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Photoemission: Spin-polarized and Angle-resolved
Photoemission: Spin-polarized and Angle-resolved Magnetism arises from the spins of electrons in partially filled outer shells of atoms in a solid which interact with each other via the exchange interaction. In a paramagnetic material all electronic states are degenerate with respect to spin, and consequently are occupied by two electrons, one with spin up and one with spin down. The exchange interaction lifts this degeneracy, lowering the energies of spin up, and raising those of spin down states. The energy difference between these states is the exchange splitting. Therefore, the spin-polarized electronic (band) structure is the key ingredient for understanding magnetism (see Density Functional Theory: Magnetism). Photoemission is commonly used to probe the electronic structure of solids. By also analyzing the spin polarization of the photoelectrons, information on the spin-polarized band structure is obtained. One speaks of electron spin polarization if one can find a direction in space with respect to which the two possible spin states are not equally populated. For ferromagnetically ordered materials, this direction is naturally the magnetization direction. The exchange splitting between majority and minority states of the same symmetry can be measured directly by spin-polarized photoemission. From temperature-dependent measurements, the change of the band structure on approaching the Curie temperature can be compared with various models of the ferro- to paramagnetic phase transition. The exchange coupling of ultrathin layers adsorbed on ferromagnetic surfaces can be studied. The origin of oscillating interlayer exchange coupling between ferromagnetic layers via a nonferromagnetic interlayer was clarified by spin-resolved photoemission. The degree of spin polarization at the Fermi level is important for devices utilizing spin-dependent transport phenomena. Core-level photoelectron spectra also show spin polarization which can be used as an element-specific indicator for magnetic order. While such spectra involving inner shell excitations do not give direct evidence on the spin-polarized electronic structure of the partially filled outer (valence) states, which are the source of magnetism, indirect information is contained in the line shape, the degree of spin polarization, and the presence of satellites. An important aspect of spin-polarized core level spectroscopy is the possibility of characterizing the relative spin orientation of different species in a multicomponent sample because core-level spectra occur with different excitation energies. Spin-dependent mean free paths and photoelectron diffraction effects may have an influence on the measured spin-resolved photoemission spectra. Apart from a magnetic ground state, spin–orbit interaction gives rise to spin polarization in photoelectron spectra. While for valence states this is, in most cases, a relatively small effect, the
large spin orbit interaction encountered for ionized inner shells with nonzero orbital momentum will in general give rise to significant spin polarization, both for magnetic and nonmagnetic systems. By choosing a suitable geometry this effect may be avoided, so that only the exchange-related effect remains. Alternatively, for magnetic systems the combined influence of the exchange and spin orbit interactions leads to magnetic dichroism. The continuous background of secondary electrons also is spin-polarized, and the degree of polarization at low energies can be related to the ground state magnetic moment. 1. Angle-resolved Photoemission In a photoemission (PE) experiment, UV or soft x-rays are used to excite electrons from a sample. In the excitation process the photon is annihilated, and energy conservation requires that the total energy is unchanged, Eijhν l EfjEkin
(1)
where Ei and Ef are the energies of the initial and final state of the sample, Ekin is the energy of the photoelectron, and hν is energy of the photon (Kevan 1992, Hu$ fner 1995). The difference between Ei and Ef is conventionally termed binding energy EB. It is determined from the photon energy chosen for the experiment and the measured kinetic energy of the photoelectron, EB l hνkEkinkφA
(2)
where φA is the work function of the sample. The kinetic energies are usually measured by electrostatic analyzers. For solid metallic samples, the most weakly bound electrons are those at the Fermi level. Therefore, the highest kinetic energy photoelectrons are generated by ejecting electrons from states at the Fermi level EF, and this cut-off is used as reference (zero) for binding energies such that EB l EkinkEkin(EF)
(3)
In addition to energy conservation, momentum also has to be conserved. The relationship between electron energy and momentum, i.e., the band structure, leads to pronounced angular dependencies. In angleresolved photoemission, the energy distribution of the photoelectrons is measured as a function of emission angle in order to obtain information on the band structure. For making the connection between measured angle-resolved PE spectra and the band structure, the sample has to be a single crystal. Maxima in photoelectron spectra arise whenever the photon energy matches the energy difference between an occupied state and an unoccupied state in the band structure. The components of the photoelectron wave vector parallel (kR) and perpendicular (kU) to the 1
Photoemission: Spin-polarized and Angle-resolved Table 1 Characteristic parameters of spin polarimeters. If no orientation for the scattering target is given, a polycrystalline one is used. The spin asymmetry is given by the difference of differential scattering cross sections for the two channels corresponding to up and down spin electrons, normalized to the sum. The figure of merit, given by the square of the spin asymmetry times the average scattering cross section, is a measure for the performance of a spin detetctor; to reach a certain statistical uncertainty, the data acqusition time varies as the reciprocal of the figure of merit. For the LEED polarimeters, the performance depends on the crystalline quality of the surface. For VLEED, the polarization is determined by sequential measurements with reversed target magnetization, which halves the figure of merit (included). Type of spin polarimeter Mott detector Medim energy Mott detector Diffuse scattering LEED VLEED
Operating energy (eV)
Scattering target
Figure of merit i10V%
10& 2–4i10V%
Au Au
0.25 0.2
1 0.2
150–300
Au
0.07–0.11
1
105 12
W(100) Fe(100)
0.27 0.2–0.4
1.6 5–10
surface are kR[k U ] l (2mEkin\h#)"/#i sin θ [icos θ] l 0.5123i(Ekin\1 eV)"/#AH V"isin θ [icos θ] (4) where m is the electron mass, and θ the emission angle measured to the surface normal. The parallel component is conserved (to within a reciprocal lattice vector) for photoelectrons crossing the surface, so that kR measured in vacuum is identical to that in the solid. To interpret the perpendicular photoelectron wave vector component kU measured in vacuum, the relationship between E and k in the solid and the way in which the wave functions in the solid and in vacuum are matched have to be known. Structures in PE spectra are interpreted assuming that the momentum is retained within the excitation (‘‘vertical’’ or ‘‘direct transitions’’). With increasing final state energy, the allowed final states become more dense, and the finite angular acceptance of photoelectron spectrometers integrates over an electron momentum range comparable to the Brillouin zone. Spectra taken under such conditions may be interpreted in terms of density of states, which can be obtained from the momentumresolved band structure by integration in k-space. Angular variations may then still arise from diffraction effects, because the photoelectrons are scattered by the regular array of atoms in the crystal lattice.
2. Electron Spin Analysis Electron spin polarization P is defined as P l (NupkNdown)\(NupjNdown) 2
Spin asymmetry
(5)
where Nup and Ndown are the numbers of electrons with spin parallel and antiparallel to a chosen quantization axis. For magnetic materials the quantization axis is the direction of sample magnetization. To measure photoelectron spin polarization, the energy-analyzed photoelectrons are subjected to a spin-dependent scattering process (Kessler 1985, Feder 1985). The majority of spin polarimeters derive their spin dependence from spin–orbit interaction. The spin of the free electron may couple to the angular momentum in the scattering process, which gives rise to a spindependent contribution to the scattering potential. This spin-dependent contribution is generally small. A sizable magnitude of this effect is usually only found for conditions where the mean scattering cross section is small, so that the spin-dependent part becomes significant. In general a compromise has to be found between the requirements of a large analyzing power and a large mean scattering cross section. For spin– orbit based detectors it is possible in principle to measure both transverse spin components simultaneously. The optimum scattering energy for socalled Mott detectors is around 100 kV, and this provides scattering asymmetries between 0.2 and 0.3. Mott detectors have been designed and are commercially available with scattering energies of around 30 kV. The lower scattering energy reduces the size, complexity, and cost of such a detector at the expense of lower asymmetries and scattering efficiency. Low energy scattering is employed either in a LEED type arrangement where spin–orbit interaction influences the scattering efficiency for higher-order LEED beams scattered from the surface of a heavy material, or in diffuse scattering off a polycrystalline target composed of a heavy element. Finally, scattering off the surface of a magnetized single crystal of iron has been exploited for spin analysis (Hillebrecht et al. 1992).
Photoemission: Spin-polarized and Angle-resolved This technique offers a superior performance in comparison to Mott detectors. However, it is much more complicated as it requires careful preparation of the scattering target. Details are summarized in Table 1, and can be drawn from the literature. 3. Technical Aspects
Intensity (arb. units)
The elastic mean free path for electrons in solids is of the order of 0.5 to 5 nm. Therefore, photoemission is a highly surface-sensitive technique. Clean surfaces are prepared in ultrahigh vacuum, e.g., by sputtering and annealing, cleaving, or deposition. In order to correlate the angular dependencies of photoemission with the band structure, single crystalline samples are required. To exploit fully the potential of the technique, tunable, monochromatic, and polarized light is needed, which is readily available at synchrotron radiation sources. Because of the limited elastic mean free path, photoelectrons undergo numerous inelastic scattering processes, generating secondary electrons with reduced energy. This leads to a continuous background of secondary electrons. For ferromagnetic materials, this background is also spin-polarized (Kisker et al. 1982). Photoemission experiments have to be carried out on remanently magnetized samples, and the influence of stray fields on the electron trajectories has to be excluded. Ultrathin films grown in situ are easy to magnetize within the film plane, and have negligible stray fields. 4. 3d Ferromagnets
Binding energy (eV)
Figure 1 Spin-resolved photoemission spectra for the 3d ferromagnets, taken with 20 eV photons (21.2 eV for cobalt) in normal emission: data for Fe(100) with normal light incidence (from Kisker et al. 1985); for Co(0001) light incidence under 30 m to surface normal, magnetization in the surface plane (Getzlaff et al. 1996); for Ni(110) light incidence 20 m to surface normal (Ono et al. 1998). For all examples filled triangles pointing up represent majority spin electrons, empty triangles pointing down are for minority spin electrons.
Figure 1 shows spin-resolved photoemission spectra for iron, cobalt, and nickel taken in normal emission with 20 eV photons (21.2 eV for cobalt) from single crystal surfaces. With calculated band structures available, the features in the spectra can be attributed to transitions from specific occupied bands, allowing determination of the exchange splitting. In general, a large number of spectra is taken with different photon energies or for different emission geometries. The shifts of the peaks observed in such data sets allow determination of the dispersion of the electronic bands. The spectrum for iron (Kisker et al. 1985) shows a majority peak at 2.6 eV, which is present with small shifts in binding energy (BE) for all photon energies. The minority spectrum shows only a weak structure at the Fermi level, which is attributed to indirect transitions. The dispersion of the bands close to EF causes a majority spin polarization for photon energies below 33 eV, switching to minority for higher photon energies. For the spectrum of h.c.p.-cobalt (Getzlaff et al. 1996), the minority peak is caused by transitions from bands of ∆ and ∆ symmetry, which cross the Fermi * ( level and consequently have a high density of states at 3
Photoemission: Spin-polarized and Angle-resolved
Intensity (arb. units)
(a)
Binding energy (eV)
Spin polarization (%)
(b)
Fe coverage (ML)
Figure 2 (a) Evolution of spin-resolved photoemission spectra for Fe films grown on f.c.c. Co(100); photon energy 34 eV, normal emission, plane-polarized light under 45 m incidence; (b) spin polarization data for Fe films grown on f.c.c.-cobalt, derived from the spectra in Fig. 2(a). The polarization shows three thickness regimes, which are associated with f.c.c.-Fe (area I), a distorted Fe phase with low moment (area II), and finally a transition to b.c.c.-Fe (area III); circles for spin polarization at 0.8 eV binding energy, diamonds for 1.8 eV (from Kla$ sges et al. 1998).
4
EF. The peak in the majority spectrum appears at slightly higher BE. By analyzing the energy and angle dependence of these structures, an exchange splitting of 1.6 eV is found, in agreement with calculations. The spectrum of Ni(110) shows only a sharp structure at the Fermi level (Ono et al. 1998). At different photon energies, features up to about 3 eV BE are observed. This suggests that the bandwidth is smaller by 30% than the calculated bandwidth. This is ascribed to correlation (self energy) effects, which tend to narrow the bands. The majority and minority peaks have different binding energies. This reflects directly the exchange splitting, 0.12 eV in this case. Furthermore, the exchange splitting varies between 0.1 and 0.4 eV for different points in the Brillouin zone. For some applications of ultrathin magnetic films, a large spin polarization at the Fermi level is desired. For this purpose, the stabilization of magnetic materials in different phases is of interest as it permits the tailoring of magnetic properties at surfaces or interfaces for specific applications. Electronic structure calculations suggest that f.c.c.-Fe may show widely different magnetic properties for small variations of lattice constant, ranging from nonmagnetic to antiferro- and ferromagnetic states. The ferromagnetic f.c.c. phase is expected to have a higher magnetic moment than the b.c.c. phase, and may possibly be a strong ferromagnet, i.e., show complete (100%) spin polarization at the Fermi level. Figure 2 shows the evolution of the spin-polarized electronic structure of iron with different crystal structures (Kla$ sges et al. 1998); f.c.c.-iron is grown on f.c.c.-cobalt, which can be grown in f.c.c.-structure f.c.c.-Cu(100) up to several hundred monolayers (ML). The initial spectrum shows the spin-resolved spectrum of cobalt in the f.c.c. phase. Close to EF, one finds a minority polarization, and at higher BEs the spin polarization changes to majority. The spectrum for f.c.c.-Fe (3 monolayer film) shows a majority peak at 2.9 eV and a minority peak at 0.4 eV. This 2.5 eV splitting can be interpreted as an exchange splitting. The increased magnitude of this splitting shows that the magnetic moment is indeed increased compared with the bulk b.c.c. value. The reduced spin polarization for the 6 ML film shows that the major part of the film is ferromagnetically aligned to the substrate. Nevertheless, the finite spin polarization demonstrates that the surface layer is still ferromagnetically aligned to the cobalt magnetization. A fraction of the surface layer is still in the high moment state, as can be seen from the weak structure between 2 and 3 eV. For coverages above 10 ML, the whole film reverts to the thermodynamically stable b.c.c. structure. The polarization increases, as the whole film orders ferromagnetically; however, the exchange splitting of about 2.2 eV is typical for the b.c.c. moment. Figure 2(b) shows the polarization measured at different points in the spectrum, which tracks very well the magnetic moments derived from other experiments.
Intensity (arb. units)
Intensity (arb. units)
Photoemission: Spin-polarized and Angle-resolved
Binding energy (eV)
Figure 3 Evolution of the spin-polarized photoemission spectrum of Fe(100) on approaching the Curie temperature TC l 1043 K (Kisker et al. 1984). Photon energy 60 eV, normal emission, s-polarized light; lower panel for temperatures τ l T\TC l 0.3, upper for τ l T\TC l 0.85; triangles pointing up for majority states.
5. Ferro- to Paramagnetic Transition Figure 3 shows the change of the spin-resolved PE spectrum of b.c.c.-Fe with temperature (Kisker et al. 1984). The key issue for such studies is to gain an insight into the underlying physics of the transition from the para- to the ferromagnetic state. While the spin-averaged spectra do not change significantly on heating to 0.85 TC, the spin-resolved data show significant changes: the minority peak at 0.4 eV BE loses intensity and becomes broader, and the majority spin peak at 2.6 eV also loses intensity, with nearly unchanged width and BE. The results show that the exchange splitting is of the order of 2 eV, and does not change significantly on approaching the Curie
Binding energy (eV)
Figure 4 Evolution of the normal emission spin-polarized photoemission spectrum of Ni(110) on approaching the Curie temperature TC l 627 K; τ l T\TC; photon energy 16.8 eV, probing the X point (Hopster et al. 1983).
5
Photoemission: Spin-polarized and Angle-resolved
Intensity (arb. units)
a contribution of the local band model with temperature-independent exchange splitting. Spin- and angle-resolved photoemission of elemental 3d ferromagnets has shown that, depending on the material, different mechanisms are responsible for the ferro- to paramagnetic transition. The small changes of the exchange splitting observed for iron can apparently be understood within a local band model, while the temperature-dependent exchange splitting found for nickel can be explained within the Stoner model (see Itinerant Electron Systems: Magnetism (Ferromagnetism)). This does not rule out that in each case the nondominant mechanism is to some extent in operation (Kisker 1984, Fujii et al. 1995).
6. Quantum Well States
Binding energy (eV)
Figure 5 Spin-resolved photoemission from sp-like quantum well states of ultrathin copper grown on f.c.c.-Co(100) (Garrison et al. 1993).
temperature. Figure 4 shows similar temperature-dependent data for Ni(110) (Hopster et al. 1983). The data clearly show a scaling of the exchange splitting proportional to the macroscopic magnetization with increasing temperature, in agreement with the Stoner model. In contrast, these results are inconsistent with a so-called local band model, where the decrease of the magnetization is caused by transverse fluctuations of microscopic regions which still have the full temperature-independent exchange splitting. By choosing different excitation conditions, Fujii et al. (1995) probed a different region of the Brillouin zone. The results showed aspects of both types of behavior: an exchange-splitting decreasing with temperature, and 6
The magnetization between two ultrathin films, forming a sandwich with a nonmagnetic layer in-between, may be coupled by exchange interaction via the nonmagnetic interlayer (Gru$ nberg et al. 1986). The coupling strength oscillates periodically with interlayer thickness between ferro- and antiferromagnetic coupling, and furthermore decays with interlayer thickness. The most widely used material combinations are Fe–Cr and f.c.c.-Co–Cu (Parkin 1994). The thickness of the interlayer is up to about 20 monolayers. The coupling can be understood in terms of a modified RKKY theory (see Magnetism in Solids: General Introduction), which was originally proposed to describe the interaction between magnetic impurities in nonmagnetic host materials. In this picture, the oscillation period of the coupling is related to the size and shape of the Fermi surface of the nonmagnetic interlayer. The oscillation period is given by 2π\kN, where kN is a Fermi surface nesting vector of the bulk band structure of the interlayer material. The small thickness of the interlayer may lead to quantization of the bulk bands in the direction normal to the film. This affects in particular the sp-like states of copper, which in bulk copper metal are free electron-like. Figure 5 shows spin-resolved photoemission spectra for ultrathin copper films on Co(100) (Garrison et al. 1993). The copper d states have binding energies of 2 V or more, so that the region shown is dominated by copper sp-like states (with some residual emission from cobalt d states for the lowest copper coverage). The minority (with respect to cobalt majority) spectra show clearly discrete states that occur with different binding energies for different coverages. In contrast, the majority states do not show discrete states, indicating that the quantum well states are strongly minority-polarized. Depending on the thickness of the copper layer, the quantum well states occur at different energies for certain thicknesses at the Fermi level. The intensity and spin polarization at the Fermi level oscillate with thickness, and this oscillation correlates directly with
Photoemission: Spin-polarized and Angle-resolved the oscillation of the interlayer exchange coupling between two f.c.c.-Co films separated by a copper film (Carbone et al. 1993). These experiments show that the spin polarization of the quantum well states induced by the confining magnetic interface causes the interlayer exchange coupling.
7. Spin-resolved Photoemission from Core Levels
Counts (i 104)
Inner shells are completely filled, and consequently the total spin and angular momentum is always zero. This means that the integrated spectrum should have no spin polarization. However, ejection of an electron from an inner shell generates a hole which has a spin and, if one is not looking at an s level, an angular momentum. In a magnetic system, the spin of the core hole couples to the spin of valence electrons, and this may lead to different excitation energies depending on the spin of the photoelectron. From studies of the 3d ferromagnets it is known that at the leading edge of a core level spectrum one always finds minority spin polarization. One may state this as a generalized Hund’s rule (see Magnetism in Solids: General Introduction), because minority spin for the photoelectron means that the spin of the remaining shell from which one electron is removed has majority character, i.e., is parallel to the spin of the majority electrons. Core level spin polarization can be used as an element-specific indicator of magnetic order. For a number of nonferromagnetic elements theoretical calculations predict a ferromagnetic ground state for a monolayer film of
Binding energy (eV)
Figure 6 Spin-resolved 3p core level photoemission for 1.5 nm Cr\Fe(100) (from Hillebrecht et al. 1992). Photon energy 117 eV, normal incidence and emission. A constant background, matched to the spectrum on the low binding energy side, was substracted from the spectrum.
this element. A famous example is antiferromagnetic chromium, which in the bulk has a mean magnetic moment of 0.6 µB. For a chromium monolayer on iron an enhanced moment of 3.6 µB was derived, with ferromagnetic order within the chromium layer, coupled antiferromagnetically to the ferromagnetic iron substrate. Figure 6 shows a spin-resolved chromium 3p photoemission spectrum taken for a monolayer (0.15 nm) of chromium on Fe(100) (Hillebrecht et al. 1992). The spectrum shows a large spin polarization, which is opposite to that of the 3p spectrum of the iron substrate. This demonstrates the antiferromagnetic coupling between the iron surface and the chromium overlayer. The magnitude of the chromium 3p polarization indicates that the chromium moment is smaller than the predicted 3.6 µB. This is caused by structural intermixing between chromium and iron atoms occurring during chromium deposition, leading to a higher chromium coordination.
Bibliography Carbone C, Vescovo E, Rader O, Gudat W, Eberhardt W 1993 Exchange split quantum well states of a noble metal film on a magnetic substrate. Phys. Re. Lett. 71, 2805–8 Feder R 1985 Polarized Electrons at Surfaces. World Scientific, Singapore Fujii J, Kakizaki A, Shimada K, Ono K, Kinoshita T, Fukutani H 1995 Temperature dependence of the spin- and angleresolved valence band photoemission spectra of Ni(110). Solid State Commun. 94, 391–5 Garrison K, Chang Y, Johnson P D 1993 Spin polarisation of quantum well states in copper thin films deposited on a Co(001) substrate. Phys. Re. Lett. 71, 2801–5 Getzlaff M, Bansmann J, Braun J, Scho$ nhense G 1996 Spin resolved photoemission study of Co(0001) films. J. Magn. Magn. Mater. 161, 70–88 Gru$ nberg P, Schreiber R, Pang Y, Brodsky M B, Sowers H 1986 Layered magnetic structures: evidence for antiferromagnetic coupling of Fe layers across Cr interlayers. Phys. Re. Lett. 57, 2442–5 Hillebrecht F U, Roth C, Jungblut R, Kisker E, Bringer A 1992 Antiferromagnetic coupling of a Cr overlayer to Fe(100). Europhys. Lett. 19, 711–16 Hopster H, Raue R, Gu$ ntherodt G, Kisker E, Clauberg R, Campagna M 1983 Temperature dependence of the exchange splitting in Ni studied by spin-polarized photoemission. Phys. Re. Lett. 51, 829–32 Hu$ fner S 1995 Photoelectron Spectroscopy. Springer, Berlin Kessler J 1985 Polarized Electrons, 2nd edn. Springer, Berlin Kevan S D 1992 Angle-resoled Photoemission: Theory and Current Applications. Elsevier, Amsterdam Kisker E 1984 Photoemission and finite temperature magnetism of Fe and Ni. J. Magn. Magn. Mater. 45, 23–32 Kisker E, Gudat W, Schro$ der K 1982 Observation of a high-spin polarization of secondary electrons from single crystal Fe and Co. Solid State Commun. 44, 591–5 Kisker E, Schro$ der K, Campagna M, Gudat W 1984 Temperature dependence of the exchange splitting of Fe by spin resolved photoemission with synchrotron radiation. Phys. Re. Lett. 52, 2285–8 Kisker E, Schro$ der K, Gudat W, Campagna M 1985 Spin
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Photoemission: Spin-polarized and Angle-resolved polarized angle resolved photoemission study of the electronic structure of Fe(100) as a function of temperature. Phys. Re. B 31, 329–39 Kla$ sges R, Schmitz D, Carbone C, Eberhardt W, Kachel T 1998 Surface magnetism and electronic structure of ultrathin fcc Fe films. Solid State Commun. 107, 13–18 Ono K, Kakizaki A, Tanaka K, Shimada K, Saitoh Y, Shendohda T 1998 Electron correlation effects in ferromag-
netic Ni observed by spin- and angle-resolved photoemission. Solid State Commun. 107, 153–7 Parkin S S P 1994 Giant magnetoresistance and oscillatory interlayer exchange coupling in polycrystalline transition metal multilayers. In: Heinrich B, Bland J A C (eds.) 1994 Ultrathin Magnetic Structures. Springer, Berlin, Vol. 2
F. U. Hillebrecht
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 6929–6936 8
large spin orbit interaction encountered for ionized inner shells with nonzero orbital momentum will in general give rise to significant spin polarization, both for magnetic and nonmagnetic systems. By choosing a suitable geometry this effect may be avoided, so that only the exchange-related effect remains. Alternatively, for magnetic systems the combined influence of the exchange and spin orbit interactions leads to magnetic dichroism. The continuous background of secondary electrons also is spin-polarized, and the degree of polarization at low energies can be related to the ground state magnetic moment. 1. Angle-resolved Photoemission In a photoemission (PE) experiment, UV or soft x-rays are used to excite electrons from a sample. In the excitation process the photon is annihilated, and energy conservation requires that the total energy is unchanged, Eijhν l EfjEkin
(1)
where Ei and Ef are the energies of the initial and final state of the sample, Ekin is the energy of the photoelectron, and hν is energy of the photon (Kevan 1992, Hu$ fner 1995). The difference between Ei and Ef is conventionally termed binding energy EB. It is determined from the photon energy chosen for the experiment and the measured kinetic energy of the photoelectron, EB l hνkEkinkφA
(2)
where φA is the work function of the sample. The kinetic energies are usually measured by electrostatic analyzers. For solid metallic samples, the most weakly bound electrons are those at the Fermi level. Therefore, the highest kinetic energy photoelectrons are generated by ejecting electrons from states at the Fermi level EF, and this cut-off is used as reference (zero) for binding energies such that EB l EkinkEkin(EF)
(3)
In addition to energy conservation, momentum also has to be conserved. The relationship between electron energy and momentum, i.e., the band structure, leads to pronounced angular dependencies. In angleresolved photoemission, the energy distribution of the photoelectrons is measured as a function of emission angle in order to obtain information on the band structure. For making the connection between measured angle-resolved PE spectra and the band structure, the sample has to be a single crystal. Maxima in photoelectron spectra arise whenever the photon energy matches the energy difference between an occupied state and an unoccupied state in the band structure. The components of the photoelectron wave vector parallel (kR) and perpendicular (kU) to the 1
Photoemission: Spin-polarized and Angle-resolved Table 1 Characteristic parameters of spin polarimeters. If no orientation for the scattering target is given, a polycrystalline one is used. The spin asymmetry is given by the difference of differential scattering cross sections for the two channels corresponding to up and down spin electrons, normalized to the sum. The figure of merit, given by the square of the spin asymmetry times the average scattering cross section, is a measure for the performance of a spin detetctor; to reach a certain statistical uncertainty, the data acqusition time varies as the reciprocal of the figure of merit. For the LEED polarimeters, the performance depends on the crystalline quality of the surface. For VLEED, the polarization is determined by sequential measurements with reversed target magnetization, which halves the figure of merit (included). Type of spin polarimeter Mott detector Medim energy Mott detector Diffuse scattering LEED VLEED
Operating energy (eV)
Scattering target
Figure of merit i10V%
10& 2–4i10V%
Au Au
0.25 0.2
1 0.2
150–300
Au
0.07–0.11
1
105 12
W(100) Fe(100)
0.27 0.2–0.4
1.6 5–10
surface are kR[k U ] l (2mEkin\h#)"/#i sin θ [icos θ] l 0.5123i(Ekin\1 eV)"/#AH V"isin θ [icos θ] (4) where m is the electron mass, and θ the emission angle measured to the surface normal. The parallel component is conserved (to within a reciprocal lattice vector) for photoelectrons crossing the surface, so that kR measured in vacuum is identical to that in the solid. To interpret the perpendicular photoelectron wave vector component kU measured in vacuum, the relationship between E and k in the solid and the way in which the wave functions in the solid and in vacuum are matched have to be known. Structures in PE spectra are interpreted assuming that the momentum is retained within the excitation (‘‘vertical’’ or ‘‘direct transitions’’). With increasing final state energy, the allowed final states become more dense, and the finite angular acceptance of photoelectron spectrometers integrates over an electron momentum range comparable to the Brillouin zone. Spectra taken under such conditions may be interpreted in terms of density of states, which can be obtained from the momentumresolved band structure by integration in k-space. Angular variations may then still arise from diffraction effects, because the photoelectrons are scattered by the regular array of atoms in the crystal lattice.
2. Electron Spin Analysis Electron spin polarization P is defined as P l (NupkNdown)\(NupjNdown) 2
Spin asymmetry
(5)
where Nup and Ndown are the numbers of electrons with spin parallel and antiparallel to a chosen quantization axis. For magnetic materials the quantization axis is the direction of sample magnetization. To measure photoelectron spin polarization, the energy-analyzed photoelectrons are subjected to a spin-dependent scattering process (Kessler 1985, Feder 1985). The majority of spin polarimeters derive their spin dependence from spin–orbit interaction. The spin of the free electron may couple to the angular momentum in the scattering process, which gives rise to a spindependent contribution to the scattering potential. This spin-dependent contribution is generally small. A sizable magnitude of this effect is usually only found for conditions where the mean scattering cross section is small, so that the spin-dependent part becomes significant. In general a compromise has to be found between the requirements of a large analyzing power and a large mean scattering cross section. For spin– orbit based detectors it is possible in principle to measure both transverse spin components simultaneously. The optimum scattering energy for socalled Mott detectors is around 100 kV, and this provides scattering asymmetries between 0.2 and 0.3. Mott detectors have been designed and are commercially available with scattering energies of around 30 kV. The lower scattering energy reduces the size, complexity, and cost of such a detector at the expense of lower asymmetries and scattering efficiency. Low energy scattering is employed either in a LEED type arrangement where spin–orbit interaction influences the scattering efficiency for higher-order LEED beams scattered from the surface of a heavy material, or in diffuse scattering off a polycrystalline target composed of a heavy element. Finally, scattering off the surface of a magnetized single crystal of iron has been exploited for spin analysis (Hillebrecht et al. 1992).
Photoemission: Spin-polarized and Angle-resolved This technique offers a superior performance in comparison to Mott detectors. However, it is much more complicated as it requires careful preparation of the scattering target. Details are summarized in Table 1, and can be drawn from the literature. 3. Technical Aspects
Intensity (arb. units)
The elastic mean free path for electrons in solids is of the order of 0.5 to 5 nm. Therefore, photoemission is a highly surface-sensitive technique. Clean surfaces are prepared in ultrahigh vacuum, e.g., by sputtering and annealing, cleaving, or deposition. In order to correlate the angular dependencies of photoemission with the band structure, single crystalline samples are required. To exploit fully the potential of the technique, tunable, monochromatic, and polarized light is needed, which is readily available at synchrotron radiation sources. Because of the limited elastic mean free path, photoelectrons undergo numerous inelastic scattering processes, generating secondary electrons with reduced energy. This leads to a continuous background of secondary electrons. For ferromagnetic materials, this background is also spin-polarized (Kisker et al. 1982). Photoemission experiments have to be carried out on remanently magnetized samples, and the influence of stray fields on the electron trajectories has to be excluded. Ultrathin films grown in situ are easy to magnetize within the film plane, and have negligible stray fields. 4. 3d Ferromagnets
Binding energy (eV)
Figure 1 Spin-resolved photoemission spectra for the 3d ferromagnets, taken with 20 eV photons (21.2 eV for cobalt) in normal emission: data for Fe(100) with normal light incidence (from Kisker et al. 1985); for Co(0001) light incidence under 30 m to surface normal, magnetization in the surface plane (Getzlaff et al. 1996); for Ni(110) light incidence 20 m to surface normal (Ono et al. 1998). For all examples filled triangles pointing up represent majority spin electrons, empty triangles pointing down are for minority spin electrons.
Figure 1 shows spin-resolved photoemission spectra for iron, cobalt, and nickel taken in normal emission with 20 eV photons (21.2 eV for cobalt) from single crystal surfaces. With calculated band structures available, the features in the spectra can be attributed to transitions from specific occupied bands, allowing determination of the exchange splitting. In general, a large number of spectra is taken with different photon energies or for different emission geometries. The shifts of the peaks observed in such data sets allow determination of the dispersion of the electronic bands. The spectrum for iron (Kisker et al. 1985) shows a majority peak at 2.6 eV, which is present with small shifts in binding energy (BE) for all photon energies. The minority spectrum shows only a weak structure at the Fermi level, which is attributed to indirect transitions. The dispersion of the bands close to EF causes a majority spin polarization for photon energies below 33 eV, switching to minority for higher photon energies. For the spectrum of h.c.p.-cobalt (Getzlaff et al. 1996), the minority peak is caused by transitions from bands of ∆ and ∆ symmetry, which cross the Fermi * ( level and consequently have a high density of states at 3
Photoemission: Spin-polarized and Angle-resolved
Intensity (arb. units)
(a)
Binding energy (eV)
Spin polarization (%)
(b)
Fe coverage (ML)
Figure 2 (a) Evolution of spin-resolved photoemission spectra for Fe films grown on f.c.c. Co(100); photon energy 34 eV, normal emission, plane-polarized light under 45 m incidence; (b) spin polarization data for Fe films grown on f.c.c.-cobalt, derived from the spectra in Fig. 2(a). The polarization shows three thickness regimes, which are associated with f.c.c.-Fe (area I), a distorted Fe phase with low moment (area II), and finally a transition to b.c.c.-Fe (area III); circles for spin polarization at 0.8 eV binding energy, diamonds for 1.8 eV (from Kla$ sges et al. 1998).
4
EF. The peak in the majority spectrum appears at slightly higher BE. By analyzing the energy and angle dependence of these structures, an exchange splitting of 1.6 eV is found, in agreement with calculations. The spectrum of Ni(110) shows only a sharp structure at the Fermi level (Ono et al. 1998). At different photon energies, features up to about 3 eV BE are observed. This suggests that the bandwidth is smaller by 30% than the calculated bandwidth. This is ascribed to correlation (self energy) effects, which tend to narrow the bands. The majority and minority peaks have different binding energies. This reflects directly the exchange splitting, 0.12 eV in this case. Furthermore, the exchange splitting varies between 0.1 and 0.4 eV for different points in the Brillouin zone. For some applications of ultrathin magnetic films, a large spin polarization at the Fermi level is desired. For this purpose, the stabilization of magnetic materials in different phases is of interest as it permits the tailoring of magnetic properties at surfaces or interfaces for specific applications. Electronic structure calculations suggest that f.c.c.-Fe may show widely different magnetic properties for small variations of lattice constant, ranging from nonmagnetic to antiferro- and ferromagnetic states. The ferromagnetic f.c.c. phase is expected to have a higher magnetic moment than the b.c.c. phase, and may possibly be a strong ferromagnet, i.e., show complete (100%) spin polarization at the Fermi level. Figure 2 shows the evolution of the spin-polarized electronic structure of iron with different crystal structures (Kla$ sges et al. 1998); f.c.c.-iron is grown on f.c.c.-cobalt, which can be grown in f.c.c.-structure f.c.c.-Cu(100) up to several hundred monolayers (ML). The initial spectrum shows the spin-resolved spectrum of cobalt in the f.c.c. phase. Close to EF, one finds a minority polarization, and at higher BEs the spin polarization changes to majority. The spectrum for f.c.c.-Fe (3 monolayer film) shows a majority peak at 2.9 eV and a minority peak at 0.4 eV. This 2.5 eV splitting can be interpreted as an exchange splitting. The increased magnitude of this splitting shows that the magnetic moment is indeed increased compared with the bulk b.c.c. value. The reduced spin polarization for the 6 ML film shows that the major part of the film is ferromagnetically aligned to the substrate. Nevertheless, the finite spin polarization demonstrates that the surface layer is still ferromagnetically aligned to the cobalt magnetization. A fraction of the surface layer is still in the high moment state, as can be seen from the weak structure between 2 and 3 eV. For coverages above 10 ML, the whole film reverts to the thermodynamically stable b.c.c. structure. The polarization increases, as the whole film orders ferromagnetically; however, the exchange splitting of about 2.2 eV is typical for the b.c.c. moment. Figure 2(b) shows the polarization measured at different points in the spectrum, which tracks very well the magnetic moments derived from other experiments.
Intensity (arb. units)
Intensity (arb. units)
Photoemission: Spin-polarized and Angle-resolved
Binding energy (eV)
Figure 3 Evolution of the spin-polarized photoemission spectrum of Fe(100) on approaching the Curie temperature TC l 1043 K (Kisker et al. 1984). Photon energy 60 eV, normal emission, s-polarized light; lower panel for temperatures τ l T\TC l 0.3, upper for τ l T\TC l 0.85; triangles pointing up for majority states.
5. Ferro- to Paramagnetic Transition Figure 3 shows the change of the spin-resolved PE spectrum of b.c.c.-Fe with temperature (Kisker et al. 1984). The key issue for such studies is to gain an insight into the underlying physics of the transition from the para- to the ferromagnetic state. While the spin-averaged spectra do not change significantly on heating to 0.85 TC, the spin-resolved data show significant changes: the minority peak at 0.4 eV BE loses intensity and becomes broader, and the majority spin peak at 2.6 eV also loses intensity, with nearly unchanged width and BE. The results show that the exchange splitting is of the order of 2 eV, and does not change significantly on approaching the Curie
Binding energy (eV)
Figure 4 Evolution of the normal emission spin-polarized photoemission spectrum of Ni(110) on approaching the Curie temperature TC l 627 K; τ l T\TC; photon energy 16.8 eV, probing the X point (Hopster et al. 1983).
5
Photoemission: Spin-polarized and Angle-resolved
Intensity (arb. units)
a contribution of the local band model with temperature-independent exchange splitting. Spin- and angle-resolved photoemission of elemental 3d ferromagnets has shown that, depending on the material, different mechanisms are responsible for the ferro- to paramagnetic transition. The small changes of the exchange splitting observed for iron can apparently be understood within a local band model, while the temperature-dependent exchange splitting found for nickel can be explained within the Stoner model (see Itinerant Electron Systems: Magnetism (Ferromagnetism)). This does not rule out that in each case the nondominant mechanism is to some extent in operation (Kisker 1984, Fujii et al. 1995).
6. Quantum Well States
Binding energy (eV)
Figure 5 Spin-resolved photoemission from sp-like quantum well states of ultrathin copper grown on f.c.c.-Co(100) (Garrison et al. 1993).
temperature. Figure 4 shows similar temperature-dependent data for Ni(110) (Hopster et al. 1983). The data clearly show a scaling of the exchange splitting proportional to the macroscopic magnetization with increasing temperature, in agreement with the Stoner model. In contrast, these results are inconsistent with a so-called local band model, where the decrease of the magnetization is caused by transverse fluctuations of microscopic regions which still have the full temperature-independent exchange splitting. By choosing different excitation conditions, Fujii et al. (1995) probed a different region of the Brillouin zone. The results showed aspects of both types of behavior: an exchange-splitting decreasing with temperature, and 6
The magnetization between two ultrathin films, forming a sandwich with a nonmagnetic layer in-between, may be coupled by exchange interaction via the nonmagnetic interlayer (Gru$ nberg et al. 1986). The coupling strength oscillates periodically with interlayer thickness between ferro- and antiferromagnetic coupling, and furthermore decays with interlayer thickness. The most widely used material combinations are Fe–Cr and f.c.c.-Co–Cu (Parkin 1994). The thickness of the interlayer is up to about 20 monolayers. The coupling can be understood in terms of a modified RKKY theory (see Magnetism in Solids: General Introduction), which was originally proposed to describe the interaction between magnetic impurities in nonmagnetic host materials. In this picture, the oscillation period of the coupling is related to the size and shape of the Fermi surface of the nonmagnetic interlayer. The oscillation period is given by 2π\kN, where kN is a Fermi surface nesting vector of the bulk band structure of the interlayer material. The small thickness of the interlayer may lead to quantization of the bulk bands in the direction normal to the film. This affects in particular the sp-like states of copper, which in bulk copper metal are free electron-like. Figure 5 shows spin-resolved photoemission spectra for ultrathin copper films on Co(100) (Garrison et al. 1993). The copper d states have binding energies of 2 V or more, so that the region shown is dominated by copper sp-like states (with some residual emission from cobalt d states for the lowest copper coverage). The minority (with respect to cobalt majority) spectra show clearly discrete states that occur with different binding energies for different coverages. In contrast, the majority states do not show discrete states, indicating that the quantum well states are strongly minority-polarized. Depending on the thickness of the copper layer, the quantum well states occur at different energies for certain thicknesses at the Fermi level. The intensity and spin polarization at the Fermi level oscillate with thickness, and this oscillation correlates directly with
Photoemission: Spin-polarized and Angle-resolved the oscillation of the interlayer exchange coupling between two f.c.c.-Co films separated by a copper film (Carbone et al. 1993). These experiments show that the spin polarization of the quantum well states induced by the confining magnetic interface causes the interlayer exchange coupling.
7. Spin-resolved Photoemission from Core Levels
Counts (i 104)
Inner shells are completely filled, and consequently the total spin and angular momentum is always zero. This means that the integrated spectrum should have no spin polarization. However, ejection of an electron from an inner shell generates a hole which has a spin and, if one is not looking at an s level, an angular momentum. In a magnetic system, the spin of the core hole couples to the spin of valence electrons, and this may lead to different excitation energies depending on the spin of the photoelectron. From studies of the 3d ferromagnets it is known that at the leading edge of a core level spectrum one always finds minority spin polarization. One may state this as a generalized Hund’s rule (see Magnetism in Solids: General Introduction), because minority spin for the photoelectron means that the spin of the remaining shell from which one electron is removed has majority character, i.e., is parallel to the spin of the majority electrons. Core level spin polarization can be used as an element-specific indicator of magnetic order. For a number of nonferromagnetic elements theoretical calculations predict a ferromagnetic ground state for a monolayer film of
Binding energy (eV)
Figure 6 Spin-resolved 3p core level photoemission for 1.5 nm Cr\Fe(100) (from Hillebrecht et al. 1992). Photon energy 117 eV, normal incidence and emission. A constant background, matched to the spectrum on the low binding energy side, was substracted from the spectrum.
this element. A famous example is antiferromagnetic chromium, which in the bulk has a mean magnetic moment of 0.6 µB. For a chromium monolayer on iron an enhanced moment of 3.6 µB was derived, with ferromagnetic order within the chromium layer, coupled antiferromagnetically to the ferromagnetic iron substrate. Figure 6 shows a spin-resolved chromium 3p photoemission spectrum taken for a monolayer (0.15 nm) of chromium on Fe(100) (Hillebrecht et al. 1992). The spectrum shows a large spin polarization, which is opposite to that of the 3p spectrum of the iron substrate. This demonstrates the antiferromagnetic coupling between the iron surface and the chromium overlayer. The magnitude of the chromium 3p polarization indicates that the chromium moment is smaller than the predicted 3.6 µB. This is caused by structural intermixing between chromium and iron atoms occurring during chromium deposition, leading to a higher chromium coordination.
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