolated experimental value is 280 + 50 meV. In conclusion, even for the magnetic Z, band strong evidence of collapsing band behaviour was found in contrast to predictions of the LBT. Nevertheless, an extremely valuable experimental supplement to the IPE data would be PE data on the temperature behaviour of the majority Z, band. Since the integral IPE intensity does not change with temperature, one expects considerable PE intensity whose line-shape changes as a function of temperature would be of interest. Summarizing all (IlPE results reported so far yields an important result. No clear indication of a stationary exchange splitting independent of temperature has been found. Due to

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many-body effects the line shapes become complex with temperature at some k points, but the exchange splitting probed by (IlPE unambiguously decreases with temperature. Even a magnetic band does not exhibit a temperature-independent AE,,. Does this mean that the LBT must be rejected? Not necessarily. It may only mean that the amount of short-range magnetic order in nickel at and above T, is small enough to prevent the local magnetic moments from showing up in the (1)PE spectra as a temperature-independent AE,. This conclusion is somewhat disillusioning. Since model calculations starting from different limits often expect similar results [194], (1)PE is not able to distinguish unambiguously between different models. Another difficulty lies in the fact that no material-specific calculations within the LBT and DLM models for identical k points are available that could be directly compared. The most striking theoretical results so far have been obtained by approximate many-body calculations within a generalized Hubbard model that describe all available spectroscopic data very well [131,132,184]. In conclusion, the experimental data are compatible with both a temperature-dependent exchange splitting Al?,, which is likely to vanish at T, and a temperature-independent local AE,, with only small amounts of magnetic order at and above T,. It becomes clear that the theoretical description of the temperature behaviour of ferromagnetic nickel with its small AE,, and strong d-d correlations is too complex to be described within a simple model, a not at all novel conclusion [177]. The question remains why data obtained by electron-energy-loss spectroscopy, which is a k-integrating method, suggest a temperature-independent A E,,. Still, one must admit that the asymmetry data of the energy loss show a rather broad feature, difficult to assign to an average A E,,, in particular with increasing temperature where the asymmetry decreases [165,53]. Nevertheless, a vanishing AE, is expected to show up somehow in the data. All in all, one is not mistaken in emphasizing the fact that spin-resolved (1)PE data have contributed the most direct and detailed, i.e. k-dependent, information on the temperature behaviour of the exchange splitting AE, in nickel.

4. Surface electronic states 4.1. Crystal-induced surface states So far, the discussion of (1)PE results has been focused on electronic states characteristic of the bulk material that can be described by bulk band structure calculations. Since ferromagnetism is a phenomenon of collective order, modified properties are expected when the dimensionality is smaller than three, which means lack of translational invariance in certain directions and reduced number of neighbouring atoms. The report of magnetically “dead” layers at the surface of nickel films [195] attracted a lot of interest. During the following years numerous theoretical and experimental studies dealt with the magnetic properties of nickel surfaces. Soon it became clear that the “dead” layers were caused by surface contamination. It is now well established that the low-index nickel surfaces are magnetically “alive” (see, for example, Refs. [196,50,197,140,198]). Theoretically, early slab calculations found a substantial decrease of the surface magnetic moment compared with the bulk moment [199]. Since then, the computational methods have been improved and there is now general agreement that the surface magnetic moment is increased relatively to the bulk moment [200-204,121. Going from

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bulk nickel to the (001) surface, then to a linear chain and finally to the free atom, the magnetic moments are 0.56, 0.68, 1.1 and 2.0 pn [204]. The cause of the enhancement is d-band narrowing and sp-d dehybridization resulting from the reduced number of nearest neighbours. For Ni(llO), (001) and (111) the enhancement of the magnetic moment in the surface layer compared with the centre (bulk) layer of the slab is calculated as 13% [205], 23% [203], and 9% [206], respectively. Because of the close-packed character of the (111) surface, the enhancement is smallest for this surface. The fact that the (110) surface exhibits a smaller enhancement than the (001) surface demonstrates that surface magnetism depends not only on the coordination number, but also on details of the atomic arrangement [12]. Changes in symmetry and coordination number at the surface also lead to changes of the electronic structure [207]. Bulk electron wave functions exist with periodically varying amplitude throughout the crystal. In the surface region the states are reflected by the vacuum barrier. In contrast, true surface states are characterized by wave functions which decay exponentially into the solid as well as into the vacuum, hence being confined to the surface region. Consequently, they are two-dimensional states which exhibit E(k,,) dispersion, but do space, not show any dependence on k I. They are restricted to regions in energy-momentum where no bulk states of the same symmetry and spin quantum number exist. Consequently, they appear in gaps of the projected bulk band structure with given symmetry and spin character. Surface resonances are defined as electronic states which have an enhanced amplitude of their wave function at the surface, but they mix with bulk states of the same symmetry and spin. Therefore, they are not as confined to the surface region as true surface states and do not appear in gap regions of the projected bulk band structure. Describing bulk and surface electronic structure in a tight-binding approach leads to surface states split from fairly localized states. Good approximations of these Tamm states [208], as they are often called, are surface core levels and surface states split off narrow d-bands. A description in a nearly-free-electron model leads to energy gaps caused by the hybridization of crossed bands. Surface states located in hybridizational band gaps are called Shockley states [209-2111. Both kinds of surface states depend critically on the bulk electronic structure of the material and are therefore called crystal-induced surface states (SS). Studying the exchange splitting of surface states at ferromagnets helps to develop a microscopic picture of the magnetic properties within the uppermost layers. Spin-dependent calculations of the electronic structure of nickel surfaces predict a number of exchange-split surface states [212,213,200-2031. Surface states occurring on low-index metal surfaces have also been analyzed by means of a combination of a multiple-reflection model and nearly-free-electron theory [214-2191. Surface states are viewed as standing waves trapped between the surface barrier and the bulk crystal, provided there is a bulk band gap. Bound surface states exist by multiple reflection between the two barriers. A nearly-free-electron two-band model is used to describe the semi-infinite periodic crystal. The surface barrier is given by the image potential decaying as l/42 towards the vacuum level. A simple connection between the two is, for example, a flat potential of given depth and width. In many calculations saturated image-potential barriers have been used as model barriers that provide for smooth continuity between inner potential and image-like behaviour [220]. The amplitude of the reflectivities of the crystal and surface barrier are represented by rc e’@c and rB ei@B, respectively. The total amplitude of the wave after an infinite number of reflections then becomes (1 - rCrB eic@c+@B))-l. r and @ denote the

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reflection coefficients and phase changes, respectively. A pole in the expression appearing for rB = rc = 1 and @u + ac = 2~11, where n is an integer, describes a bound surface state. The condition may be met by a rapid variation of either @u or Qc as a function of energy. Surface states induced primarily by a rapid variation of Gc (CD,) are therefore called crystal-induced (barrier-induced) states [215]. The simple model gives fairly good predictions for both kinds of surface states [217-2191. The barrier-induced image potential states are the subject of Section 4.2. Since ferromagnets are described by two subsystems, namely the minority- and the majority-spin system, one can apply the model to the two spin systems separately. Usually, the image-potential surface barrier is assumed to be spin-independent in these calculations [73]. In this approximation, the exchange splitting of surface states is only a consequence of the spin-split band-gap boundaries. Experimentally, a spectral (1)PE feature is identified as a surface state if three requirements are met: no dependence on k I, sensitivity to changes of surface conditions, and appearance in a gap of the projected bulk band structure as described above. IPE performed in an isochromat mode is not able to check for the first criterion. Only by means of a monochromator can the dependence on k ,_ be investigated. The same is true of PE when synchrotron radiation is used instead of a monochromatic light source. In the meantime, however, the wealth of experimental and theoretical information has grown so much that the identification of surface states in (I)PE spectra is unambiguous in most cases. PE experiments detected surface states just below the Fermi level E, on all low-index surfaces of nickel. An sp-like surface state of A, symmetry was found on Ni(ll1) with a binding energy of 0.25 eV at l? between the bulk states L,, (-0.15 eV) and L,, (- 0.9 eV> [221]. It disperses downwards in energy with increasing k,,. Two studies report on truly magnetic surface states on Ni(001) [222,143]. One feature originally interpreted as a majority surface state around F [143] had to be re-interpreted as minority bulk emission on the basis of spin-resolved PE data [llO]. The other ones appear in symmetry gaps of the majority (minority) spin system -around the M (x) point. It appears that there is an odd majority surface state in the TM direction and an even minority surface state in the ?;x direction. It is not clear, however, why the majority counterpart of the surface state around x was not observed experimentally, yet expected by calculations [212]. In any case, a spin-resolved study would shed more light on this issue. A surface state on Ni(ll0) at the S point was observed as a two-peak structure at T = 100 K, which was interpreted as minority- and majority-spin emissions with a magnetic exchange splitting of 300 &-20 meV [223]. With increasing temperature, collapsing band behaviour similar to the bulk-band behaviour discussed in the foregoing section was observed. No conclusion can be drawn on the surface magnetic moment, which is predicted to be different from the bulk moment, because the observed splitting is equal to the size of AE, of the bulk bands from which the surface state is derived. There are as yet no spin-resolved PE data on surface states of nickel. In nickel, where the d-bands are almost completely occupied, empty surface states are expected to appear in hybridizational sp-band gaps. The X,, + X, band gap (see Fig. 7) associated with reciprocal lattice vectors of the (0,0,2) type occurs at I on Ni(001) and X on Ni(ll0). The second band gap spanning_from L,, to L, is associated with reciprocal lattice vectors of the (l,l,l) type. It appears at I on Ni(lll), partially at x on Ni(OOl), and at ‘j7 on Ni(ll0). This gap is traversed by the d-band of L, symmetry in nickel. However, the d-band is

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28.5

Ni(ll0) FTT s

.Z

5

0

I

2

4

6

I

1

I

5.0

6.0

7.0

E-E,

8

(eV)

Fig. 15. Spin-resolved IPE data (Aw = 9.6 eV) of the crystal-induced surface state SS on Ni(ll0) around x. Inset: Spin-integrated overview spectrum. Emission of SS is emphasized by filled symbols in the inset (from Ref. [118]).

of different symmetry and cannot mix into the L,, + L, gap states. Both gaps are Shockley-inverted, which means the gaps are p-like at the bottom and s-like at the top. This has important consequences for the magnetic exchange splitting of surface states because the s-like states can mix with the magnetic d-states, while this is symmetry-forbidden for the p-like states. The gaps and their dependence on k,, are shown as nonhatched areas in Fig. 8. Inspecting the E(k,,) plots for observed emissions within the gaps reveals three surface bands labeled SS. The barrier-induced image-potential states are labeled IS (see Section 4.2). . Ni( 1 lo>-% The first spin-resolved measurements on exchange-split surface states, occupied or empty, were performed with IPE on Ni(ll0). The surface band SS around % on Ni(ll0) appears about 6 eV above E, almost in the middle of the X,, + X, band gap. It was identified by IPE [152] and theoretically confirmed by calculations within the multiple-reflection model [157], but at 7.15 eV. It should be mentioned that the second calculated surface state within this gap just above the lower band-gap boundary has not been observed experimentally. Still, the transition B,, close to the gap boundary may contain some surface contribution. Fig. 15 displays -spin-resolved IPE data of SS recorded for 0 = 45” in the TX azimuth [118]. The inset presents a spin-integrated overview spzctrum featuring B, close to E,, B,, at 3.6 eV and SS at 6.1 eV. k,, for SS corresponds to 1.2 A-‘, close to x. The spin splitting of SS has been determined for, 0 = 45”, 55” and 65” as 170 f 30 meV. Since SS is stationary in energy as a function of k,,, the spin splitting is identical to A E,,. Even though the lifetime broadening is considerably larger than the magnetic splitting, AE, could be deduced from the partial spin spectra. The critical points terminating the gap, the p-like X,, point and the s-like X, point with considerable sd

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hybridization, have been calculated to be exchange-split by 80 and 200 meV, respectively [163]. Experimentally, an exchange splitting of 230 + 70 meV was found for the X, point [160]. No calculation so far has predicted any value for A E, of SS. The size of the observed A E,, is of the same order as the splitting of the band-gap boundaries. As a consequence, it can safely be concluded that the first atomic layer of Ni(ll0) is magnetically “alive”. However, without additional information on the penetration depth of the wave function of SS and the influence of the two band-gap edges on the size of its exchange splitting, no estimate of an enhanced magnetic moment at the surface can be given. Nevertheless, in view of the large splitting a slightly enhanced magnetic moment at the surface, as predicted by calculations [205], may not be unreasonable. . Ni(OOl)-X: On Ni(001) an exchange-split empty surface band at about 4.5 eV at the surface Brillouin zone boundary X was already predicted by early thin-film calculations [212]. A self-consistent slab calculation found the free-electron-like surface state at about 5 eV with an exchange splitting of about 250 meV [203]. Experimentally, the state was detected as a weak spectral feature 5.5 eV above E, by IPE using an angle-integrating photon detection geometry [152]. Calculations within the multiple-reflection model reproduced the state at 5.26 eV above the Fermi level [157]. Recently, spin-resolved IPE allowing different photon detection angles succeeded in resolving the surface state SS on Ni(001) (see Fig. 8) as a strong spectral feature with an exchange splitting of 180 + 60 meV at 4.7 eV [158,160]. Spin-dependent calculations based on the multiple-reflection model estimated the exchange splitting to be about 200 meV [160] due to the upper band-gap edge L,, exchange-split by 230 meV [163]. Fig. 16 displays spin-resolved IPE data of SS for an angle of electron incidence on Ni(001) of 50” (left panel) together with calculations within the one-step model of IPE (right panel) [161]. The one-step calculation reproduces not only the exchange splitting well, but even details of the line shape. The minority-peak width is slightly larger than the majority one, both in experiment and calculation. The shorter lifetime of the spin-down state follows from the slightly higher energy

Ni(O0 1)

crystal-induced

state FR 0=50”

F

min

maj

ss

I

4.0

E-EF

5.0

(eV)

6.0

4.0

E-EF

5.0

I

6.0

(eV)

Fig. 16. Measured (left panel) and calculated (right panel) spin-resolved IPE spectra (ho = 9.4 eV) of transitions into the crystal-induced surface state SS on Ni(OO1) around x (from Ref. 11611).

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above E, and from the high density of minority d-holes just above the Fermi level [224]. The asymmetric line shape, broader to higher energies, is a result of the shorter lifetime, the closer SS gets to the gap edge. Concerning the size of the measured exchange splitting, it should be kept in mind that the experimental data were taken at elevated temperatures to avoid the influence of closure domains at the surface. According to the surface magnetization data in Ref. [112] the surface magnetization was reduced by an estimated 20% compared with the bulk magnetization at T = 0. Provided AE, scales with the magnetization, the T = 0 exchange splitting for SS may be extrapolated to be as large as 225 f 40 meV. The trend that A E, is larger for the surface state on Ni(OOl)-X than for the state on Ni(llO)-x can be understood as a consequence of their energetic distances to the sd-like upper band edges. The splitting is larger the closer SS is to the upper band-gap boundary. The difference in exchange splitting may also be an indication of an enhancement of the surface magnetic moment, which is expected to be larger for Ni(001) than for Ni(ll0) [203,205]. Detailed surface state calculations are necessary to clarify this question. . Ni(lll)-F: The observed exchange-split surface states definitely rule out the existence of magnetically “dead” surface layers on Ni(ll0) and Ni(001). Still, they do not directly contribute to the surface magnetic moment, because they are completely empty. Ni(ll1) was the first ferromagnetic surface where a surface state contribution to the magnetic moment was detected. Crystal-induced surface states on (111) surfaces of face-centred-cubic (fee) metals form at the bottom of the L,, --) L, sp-band gap and, depending on the material, they are either occupied (Cu, Ag, Au) [225] or empty (Pd) [226,227] at the centre of the surface Brillouin zone I;. With increasing k,,, they disperse to higher energy and, in the event of overlap with bulk bands of the same symmetry, they become surface resonances [228]. For nickel the situation is not as clear. The L,, + L, gap ( -0.9 + +6.0 eV) is traversed by the uppermost d-band (L3 t: -0.15 eV, L : +0.16 eV> [221]. The occupied sp-like surface state just below E, has already been d&&ribed. It disperses downwards in energy for k,, + K [221]. An unoccupied surface state was theoretically predicted [229], but not observed in early IPE experiments on Ni(ll1) [150]. Later, however, an empty surface resonance dispersing upwards in energy for k,, + M, a’ was detected [152]. From the spin-averaged measurements at T, it could not be decided whether the emission close to E, is due to transitions into minority d-states and/or into a surface state. Often the intense IPE peak from Ni(ll1) just above E, has been simply interpreted as the nickel d-band (the latest example is Ref. 123011.From a theoretical point of view, the number of surface states that may exist at r for a general shape of the surface-potential barrier at an fee (111) surface is not known [156]. If there are two surface states, then both are expected to have A, symmetry. Fo_r a rectangular surface potential the calculations predict only one (occupied) surface state at I, while for finite k,, two surface states coexist. Spin-resolved IPE capable of distinguishing between mino_rity-d-band and surface-state emission was applied to clarify the so far unresolved situation at I on Ni(ll1) [114]. An important observation is made by comparing the IPE intensities close to E, for Ni(ll0) in Fig. 9 and for normal electron incidence on Ni(ll1) in Fig. 11. While the spin-integrated emission intensities close to E, are almost the same, the spin-resolved data of Ni(ll1) exhibit considerably smaller spin asymmetry. Since at T = 0 no empty majority d-states are available in

288

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k,,@-'b[ilO]

-Fig. 17. E(k,,) diagram for Ni(ll1) in the TK azimuth: occupied surface state SS’ (open circles) [221], empty surface state/resonance SS (closed circles, spin-integrated) and bulk sp-band transition B,, (triangles, spin-resolved). The band-gap boundaries as well as calculated final-state energies of B,, are given by solid (dashed) lines for the majority (minority) spin system. The nonhatched areas define gap regions of the projected bulk band structure (from Ref. [1141).

nickel, one can safely conclude that at least the observed majority emission from Ni(ll1) at E, does not originate from transitions into d-states. One might suggest that the emission is due to transitions between sp-like bulk bands with their smaller exchange splitting compared with d-states. The hypothesis has been tested by angle-resolved measurements in the ?;K azimuth. A selection of spectra is shown in Fig. 11. The results are summarized in an E(k,,) plot shown in Fig. 17. SS’ (open circles) denotes the occupied surface state measured by PE [221]. Indirect transitions into empty minority d-states (included in Fig. 8) appearing with small intensity independent of k,, are not shown in the diagram. Apart from them, two prominent features SS and B,, are observed above E,. With increasing k,,, SS disperses upwards in energy while losing intensity and broadening the more it overlaps with bulk stttes. For finite k,,, SS represents the already observed surface resonance [152]. For k,, 2 0.15 A-‘, feature B,, crosses E, from below, first for spin-down (open triangles), then at larger k,, also for spin-up electrons (closed triangles). Bsp, already discussed in Section 3.1, is well described by calculations within a combined interpolation scheme (dashed and solid lines in Fig. 17). Note that for k,, around F this transition is well below E, and does not contribute to the IPE intensity. As a consequence, the observed strong IPE intensity from Ni(ll1) close to E, around f; does not originate from transitions between sp-like bulk states either. To clarify the origin of feature SS in the vicinity of r, its sensitivity to surface contamination was checked. Spectra for clean and contaminated Ni(lll), i.e. exposed to 0.9 L of CO (1 L = lop6 Torr - s), are shown together with their difference spectra in panel (a) of Fig. 18. The remaining feature close to E, on the contaminated surface exhibits high spin asymmetry. Therefore, it is interpreted as originating from indirect transitions into minority d-states, which are known ‘to be not very surface-sensitive [18]. The spin-resolved difference spectra reveal a surface-sensitive feature with spin-split high-energy, but identical low-energy flank. This result provides evidence of the interpretation of SS as an exchange-split surface state which is cut off by the Fermi function at least for the majority part and therefore only partially empty/ occupied. To deduce the exchange splitting of SS, measurements for off-normal electron incidence were

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E -E,

289

(eV)

Fig. 18. Spin-resolved IPE spectra (ho = 9.4 eV) of Ni(ll1) for normal electron incidence (a) and 0 = - 12” (b): clean surface (open and closed circles), surface exposed to 0.9 L of CO (dashed and solid lines) and difference spectra (open and closed squares). The spectra have been normalized to equal background intensity (from Ref. [1141).

performed, where SS appears completely above E, in both spin channels. Panel (b) of Fig. 18 displays spectra taken at 0 = - 12” for clean and contaminated Ni(ll1) recorded at a different photon detection geometry than the one used to obtain the data shown in Fig. 11. The photon detection angle was chosen within the experimental constraints (see Section 2.4) such that the spectra are not influenced by transition B,, due to photon polarization effects. The difference spectra reveal SS well separated from the background and d-state intensities. Fitting them with Gaussian functions (solid lines through the data points) determines a magnetic exchange splitting of 106 + 22 meV (for 0 = - 12”). Analyzing the angular distribution of the emitted photons to characterize the symmetry of SS at T shows increasing photon intensity with increasing photon take-off angle relative to the surface normal. The observed z polarization proves SS to have A, symmetry. Consequently, it is derived from the p-like L,, point rather than the d-like L, point. It is a true surface state in a symmetry gap at f;, derived from the p-like gap boundary of symmetry L,, as its occupied counterpart SS’. The exchange splitting of SS is of the same size as the splitting of the band edge [163]. With increasing k,, and therefore reduced symmetry, SS develops into a surface resonance overlapping with bulk states of the same symmetry.

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290

Table 1 Exchange splitting of empty crystal-induced

Ni(llO)-x Ni(OOl)-x Ni(lll)-T

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surface states on nickel

AE,, (meV)

T (K)

Ref.

170*30 180 f 60 - 100

300 -400 300

[1181 [1601 11141

On the basis of spin and angular resolution, the high IPE intensity observed for normal electron incidence on Ni(ll1) is predominantly ascribed to a partially occupied surface state. This finding together with an observed magnetic exchange splitting of about 100 meV identifies this state as a truly magnetic state contributing to the surface magnetic moment of Ni(ll1). In conclusion, three empty exchange-split crystal-induced surface states have been detected by spin-resolved IPE on the low-index surfaces of nickel, summarized in Table 1. One of them directly contributes to the surface magnetic moment. Since the experiments give information on specific points in k space rather than averaging over the whole Brillouin zone, no quantitative conclusions about possibly enhanced surface magnetic moments can be drawn. All crystal-induced surface states under investigation exhibit exchange splittings similar in size to the splittings of the band-gap boundaries which the surface states are derived from. One further aspect has to be considered. A reduced exchange coupling at the surface, as predicted by theory and observed in experiment [231,40], leads to a reduced surface magnetization at finite temperatures, although the T = 0 surface magnetic moment may be enhanced compared to the bulk moment. In this case, no enhanced surface magnetization is expected at room temperature, where the data were taken. Electronic states like the one on Ni(lll)-?;, located at the interface crystal/vacuum, partially occupied, and spin-split, are an extremely sensitive tool for the study of magnetic properties at surfaces/interfaces. In particular, they are a sensor of changes of the exchange coupling caused by adsorption or deposition of another material (see Section 4.3). 4.2. Image-potential-induced surface states Electrons may, also be found in a different kind of surface states whose wave functions are localized a few A in front of the surface. An electron approaching a conductive surface feels the attractive force of its own image potential, created by the polarization charge it induces at the surface. Provided the reflectivity of the surface is high, i.e. there are no bulk states present to which the electron can couple, which is true in the case of a bulk band gap, the electron may be trapped between the bulk crystal barrier and the image-potential surface barrier. Owing to the long-range nature of the Coulomb potential, this gives rise to a Rydberg-like series of bound states, the image-potential-induced surface states US) [215,216,232,233]. In a one-dimensional approximation, with z being the direction normal to the surface, the image potential is given by V(z) =

--&-&. 0

(19)

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291

For an infinite crystal barrier at z = 0 the binding energies of the Rydberg-like series of states with respect to the vacuum level Ev are Ev-E(n)=Ry/16n2=0.85eV/n2, The image states are Deviations from these image state relative to free-electron-like with E(k,,) =E(n)

n=1,2,...

(20)

pinned to the vacuum level with binding energies of less than 1 eV. hydrogen-like energies occur, depending on the energy position of the the band-gap boundaries. Parallel to the surface their E(k,,) dispersion is effective masses m*/m usually close to 1:

+ ?+/2m*.

(21)

The multiple-reflection model combined with a two-band approximation to model the crystal reflectivity gives a good description of these surface states [217-2191. Unlike crystal-induced surface states, whose wave functions peak predominantly within the topmost atomic layer, the image-potential states are located a few A outside the surface, therefore only slightly overlapping with bulk states. As a consequence, typical linewidths of the states are only some tens of meV, reflecting their long lifetime [234,235]. In addition, image states are not expected to show spin splittings of the same size as bulk states or crystal-induced surface states. The unique characteristics of image states make them an interesting probe of magnetic properties at the very surface. Common surface-electronic-structure calculations, however, do not reproduce the image states, because the popular local-density-approximation neglects long-range correlations. Only recently, first-principles calculations including these correlations succeeded in producing an image-like surface barrier and describing the image states, but so far only on nonmagnetic surfaces [236]. Since image states are located in an energy region above E, and below Ev, they are inaccessible to ordinary PE. Thus, the first direct spectroscopic observation was made by IPE. A weak spectral feature at an energy within a bulk band gap and just below Ev exhibiting free-electron-like E(k,,) dispersion, it was proposed, should be interpreted as an image-potential surface state [237]. Shortly afterwards, n = 1 image states were uniquely identified by their pinning to Ev, their photon-emission characteristics, their temperature dependence [238], and their independence of k I [239]. During the following years, image states were observed on a large variety of conductive surfaces [228,240,241] and their systematics has been analyzed in great detail [219,232]. Even with no bulk band gap available, i.e. small reflectivity at the crystal surface, weak spectral features have been observed, originating from resonant bound surface states due to the image potential [242,243]. Two-photon photoemission (2PPE) measurements [244-2471 with their considerably higher energy resolution compared with state-of-the-art IPE were able to resolve the first three members of the Rydberg series as well as their lifetime broadening [248,249]. As a result of the lack of spin resolution, however, 2PPE failed to detect any spin splitting because the intrinsic linewidths turned out to be larger than the spin splittings. Nevertheless, upper limits for possible spin splittings of the rz = 1 image states were deduced from fitting procedures [249,250]. On the low-Miller-index surfaces of nickel, image-potential surface states can be expected on Ni(001) and Ni(lll), whereas on Ni(ll0) no bulk band gap in the vicinity of E, provides high surface reflectivity for normal electron incidence. Accordingly, strong image-state emission was observed from NXOOl) and NXlll) and only weak emission from Ni( 110) around T [152].

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Owing to the gaps at x and Y, image-state emission from Ni(ll0) shows up around the zone boundaries [151,118,154], well described by calculations within the multiple-reflection model [157,218]. The experimentally observed image-state dispersions are summarized in Fig. 8 as solid lines labeled with IS. For Ni(001) the effective mass m*/m was found close to 1 (1.2 f 0.2 [152], 0.95 + 0.15 [160]). The effective mass of the image state on Ni(ll1) was the subject of discussion because the first IPE study reported a large value of 1.6 + 0.3 [152]. A number of more recent experiments, however, agreed with one another in finding a value close to 1 (2PPE: 1.0 + 0.1 [251], 1.12 + 0.06 [252]; IPE: 1.05 f. 0.05 [153]). It is not clear yet what caused the large effective mass in the early experiment. Model calculations showed that finite angular resolution of the experiment can be excluded as a possible reason [153]. It should be kept in mind, however, that the peak determination of image-state emissions in IPE is hampered by the limited energy resolution, which is particularly true of measurements for off-normal electron incidence, where the intensity of IS decreases. In addition, the first IPE experiment was performed with an energy resolution of 0.7 eV only, smearing out the whole Rydberg series to a single step-like emission feature even at normal electron incidence. Recent IPE measurements in an apparatus carefully shielded from any magnetic fields and using a picture-frame single crystal with minimal stray fields confirmed the effective mass to be close to 1 [162]. From theory, the effective mass for small k,, is expected to be very close to unity independently of the particular surface [232]. Since the binding energies of the image states depend on the position relative to the band gap, considerable deviations from m*/m = 1 are only expected for image states close to gap edges [253]. In the case of Ni(lll), however, the image state appears more than 1.5 eV below the band edge, leading to an expected effective mass of almost unity [251]. A possible exchange splitting of image states is the result of two effects. First, electrons in image states are scattered from a spin-dependent crystal potential. The spin splitting is larger the more the image-state wave function overlaps with the substrate. This results in a larger spin splitting for image states close to the band edge compared with states in the middle of the gap whose wave functions exhibit small penetration into the bulk. Describing image states in the multiple-reflection picture gives a monotonic increase of the binding energy for states moving higher in the bulk band gap. The hydrogen-like binding energy is reached for states at the top of the gap [232]. Due to the spin-split band edges in ferromagnets the image states lie higher in the gap, i.e. closer to the upper band-gap boundary, for majority than for minority electrons, resulting in higher binding energies for spin-up compared with spin-down image states. The ferromagnetic exchange splitting is transferred from the substrate to the image states. This substrate contribution was first considered by one-step-model calculations to predict the exchange splitting of image states on Fe(ll0) [73]. It was also noted that AE,, in general is k-dependent as a result of spin-dependent effective masses. Further calculations along these lines for k,, = 0 yield an exchange splitting of about 10 meV for the n = 1 state on Ni(001) [161] and 27 meV for the state on Ni(ll1) [254]. The different values are accounted for by the energetic position of IS relative to the band edges. While IS on Ni(001) lies about 5 eV below the band-gap boundary, it is less than 2 eV for Ni(ll1) (see Fig. 8). Estimates based on the multiple-reflection model give values of 11 and 20 meV for Ni(lll1, depending on the assumptions made to describe the bulk bands [255]. The second effect has been neglected until recently: the exchange interaction near the crystal surface yielding a spin-dependent effective surface barrier experienced by the electrons outside the crystal. Calculations for Fe(ll0) show

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that the second effect is small compared with the substrate effect, but surprisingly of opposite sign [256]. The negative sign is a consequence of the negative spin density at the Fermi energy outside the surface due to a band-narrowing effect at the surface [257]. The main contribution to the exchange splitting of image states, however, is from the substrate. The linewidths of image states on ferromagnetic 3d metals have been found to be considerably larger than expected from simple considerations based on the penetration of the image-state wave functions into the substrate. 2PPE determined the intrinsic linewidths of the IZ= 1 image states on Ni(001) and Ni(ll1) as 70 f 8 [258] and 84 + 10 meV [249], respectively, much larger than the values of 20 to 40 meV obtained for noble-metal surfaces [247]. The penetration argument accounts for the relative difference between the linewidths for Ni(001) and Ni(ll1). To understand the absolute size of the linewidths, one has to take into account the large density of d-holes as possible decay channels. In addition, crystal-induced surface states with their quite large overlap with image states are responsible for Auger-type decay processes, which are assumed to even dominate the relaxation dynamics [259,260]. An Auger-type transition consists of an image-state electron decaying into an accessible empty state, accompanied by an electron-hole pair excitation. This explains in particular the short lifetime of IS on Ni(ll1) with its occupied and empty surface states around f;. For Ni(001) the predicted, but not experimentally confirmed empty surface resonance [157] may cause the short lifetime of IS. The fact that the lifetime broadening is considerably larger than the expected exchange splitting has important consequences. First, spin-integrated spectroscopies are not capable of resolving spin splittings of image states on nickel surfaces. Second, it is not possible to create a spin-polarized, two-dimensional electron gas at nickel surfaces by means of spin-selectively pumping the image state with a laser. Still, upper limits for possible spin splittings of the image states were deduced from high-resolution spin-integrated 2PPE measurements. With the use of fitting procedures, 35 meV was reported for Ni(001) [258] and 40 meV for Ni(ll1) [249]. IPE is constrained by its state-of-the-art energy resolution of typically 300 to 450 meV. By using the electron spin polarization as an additional experimental parameter, however, the detection of spin splittings is, as stated above, not limited by the energy resolution or intrinsic linewidths, because both partial spin spectra are recorded separately. To date, three spin-resolved IPE studies on the exchange splitting of image states are reported in the literature. On Ni(llO), where the image-state emission on the clean surface is weak due to the lack of a bulk band gap, the adsorption of sulphur produced a well pronounced image-state feature with a spin splitting of 32 + 13 meV [261]. Unfortunately, no surface electronic structure calculation for the Ni(ll0) + S system is available yet to evaluate this result. A study on clean Ni(001) indicated nonzero splitting of the n = 1 image state: 13 + 13 meV [160]. The first measurement of a significant exchange splitting on a clean ferromagnetic surface was performed on Ni(ll1) [82], whose results are described in the following. Fig. 19 shows a schematic potential diagram for Ni(ll1). It demonstrates the spin-split band-gap boundaries causing the image states to lie lower in the gap for the minority compared with the majority spin system. This is expected to result in slightly lower binding energy for the minority relative .to the majority image state. The surface barrier is shown as spin-independent, which is only an approximation as discussed above. IPE data for normal electron incidence on Ni(ll1) exhibit the II = 1 image-state emission as a clearly resolved peak at about 4.6 eV above E,. Closer inspection of the spin-integrated data,

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Vacuum 0

I 4

I

I)

8

12

-2.0

-1.0

0.0

1.0

Distance z [Al E-Ev(eV) Fig. 19 (left). Schematic potential diagram for image-potential surface states on Ni(ll1) indicating the image-potential barrier outside the crystal and the bulk sp-band gap between L,, and L, including the uppermost d-band of symmetry L, (from Ref. [82]). Fig. 20 (right). Spin-integrated IPE data (normal electron incidence, Ao = 9.4 eV) of the image-potential surface state on Ni(lll) (open circles). A convolution of the first three members of the Rydberg series plus background with a Gaussian function of (T = 195 meV fits the experimental data well (solid line through the data points) (from Ref. [1191).

given in Fig. 20, shows the image-state emission to be underlayed by an almost linear background (within the limited energy interval) with a step-like increase at the high-energy side of the peak. To model the IPE spectrum, one can take the information obtained by 2PPE on the binding energies and linewidths of the first three members of the Rydberg series [252,249]. Adding a linear background with a step-like increase at the vacuum level and convoluting the result with a Gaussian function fits the data well, as shown by the solid line through the data points in Fig. 20. This procedure also gives a good estimate of the apparatus function. It is approximated fairly well by a Gaussian function with cr = 195 meV (FWHM = 450 meV). A more detailed analysis of the apparatus function based on the maximum-entropy method gives a slightly asymmetric Gaussian function with sharply peaked evidence at o,eft = 183 meV and a,ight = 195 meV [119]. The assumed step-like increase at Ev is only a crude approximation neglecting the Rydberg series for IZ> 3. Strictly speaking, the surface density of states in the vicinity of Ev is strongly affected by the long-range Coulomb potential, giving rise to an infinite number of states below the vacuum level. Calculations show that the density of states goes continuously through the vacuum threshold to join the adjacent continuum [262]. There is no step-like increase directly at the vacuum level as proposed earlier [263]. Since the density of states smoothly joins the surface continuum states, in principle the vacuum level cannot be detected by IPE experiments [262]. As a result of modeling our IPE data, one can safely conclude that the prominent spectral feature originates from the n = 1 image state, while the

M. Llonath /Surface

4.2

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4.4

295

4.8

4.6

4.580

E-EF

(eV)

Fig. 21. (a) Spin-resolved IPE data (normal electron incidence, ho = 9.4 eV> of the image-potential surface state on NiOll). Inset: Spin-integrated overview spectrum. (b) Same data on an enlarged energy scale with the spin-dependent background offset suppressed. (c) Peak-position distribution for spin-up and spin-down image-state emission (from Ref. [82]).

higher members of the Rydberg series are part of the step-like increase just below the vacuum threshold. Spin-resolved IPE data of the image-state emission are displayed in Fig. 21a, revealing a small but significant magnetic exchange splitting. The background intensity reflects transitions of inelastically scattered electrons. It shows a spin-dependent, almost constant offset in the plotted energy interval. This spin dependence is due to the high spin asymmetry of the hole density close to E, serving as final states. The exchange splitting of IS is more obvious in Fig. 21b, which presents the data of Fig. 21a on an enlarged energy scale with suppressed spin-dependent background offset. The statistical uncertainty of the data points is within the size of the symbols. The observed linewidths of the minority and majority image states are

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almost identical, with the minority peak being marginally broader. This finding rules out the minority d-holes as dominant decay channel and supports the relevance of the sp surface states to the lifetime of the image states on Ni(ll1). The slightly higher energy of the minority image state and the lower majority density of surface states (see Section 4.1) implies a shorter lifetime of the minority image state. On the other hand, one expects slightly smaller bulk penetration for the minority state due to the larger distance from the band-gap boundary. The competing effects cannot be evaluated without further detailed analysis. To extract the size of the exchange splitting the peak positions of spin-up and spin-down emissions were determined by a least-squares fitting procedure. Since the n = 1 image state is known to have an intrinsic linewidth of 84 meV, the corresponding emission observed in IPE is dominated by the apparatus function, approximated by a Gaussian function. Both the n = 2, 3) . . . members of the Rydberg series and the step-like background increase are well reproduced by only one step function convoluted by the apparatus function. Therefore, a reasonable choice of fit function is a composition of a constant plus linear background, the described step function located just below Ev, and a Gaussian function representing the yt = 1 image state. The energetic position of the step function was allowed to shift to give the best fit. The results of the fitting procedure are shown as solid lines through the data points in Figs. 21a and 21b. The magnetic exchange splitting is determined as 18 + 3 meV [82]. This remarkable accuracy could only be achieved because all 70 data points per partial spin spectrum with up to 135 000 counts per point contribute to the peak-centre determination. Still, one may argue that a peak-position determination by a fitting procedure depends critically on the chosen fit function. By fitting the data with various other fit functions for the peak as well as for the background intensity, the absolute energy position of each partial spin emission varied within 30 meV. The relative difference between spin-up and spin-down peaks, however, was found to be between 18 and 20 meV provided the same type of fit function was used for both partial spin spectra. This reasonable assumption is supported by the experimental finding that both partial spin emissions exhibit almost identical shapes. The small error margins for AE, were confirmed by an additional test. 3000 pseudo-experimental spectra were produced by varying each measured data point randomly in accordance with the Gaussian distribution of its own statistical error. The fitting procedure described above was applied for each pseudo-experimental spectrum to determine its peak position. The resulting peak-position distributions for spin-up and spin-down emissions are shown in Fig. 21~. The well separated distributions impressively illustrate the confidence level of the determined spin splitting, which is a factor of 5 smaller than the intrinsic linewidth and a factor of 20 smaller than the experimental energy resolution [82]. At this point one might wonder why so far the asymmetry function has not been used as a sensitive indicator of a small spin splitting. Fig. 22 reproduces the spin-integrated data of Fig. 20 in the upper part and shows the corresponding asymmetry data (crosses) in the lower part varying from - 13.7% to -7.5% within the 3.5 eV energy range. The difficulty of extracting spin splittings from asymmetry data in case of spectral features underlayed by a spin-dependent background has already been discussed in Section 2.4. Here, the detection of a splitting is additionally hampered by the step-like background increase. Nevertheless, the asymmetry data exhibit a dip at an energy significantly different from the energy position of the image-state peak. This clearly indicates the existence of an exchange splitting (see Fig. 61, yet its size cannot be directly deduced. To estimate the size, simulated asymmetry data were produced. The

M. Donath /Surface

J....“‘..‘““‘” 3.0

297

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5.0

4.0

6.0

E - EF (eV)

Fig. 22. Upper part: Spin-integrated IPE data of the image state on Ni(ll1) (diamonds) and a least-squares fit (solid line). Lower part: Spin asymmetry (crosses) varying from - 13.7% to -7.5% within the shown energy range compared with simulated asymmetry curves (solid lines) obtained for three different splittings AE (from Ref. [82]).

least-squares fit curve through the IPE data in Fig. 22 was duplicated and an offset was added (subtracted) to get a “spin-down” (“spin-up”) spectrum with realistic background intensity. Shifting these two spectra against one another in energy simulates an image state with variable exchange splitting. Comparing the corresponding “asymmetry” curves (solid lines in the lower part of Fig. 22) for three simulated splittings (AE = 0, 20 and 40 meV) with the measured data provides evidence of an exchange splitting of the order of 20 meV, in agreement with the result obtained above. It should be kept in mind that this method is only applicable in the case of almost identical line shapes in the two spin channels. The almost constant spin-dependent background offset in the energy interval under consideration was an additional favourable circumstance. A summary of the few available experimental results on exchange splittings of image-potential states on nickel surfaces is given in Table 2 together with data of their binding energies and linewidths r. The splittings are mainly a consequence of the spin-split band-gap boundaries of the substrate. In agreement with expectation from theory, AE,, of the n = 1 image state on Ni( 111) is about 10 times smaller than the spin splitting of the band-gap boundary L, and the splitting of a crystal-induced surface state on Ni(ll0) appearing in the same gap (see Table 1).

Table 2 n = 1 image-potential-induced

Ni(OOl)-r Ni(1 11)-r

surface states on nickel

E, - E (eV)

I (meV>

AE,, CmeV) [2PPE]

AE,, (meV) lIPE1

0.61 f 0.03 [258] 0.80 f 0.03 [252]

70f 8 [258] 84 f 10 12491

< 35 [258] < 40 [249]

13f13 [160] 18f 3 [82]

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The measured splitting of 18 + 3 meV is in good agreement with the theoretical prediction of 27 meV [254] based on one-step-model calculations assuming the barrier potential as spin-independent. The somewhat larger theoretical value may be a consequence of insufficient treatment of electron correlations in the bulk band structure used. The theoretical prediction of a negative contribution of the spin-dependent surface barrier to the exchange splitting of image states [256] can neither be confirmed nor neglected on the basis of the results available. Image states on Fe with its considerably larger AE,, are more favourable candidates for testing the small influence of the surface barrier. 4.3. Adsorbate-induced changes Probing the spin-dependent electronic structure of clean nickel surfaces reveals that the three low-Miller-index surfaces are magnetically “alive”. Whether or not they exhibit enhanced magnetic moments compared with the bulk moment cannot be decided from studying the spin dependence of surface states at selected points in k space. The following discussion is focused on changes of surface magnetism, caused by adsorption of foreign atoms, and understanding them on the basis of the spin-dependent electronic structure. It has already been mentioned that in early experiments on nickel the detection of magnetism within surface layers was hindered by contamination, leading to the conclusion of “dead” layers [195]. After experimental evidence had been found for magnetically “alive” clean surfaces, a number of experiments tested their reaction to well defined adsorption of foreign atoms. The spin polarization of field-emitted electrons from a Ni(OO1) tip was observed to be reduced by hydrogen adsorption from - 3% to almost zero [264]. Electron capture spectroscopy from Ni(ll0) found a reduction of the spin polarization signal from -96% to -8% upon adsorption of one monolayer of hydrogen [265]. Chemisorption experiments with ferromagnetic resonance on thin nickel films reported on the existence of chemisorption-induced “magnetically dead layers”. One hydrogen atom was found to kill one nickel moment, one CO molecule the moments of two nickel atoms [266]. From spin-resolved secondary electron spectroscopy data of oxygen on Ni(ll0) two “dead” layers were deduced for the (2 X 1)-O reconstructed surface and even 3 to 4 “dead” layers for the oxidized surface [106]. Oxygen chemisorption on Ni(ll1) was studied by torsion oscillation magnetometry. A giant loss of 4.5 nickel magnetic moments per oxygen atom was found for the initial stage of chemisorption [267]. The experimental results conform to theoretical expectation [268]. A 90% reduction of the surface magnetic moment is, for example, predicted for Ni(OOl)-p(1 X 1)-H [231]. All cited studies agree with each other on the conclusion that, in general, adsorption of adatoms on nickel (as well as other ferromagnetic) surfaces considerably reduces their magnetic moment. Spectroscopies probing the spin-dependent electronic structure have been (and still are) searching for a direct relationship between primary magnetic quantities and electronic states. Spin-resolved (1)PE studies were concentrated on adsorbate-induced changes of the d-states, which are responsible for the magnetic properties of nickel. The d-states were expected to reflect the adsorbate-induced reduction of the magnetic moment. Adsorption of 1 L of 0 (CO) on Ni(ll0) caused a quite dramatic 35% (50%) decrease of the PE intensity originating from both S, and S, d-states [269]. In addition, a reduced AE,, was reported, which could only be described theoretically by assuming 3 to 4 magnetically “dead” layers at the Ni(ll0) surface

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[270]. A later, polarization-dependent PE study on Ni(llO)-(2 x 1)-O, capable of distinguishing between S, and S, states, reproduced the considerable intensity decrease, but did not detect any change of the exchange splitting of the S, d-band [271]. The S,, d-state emission was observed to be not significantly attenuated, but slightly shifted by 50 meV to lower binding energy. The minority S, counterpart is empty, and is thus not observable by PE. Another remarkable result of this study was the detection of depolarization effects, interpreted as due to exchange scattering in a ferromagnetically aligned adsorbate layer. Qualitatively similar results were obtained for Ni(llO)-c(2 X 2)-S, except that the S, t d-band emission was almost completely quenched [271]. As overall result of this PE study, adsorption was found to have no strong effect on the surface magnetism. The binding energies of the observed d-bands stayed almost constant, as did the exchange splittings. The photoelectron spin-flip scattering invoked to describe the anomalous PE line shapes even suggests a partially spin-polarized adsorbate layer. Such a considerable influence of spin-flip scattering on PE intensities, however, has not been reproduced by calculations so far [272]. In contrast to the results of this spin-resolved PE study of Ni(llO)-(2 X 1)-O, spin-integrated PE measurements of Ni(lll)-p(2 X 21-O found a small (6% to 17%) oxygen-induced reduction of AE,, for surface-sensitive band-gap emission from the S, band close to X, [273]. The discrepancy between the two results on the same band was traced back to the oxygen-induced (2 X 1) reconstruction of the Ni(ll0) surface compared with the nonreconstructed oxygen-covered Ni(ll1) surface. For symmetry reasons, the S,-band emission from Ni(ll0) is not expected to provide information on the uppermost nickel layers, which are predominantly influenced by the oxygen. Spin-resolved IPE studies of the chemisorption systems Ni(llO)-0 and -CO were focused on the intensity of direct transitions into the uppermost minority d-band. Similarly to the PE results, a strong decrease of the emission intensity was observed upon 0 [274] and CO adsorption [275]. It was interpreted as filling of the d-holes, hence reduction of the magnetic moment. In these studies the fact that the intensity of a bulk direct transition is not a direct measure of the density of states was neglected. Changed coupling conditions of the free-electron wave function to the Bloch state inside the crystal caused by the adsorbate were not considered as a possible reason for the chemisorption-induced intensity decrease. This issue will be addressed in more detail below. In summary, all PE as well as IPE studies dealing with the substrate d-bands detected a considerable decrease of emission intensities, while one PE study reported on a reduced exchange splitting. It should be kept in mind that PE and IPE do not exclusively probe the electronic structure of the first atomic layer, but also the states of some bulk-like layers underneath. In addition, adsorbate-induced modifications of substrate bands are expected to depend critically on their symmetry. One step further in the study of adsorbate-induced modifications of surface magnetic properties is to look at the substrate/adsorbate interface in more detail. From a chemical point of view, the adsorption of adatoms is characterized by adsorbate-substrate and adsorbate-adsorbate bonding. In general, adsorption is accompanied by structural relaxation or even reconstruction of the uppermost substrate layers. It is a nontrivial problem to describe the interplay between atomic geometry, electronic structure and magnetic behaviour. Chemical and structural changes at the surface certainly influence the surface electronic structure. The modifications depend on the bonding mechanism and, in general, are not easy to interpret. Adsorbate-induced changes appear in (I)PE spectra as energetic shifts and/or (dis)appearance

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of spectral features. Often, primarily surface-state emissions, but also bulk-state emissions of the clean surface, are simply quenched by adsorption. An exception is image-potential surface states (see Section 4.2), which are shifted according to the work-function change because they are pinned to the vacuum level. Their intensity depends on the surface reflectivity, which may be increased or, as observed in most cases, decreased by adsorption. In many adsorption systems additional spectral features appear which carry important information. The additional emission can stem from (anti)bonding states containing essential contributions from adsorbate electronic states. Detailed layer-dependent calculations are needed to ascribe the emissions to specific adsorbate-adsorbate or adsorbate-substrate interactions and thereby define their spatial origin. Provided the adsorbate forms an ordered overlayer or causes a surface reconstruction, adsorbate-induced spectral features can also simply be due to bulk band transitions via surface umklapp effects. The new surface geometry provides a new set of reciprocal lattice vectors which open additional elastic scattering channels for the incident electrons. The electrons may be diffracted to points in k space where bulk transitions occur that are not observable on the clean surface. Spectral emission due to surface umklapp effects give, however, no additional information on the adsorbate apart from the overlayer geometry. Fig. 23 shows surface Brillouin zones of an fee (110) surface with three overlayer geometries: (2 X l), (3 X 1) and c(2 x 2). Shaded areas indicate the surface Brillouin zones created by the overlayer geometry. The G,, vectors of the overlayer (arrows with dashed lines) lead to nonequivalent k points, where transitions between bulk bands may occur. Adsorbate-induced bulk emissions via surface umklapp have been observed with considerable intensity in PE [276,277] as well as IPE spectra [278]. As a consequence, adsorbate-induced spectral features have to be interpreted with care. For a general discussion of adsorption phenomena and the electronic structure of chemisorption systems, the reader is referred to the literature [279-2821. The purpose of this section is to analyze the spin dependence of adsorbate-induced changes of the electronic structure in order to arrive at conclusions which are of relevance for surface magnetic properties. With respect to surface electronic structure calculations, oxygen and sulphur on Fe(001) were the first chemisorption systems that were studied in detail, remarkable results on magnetism being obtained [283-2861. Exchange-split adsorbate-induced bands were found, which reflect magnetic moments induced at the adsorbate atoms. Furthermore, in the case of sulphur as adsorbate, antibonding surface states in the vicinity of E, were shown to play an important role in reducing the magnetic moment of the surface atoms of the substrate. Experimentally, spin analysis of Auger electrons provided evidence of nonvanishing magnetic moments at the adsorbate atoms, induced by hybridization of the electronic states of the adatoms with the spin-split bands of the ferromagnetic substrate (Fe(OOl)-0 [287], Fe(OOl)-S [288]). Intensive studies on the exchange splitting of adsorbate-induced states within the valence bands were performed by spin-resolved IPE on nickel surfaces [123,18] and by spin-resolved PE on Fe [289-2931 and Co surfaces [294]. They all agree in finding considerable exchange splittings of adsorbate-induced spectral features indicative of induced magnetic moments at the adsorbates. The bands under investigation were either completely occupied or empty, and thus do not directly contribute to the magnetic moments. Nevertheless, the studies provide a picture of the relationship between chemisorption and magnetism that describes the physics in more detail than simply by reduction of surface magnetization. In summary, there are

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(IlO)- c(2x21 Fig. 23. Surface Brillouin zones of the (110) surface of an fee crystal with (2 X l), (3 x 1) and ~$2x 2) superstructures (shaded areas confined by solid lines) in comparison with the original Brillouin zone (dashed lines).

two kinds of results which, on the one hand, seem to be at variance and, on the other, complement each other: magnetization measurements tell about strong reduction of the surface magnetic moment or even magnetically “dead” layers and studies on the electronic structure imply magnetic moments at the adsorbate atoms. . Ni(ll0) + 0, +S: In the following, the results of spin-resolved IPE studies on adsorbate-covered nickel surfaces are reviewed. Let us first look at the system Ni(ll0) + 0 in its various stages of dissociative oxygen chemisorption [295]. Fig. 24 displays spin-resolved IPE spectra for normal electron incidence for different adsorption geometries. With increasing oxygen exposure the LEED pattern shows at 2 L (1 L = 10V6 Torr - s) a (2 X l), at 10 L a (3 X 1) and at 40 L a (9 x 4) superstructure, until at much higher exposures a diffuse square (1 x 1) structure indicates the starting NiO formation. The (9 X 4) pseudo-oxide phase corresponds to one monolayer of NiO on the surface. The minority spectrum of the clean surface exhibits indirect transitions into d-states just above E, [118], but no further prominent structure apart from that. The majority spectrum is dominated by the step-like increase of the background intensity at the Fermi level. Two adsorbate-induced features A and A’ appear for the (2 x 1) phase,

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0

2

L

E-E,(eVI

Fig. 24. Series of spin-resolved IPE spectra (ho = 9.6 eV) together with the corresponding asymmetry (triangles) for normal electron incidence on Ni(ll0) with different geometries of oxygen adsorption.

data

which corresponds to a missing-row reconstruction of the substrate with the oxygen atoms sitting in slightly asymmetric long-bridge sites [296,297]. Feature A disappears for the structurally less defined (3 x 1) phase. The spectra for the (9 x 4) superstructure do not exhibit any features apart from the nickel d-band emission, whereas the starting NiO formation is characterized by a broad peak around 3 eV above E, known from earlier work [298,299]. The remaining d-state intensity as well as the spin asymmetry indicate that the formation of the antiferromagnetic oxide is still limited to the surface region. What can be learned from the data? The intensity of indirect transitions into empty minority d-states reflecting the density of states is only slightly reduced for the (2 x 1) and (3 x 1) chemisorption phases. Consequently, a substantial reduction of the density of d-holes cannot be deduced from the data as long as no oxide is formed. The slight increase of majority intensity just above E, with increasing oxygen coverage may indicate depolarization effects or a real increase in the majority density of states. The background asymmetry considerably decreases with starting oxide formation. With respect to the adsorbate-induced features A and A’, their origin has to be identified. Whether A’ represents antibonding states characteristic of Ni-0 rows, which are present in both geometries, or is due to sp-like bulk transitions via surface umklapp cannot be decided. An early study favoured the first explanation [3OO],whereas closer inspection of the bulk band structure in combination with the altered surface Brillouin zones in Fig. 23 reveals the possibility of the latter [18]. Bulk-band transitions are accessible via surface umklapp in both geometries. The spin splitting of about 150 meV for A’, deduced from the data of the (3 X 1) phase, is in accord with results for the corresponding bulk transitions.

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Fig. 25. IPE data (ho = 9.4 eV) of clean and oxygen-covered Ni(ll0) for normal electron incidence. Inset: Spin-resolved data of the adsorbate-induced feature A with the spin-dependent background offset suppressed (from Ref. [1231).

An explanation in terms of bulk transitions via surface umklapp does not hold for feature A at about 3.3 eV above E,. Therefore, A is a candidate that may give information on the adsorbate-substrate interaction. This is supported by E( k,,) measurements: A shows considerable dispersion in the direction of the nickel rows, but none perpendicular to it [300]. The interpretation as antibonding state is, however, questioned by considering the long-debated equivalent state observed for Cu(llO)-(2 x 11-O [301-3041. There now seems to be agreement that A on Cu represents a surface state modified by adsorption and backfolded to l! by the overlayer geometry [279]. The amount of antibonding character of the state is estimated to be small or negligible. Adopting this interpretation for A on Ni(llO)-(2 X 11-O limits its relevance to the adsorbate-substrate bonding. Nevertheless, A is an electronic state confined in the surface region that tells about the magnetic properties there. Spin-resolved IPE data of A recorded with improved energy resolution compared with the data of Fig. 24 are presented in Fig. 25. The exchange splitting of A is determined as 80 + 20 meV [123], about half the size of the exchange splitting of a crystal-induced surface state at x (see Section 4.1). This may indicate a reduced magnetic moment at the Ni(ll0) surface, but excludes the assumption of magnetically “dead” surface layers. The result is in agreement with calculations that report a reduced magnetic moment (by about 30%) of the first-layer nickel atoms, but also a small magnetic moment of about 0.1 pa picked up by the oxygen atoms [305]. The reduced coordination number of the nickel atoms within the Ni-0 chains strengthens their magnetic moment, so that the oxygen atoms fail to quench it completely. Fig. 26 shows the influence of oxygen and sulphur adsorption on the Z, + Z, transition into the uppermost minority d-band, which was already the subject of discussion in Sections 3.1 and

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Fig. 26. Spin-averaged (left panel) and spin-resolved (right panel) IPE data (hw = 9.4 eV) of Ni(ll0) taken at -0 = 25” in the TX azimuth for three different sample preparations: clean, (2 x 1)-O and c(2x 2)-S (from Ref. [19]).

3.2. While oxygen adsorption in the (2 X 1) phase has almost no influence on the intensity of indirect transitions (see Figs. 24 and 25), the emission from a direct transition is somewhat attenuated, possibly due to scattering at the adsorbate atoms. A much larger effect on the d-band transition is exerted by sulphur, which adsorbs on Ni(ll0) in the four-fold hollow site and forms a c(2 X 2) overlayer on the unreconstructed surface [306]. The sulphur almost completely quenches the direct transition. No energetic shift of the minority d-band, however, was detected for either adsorbate. A sulphur-induced feature at about 1.5 eV above E, exhibits a magnetic spin splitting of about 250 meV. Inspection of the bulk band structure for the YS direction (see Fig. 23) allows an interpretation as sp bulk transition accessible via surface umklapp [108]. The stronger impact of sulphur on the surface electronic structure of Ni(ll0) compared with oxygen is demonstrated by the quite different attenuation of the bulk transition. It may be due to the adsorption geometry of sulphur providing more overlap of substrate and adsorbate electron wave functions than in the case of oxygen, where the adatoms sit between the nickel atoms on the exposed nickel rows. It may, however, also indicate a different local bonding. Calculations for oxygen and sulphur on Ni(OOl), both in the same c(2 X 2) adsorption geometry, predict a more covalent bonding for S-Ni and a more ionic bonding for 0-Ni, resulting in a more reduced surface magnetic moment for sulphur (0.12 pa) [307] than for oxygen adsorption (0.45 p,J [308]. Sulphur is therefore called a prototypical adsorbate catalytic poisoner. The calculations predict that the t,,-type spin density is completely quenched due to the formation of S-Ni covalent bonds. This may explain the strong reduction of the IPE intensity originating from the uppermost d-band, yet observed for Ni(ll0). Recent calculations for Ni(llO)-c(2 x 2)-S also find a strong reduction of the magnetic moment of the first nickel layer to about 0.1 pB [309]. The quenching is found to be a rather local effect. In the next nickel layer below, the magnetic moment of the atoms directly below the sulphur atoms is reduced to 0.28 pB, whereas the other nickel moments retain a bulk-like value. Consequently,

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bands of different symmetry may exhibit quite different spin splittings. Detailed band structure calculations are necessary to evaluate the experimental IPE results for Ni(llOM2 X 2)-S, which show a variety of adsorbate-induced spectral features [18]. One further result on Ni(ll0) + S is worth mentioning. Target current spectroscopy data for normal electron incidence on Ni(ll0) exhibit a considerably enhanced surface reflectivity around E, with increasing sulphur coverage [261]. This gives rise to well pronounced imagestate emission in IPE for Ni(llO)-c(2 x 2)-S which is weak for the clean surface due to the fact that no gap of the projected bulk band structure provides sufficiently high crystal reflectivity in the important energy range around the vacuum level. Even more surprisingly, the image-potential state on Ni(ll0) with a c(2 X 21-S overlayer is found to be exchange-split by 32 + 13 meV [261]. This value is unexpectedly large for an image state at an adsorbate-covered surface with strongly reduced magnetic moment. It can only be understood by assuming a quite considerable penetration of its wave function into the bulk, therefore having strong interaction with exchange-split bulk states. Again, the results of the enhanced surface reflectivity upon sulphur adsorption confirm the strong influence that sulphur adsorption has on the surface electronic structure of Ni(ll0). . Ni(ll1) + 0: The results of oxygen and sulphur adsorption on Ni(ll0) provide detailed insight into adsorbate-induced changes of the spin-dependent surface electronic structure. Yet, they have not shown clear-cut evidence of a reduced surface magnetic moment being reflected in electronic-structural data. For the following reasons, the chemisorption system Ni(ll1) + 0 is a perfect candidate for studying the influence of an adsorbate on the spin-dependent surface electronic structure. First, a spin-split partially occupied surface state was detected on the clean surface, which directly contributes to the surface magnetic moment [114]. Second, a torsion oscillation magnetometry study reports on the decrease of about 4 nickel moments per oxygen atom for Ni(llGp(2 X 2)-O [267]. This is equivalent to about one magnetically “dead” nickel surface layer induced by an oxygen coverage of 0.25. Furthermore, the first determination of an empty adsorbate band dispersion E(k,,) was reported for the same adsorption system [299]. Fig. 27 displays spin-averaged and spin-resolved IPE spectra for normal electron incidence on Ni(ll1) as a function of oxygen exposure. A sharp p(2 x 2) superstructure in LEED was observed for an exposure of 6 L. The data of the clean surface exhibit two distinct features SS and IS, originating from crystal-induced and image-potential-induced surface states. They have been discussed in detail in Sections 4.1 and 4.2. With increasing oxygen exposure, IS loses intensity and shifts upwards in energy according to the oxygen-induced work function increase of about 0.9 eV for the p(2 X 21-O overlayer [299,311]. The intensity loss is caused by a reduced surface reflectivity which has been detected in target current spectra. In a fashion similar to IS, feature SS shifts continuously to higher energy as a function of increasing oxygen exposure. It is found 1.1 eV above E, for the p(2 X 2) overlayer, now being completely empty and no longer contributing to the surface magnetic moment. Spectra taken at different photon take-off angles show low intensity emitted normally to the surface and high intensity for large angles, indicating that SS keeps its A, symmetry. Remarkably, the development from partially occupied to totally empty is reflected in an intensity increase for small oxygen exposures, which can be seen by comparing the data for 2.3 L with the data of the clean surface (solid line in Fig.

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. maj. f%

0

2

E-EF

4

(eV)

0

min.

6

E -E,

(eV)

Fig. 27. Spin-averaged (left panel) and spin-resolved (right panel) IPE spectra (hw = 9.4 eV) for normal electron incidence on Ni(ll1) as a function of oxygen exposure. SS and IS denote emission features originating from crystal-induced and image-potential surface states, respectively. For reasons of comparison, the spectrum of the clean surface is included in the spectrum for 2.3 L in the vicinity of E, as a solid line without data points (from Ref. [31011.

27). In addition, the spin-resolved data show the Fermi level onset of spin-up and spin-down spectra slightly more separated for 2.3 L than for the clean surface. With SS shifted away from E,, a feature of mainly minority character remains close to E,, which is attributed to indirect transitions into minority d-states. For oxygen exposures larger than 6 L, the LEED pattern becomes less sharp and the spin-dependent electronic structure exhibits further changes (see spectra for 6.8 L), e.g. an increase of the majority intensity just above E,, which will not be discussed here. The continuous energy shifts of both IS and SS as a function of oxygen exposure are plotted in Fig. 28a. The results of angle-resolved measurements in the Fi? azimuth for the clean surface as well as for 3.8 and 6 L of oxygen, the latter corresponding to p(2 X 2)-O, are summarized in the E(k,,) diagram of Fig. 28b. The dispersions roughly follow the gap boundary of the projected bulk band structure. The effective mass m*/m increases from 0.4 for the clean surface to about 0.6 for the p(2 x 2) oxygen overlayer, the more the state moves away from the bottom of the gap. An additional experimental result has been obtained by IPE measurements with variable photon energy which prove SS to be independent of k I , showing its two-dimen-

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5.5 s 2

5.a

w: w L.5

ul -l-l7

n

k.. ..,(

0.2

ffi-’I,.

.

0.L

0.6

CilOl

Fig. 28. (a) Energy above the Fermi level E, of surface state SS and image-- state IS for normal electron incidence on Ni(ll1) as a function of oxygen exposure. (b) E(k,,) diagram of SS in the TK direction of the surface Brillouin zone. The solid lines through the data points for 0, 3.8 and 6.0 L of oxygen exposure are parabolas describing free-electron-like dispersions with effective masses m*/m = 0.4, 0.5 and 0.6, respectively. The white area denotes a gap of the projected bulk band structure (spin-averaged) (from Ref. [3101X

sional character [312]. All these findings lead to the conclusion that the adsorbate-induced feature at 1.1 eV above E, in the system Ni(lll)-p(2 x 2)-O represents a surface state modified by the oxygen adsorbate rather than an adsorbate band characteristic of the adsorbate-adsorbate or adsorbate-substrate interaction. Direct oygen-oxygen interaction can be excluded anyhow if one considers the distance of about 5 A between the oxygen atoms. In addition, for an adsorbate band characteristic of the ordered p(2 X 2) oxygen overlayer one would expect the appearance of a new feature at a fixed energy with increasing oxygen exposure, i.e. the more islands of the ordered overlayer are formed. SS, however, is apparently not sensitive to the local bonding of the adsorbate, rather it reflects long-range electronic effects. It develops continuously from the p-like crystal-induced surface state of the clean surface. This conclusion goes beyond the earlier interpretation of SS as adsorbate band [299]. One should keep in mind that the distinction between surface band and adsorbate band is somewhat artificial because both are localized at the surface. The label “surface state” just indicates its origin. Future theoretical work will have to explain the continuous energetic upwards shift and will hopefully evaluate to what extent SS contains antbonding character and where its wave function is located. Nevertheless, it represents an electronic state located at a ferromagnetic surface, serving as sensor of any adsorbate-induced magnetic changes. Measurements of the magnetic exchange splitting Al?,, of SS are shown in Fig. 29. Data of the clean surface in the lower part of the figure are reproduced from Fig. 18. Spectra for the p(2 x 21-O overlayer recorded for a similar angle of incidence (0 = 10”) are shown in the upper part. They reveal a AEe, of only 22 + 10 meV, five times smaller than on the clean surface. Similar values for AE, ranging from 15 to 25 meV have been found in spectra for a number of different 0 (see, for example, the 0 = 0 spectra in Fig. 27). In order to test the oxygen-induced changes of the bulk electronic structure of Ni(lll), a transition between sp bulk bands has been studied as well. Fig. 30 shows spin-resolved IPE data of an sp bulk band transition B,, observed at about 1.5 eV above E, for 0 = 40” in the I% azimuth (see Section 3.1). Comparing the data for B,, of the clean surface with those of the p(2 x 2)-O overlayer reveals an oxygen-induced attenuation of the intensity, but no change of the spin splitting of about 280 meV. The slight

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l maj.

0 min.

E - EF (eV) Fig. 29 (left). Spin-resolved IPE spectra of Ni(ll1) (ho = 9.4 eV) for 0 = - 12” (lower part, taken from Fig. 18) and of Ni(lll)-p(2X2)-0 for 0 = lo” (upper part). The exchange splitting of SS is reduced from about 100 meV at the clean surface to less than 25 meV for the p(2 x 2) oxygen overlayer (from Ref. [310]). Fig. 30 (right). Spin-resolved IPE spectra (hw = 9.4 eV) of an sp bulk-band transition B,, observed on Ni(lll) for 0 = 40” in the I% direction. The spin splitting of B,, on the clean surface remains unaffected by the ~(2 X 2) oxygen overlayer (from Ref. [310]).

shift to lower final energy of B,, accounts for the work function change, leading to a different k,, for spectra recorded at the same 0. The data of Ni(ll1) + 0 demonstrate on a microscopic level adsorbate-induced modifications of surface magnetic properties. A truly magnetic surface state becomes nonmagnetic by oxygen adsorption, while the exchange splitting of bulk sp bands remains unchanged and surface-sensitive band-gap emission from a bulk d-band shows only a slightly reduced AE,, [273]. All these findings indicate that the oxygen-induced reduction of the magnetic moment is limited to the very surface. In conclusion, the adsorption of foreign atoms on ferromagnetic surfaces changes their electronic structure and magnetic properties. In general, the magnetic moment at the surface is reduced upon adsorption. Electronic-structural data exhibit adsorbate-induced emission features which are not easy to interpret. In particular, it is not known a priori where the wave functions of the adsorbate-induced states are concentrated and what degree of localization they have. Hybridization with electronic states of the substrate has to be considered as well. Consequently, the spin splitting of adsorbate-induced states cannot be translated directly into

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numbers for magnetic moments of the adsorbate or the first-layer substrate atoms. Nevertheless, in case the origin of adsorbate-induced spectral features is known, they provide detailed information about the bonding mechanism between substrate and adsorbate and about changes of surface magnetic properties. One example has been presented that shows directly the reduced magnetic moment being reflected in the spin-dependent surface electronic structure: a spin-split partially occupied surface state of the clean surface becomes completely empty and loses its exchange splitting with increasing adsorbate coverage.

5. Summary

and outlook

The spin-dependent electronic structure of nickel surfaces has been the subject of this report. Spin-resolved inverse photoemission results on the empty states have been presented and discussed along with photoemission data on the occupied states to review the current knowledge on the spin-dependent electronic structure of nickel in the vicinity of the Fermi level. The exchange splitting of the magnetic d-bands at low temperature and upon approaching the Curie temperature are essential ingredients for theoretical models describing the ferromagnetism of nickel. Exchange-split surface states localized within the topmost layer or in front of the surface tell about magnetism at the very surface. Adsorption of foreign atoms changes the spin-dependent surface electronic structure, whose investigation provides insight into bonding mechanisms as well as modifications of the magnetic properties. The relationship between primary magnetic quantities and the spin-dependent electronic structure has been discussed. In summary, comprehensive information on the bulk/ surface/vacuum and bulk/ adsorbate/vacuum interfaces has been gained during the last decade. A profound understanding of the spin-dependent electronic structure at ferromagnetic surfaces may serve as a solid foundation for studying thin films and layered structures, which attract a lot of attention today. Novel magnetic phenomena such as giant magnetoresistance effects and oscillatory exchange coupling between magnetic layers, mediated by nonmagnetic spacers, have been detected in artificially made layered structures [l]. Yet, the understanding of these phenomena on an electronic-structural basis is still fragmentary. Detailed information is needed on the spin dependence of interface electronic states in layered systems consisting of ferromagnetic and nonmagnetic materials. Spin-resolved PE has already achieved first results on electronic states localized at interfaces of different materials [313-3151. Quantum-well states observed by spin-integrated IPE have been proposed as mediators of magnetic coupling in superlattices [316,317]. The need for spin-resolved data in this field will certainly influence future activities, promising valuable contributions to a more microscopic understanding of the fascinating phenomena in interface magnetism.

Acknowledgements

I wish to express my gratitude to V. Dose for providing continuous support and a scientifically stimulating environment. Enjoyable collaboration with K. Ertl, U. Kolac, F. Passek and K. Starke is gratefully acknowledged. I thank M. Campagna and G. Giintherodt for lending nickel

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crystals. It is a pleasure to thank E. Bertel, A. Hubert, W. von der Linden and W. Nolting for many helpful discussions and E. Kay and H.C. Siegmann for stimulating my interest in a variety of magnetic issues. I am indebted to Th. Fauster, A. Goldmann, N. Memmel and A.M. Nicol for critical readings of the manuscript and to E. Sombach for helping to prepare some of the figures.

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