Spin-Polarized Electrons in Solid-State Physics

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS. VOL. 62

Spin-Polarized Electrons in Solid-state Physics H . C. SIEGMANN. F. MEIER. M. ERBUDAK. AND M . LANDOLT Laboratoryfor Solid State Physics Swiss Federal Institute of Technology Zurich. Switzerland I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Production of Spin-Polarized Electron Beams . . . . . . . . . . . . . . . . . B. Measurement of Spin Polarization . . . . . . . . . . . . . . . . . . . . . . . C. Various Types of Experiments with Polarized Electrons . . . . . . . . . . . . 111. Magnetism in Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Bulk Electronic Structure in Elemental 3d Ferromagnets . . . . . . . . . . . B. Many-Body Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Temperature Dependence of the Surface Magnetization . . . . . . . . . . . . D.Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Magnetism in Systems with Localized Magnetic Moments. . . . . . . . . . . . . A . Rare-Earth Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. 3d Transition-Metal Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Actinide Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. The Symmetry of Electronic States . . . . . . . . . . . . . . . . . . . . . . . . . A. Identification of Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Mixing of Orbitals (Hybridization) . . . . . . . . . . . . . . . . . . . . . . . C. The 100%Polarized-Electron Source . . . . . . . . . . . . . . . . . . . . . . D . The Effect of Lattice Disorder . . . . . . . . . . . . . . . . . . . . . . . . . . VI . The Spin Dependence of the Elastic Scattering of Electrons from Solids . . . . . A . Surface Structures in Nonmagnetic Materials (SPLEED). . . . . . . . . . . . B. Surface Resonances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Exchange Scattering on Magnetic Surfaces . . . . . . . . . . . . . . . . . . . D . The Special Case of Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . VII. Secondary Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Emission of Secondary Electrons from Nonmagnetic Metals . . . . . . . . . B. Secondary Electrons from Ferromagnets . . . . . . . . . . . . . . . . . . . . VIII. Surface Magnetochemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Surface Magnetization and Segregation . . . . . . . . . . . . . . . . . . . . . B. Surface Magnetism Induced by Surface Chemical Reactions. . . . . . . . . . C. Spin-Flip Scattering on Paramagnetic Surface Atoms . . . . . . . . . . . . . IX . Surface Magnetization Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Magnetization Perpendicular to Surface. . . . . . . . . . . . . . . . . . . . . B. Magnetization Parallel to Surface . . . . . . . . . . . . . . . . . . . . . . . . X . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

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Copyright 0 1984 by Academic &ss Inc. All rights of reproduction in any form mrvd. ISBN 0-12-014662-2

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I. INTRODUCTION In the present era of solid-state physics, innovations are often direct applicationsof the basic principles of quantum mechanics as exemplified by the Josephson junction, the K. von Klitzing quantum Hall effect, or the G . Binnig tunneling microscope. Spin-polarized electrons exhibit quantum character in a pure form: for a given direction in space, there are only spin-up and/or spin-down electrons, nothing in between. This is one of the puzzling foundations of quantum mechanics. The availability of sources and detectors of spin-polarized electrons allows direct application of this phenomenon such as in the probing of the famous Heisenberg-Dirac exchange interaction. Progress in spin-polarized electron-beam techniques has been closely connected to progress in surface physics. It was only one year after the first true photoelectron spectra of polycristalline nickel had been obtained (1) that the spin polarization (SP) of these photoelectrons was discovered (2). Several earlier attempts to extract SP electrons from magnetic materials had failed. With linearly pciarized light, and with atomically flat and magnetically soft single crystalline surfaces, the photoelectron spin polarization (photo-ESP) from Ni reached its ultimate threshold value of -100% (3). In the scattering of SP electrons from solid surfaces, development accelerated with the invention of the GaAs spin-polarized electron source (4). It relies largely on the sophisticated technique of producing GaAs surfaces with negative electron affinity. The source produces a spin-modulated electron beam which makes possible the detection of spin dependence in electron interactions down to a level of, at present, one part in lo5. The unique potential of this technique is by no means exhausted. The development of simpler and more efficient, or more accurate, detectors of spin polarization has also contributed to a remarkable expansion of the field. There have been quite a few surveys on SP electrons, however, they were either rather general (5, 6) or quite specialized; e.g., photoemission (7), electron scattering (8), and low-energy electron diffraction (LEED) (9). In the present survey, we try to cover all the important applications in solidstate physics known up to the present time. However, all experimentscould not be discussed due to the large diversity of this field, which ranges from certain antiferromagnetic 3d transition-metal oxides over the actinides to nonmagnetic metals and semiconductors on the material side, and from secondary-electron emission, LEED, Auger spectroscopy, and normal and inverse photoemission on the technical side. We wish to apologize to our colleagues whose work could not be included. We hope that this review will

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be useful to scientists intending to start their own research work in this promising field as well as to surface or solid-state physicists or chemists wishing to be informed. With the aim of reaching a large audience, the description of apparatus as well as the use of mathematics was kept minimal. For a full quantum mechanical treatment of spin-polarized electrons, the reader is refered to J. Kessler’s book (10) and to a paper by P. S. Farago (11). In most solid-state physics applications, the nonrelativistic limit applies, and the vector of spin polarization is given by P = ((a,), (a,,),. (az)} where a, are the Pauli matrices. The degree of SP along a direction in space is given by P = (nt - nJ)/(nT nJ) with nt(J) the numbers of up(down)-spin electrons. The degree A of the spin asymmetry in the interaction of electrons iJ) where it(J)is the current of with an object is given by A = (it - iJ)/(if particles (electrons or photons) emitted from the object under bombardment with the incident electron beam polarized completely parallel(antiparallel) to a direction in space; A measures the strength of the spin-dependent part of the interaction.

+

+

11. EXPERIMENTAL TECHNIQUES A . Production of Spin-Polarized Electron Beams

During the past 20 years, a wide variety of sources of SP electrons have been developed based on a diversity of physical principles. Many sources rely on techniques employed in atomic physics: electron scattering from an unpolarized Hg beam (12); photoionization of unpolarized alkali atoms by circularly polarized light (13); photoionization of polarized Li atoms (14); optical pumping of an He discharge (15); and resonant two-photon ionization of alkali atoms (16). Sources employing solids or solid surfaces include field emission from W coated with ferromagnetic EuS (17); photoemission from ferromagnetic EuO (18); electron diffraction at a single crystal (19); photoemission with unpolarized light from W single crystals (20); and photoemission from negative electron affinity (NEA) GaAs (4). The quality of a source can be measured by the following characteristics (21): intensity fi degree of polarization P ; figure-of-merit P2fidirection of polarization and ease of its reversal; emittance or richtstrahlwert; brightness, energy spread of the electrons; and short- and long-term stabilities. For most applications the solid-state source based on photoemission from a 111-V

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compound is superior to all others and is presently used in many laboratories. Since the electrons are emitted by irradiation of the cathode with circularly polarized light, the emission intensity is large and pulsed operation is easy. The intensity of the SP beam is usually space-charge limited. The GaAs cathode can be operated under NEA conditions where the quantum yield is of the order of 0.1. The degree of electron spin polarization (ESP) is theoretically 50%(22), the sign of which can be rapidly and easily reversed by changing the direction of the circularly polarized light without otherwise affecting the characteristics of the electron beam. The energy spread of the electron beam is 0.1 -0.2 eV (23). The emittance as well as the brightness of the GaAs photoemission source is better than that for the other sources (21) due to the unique properties of the NEA surface (23). An SP electron gun consists of the GaAs photocathode, electron extraction and deflection electrodes, and electron optics to collimate the photoemitted electrons into a beam of transversally polarized electrons (Fig. 1). The spherical deflector rotates the momentum vector through 90" without influencing the polarization vector and thereby converts longitudinal into transverse polarization. Transverse polarization is necessary in most solidstate applications. The spherical condenser also produces an image of the cathode at the effective entrance aperture within the first element of the zoom lens. The latter focuses the beam onto the target at the desired kinetic energy of the electrons. The source material is a degenerately Zn-doped GaAs crystal. There can

W EH N ELT

FIG. 1. A perspective view of the GaAs photoemission source of polarized electrons employed at the Swiss Federal Institute ofTechnology in Zurich. The first element ofthe zoom lens (nearest to the spherical deflector) is at ground potential; it is a straight-through valve separating the source chamber from the experimental chamber. The second lens element with the applied potential V, decelerates the electrons by a factor of 10. The electrons are again accelerated by the third lens element (at a potential V,) such that V,/V, = 3.6. The potential V4 of the final lens element determines the kinetic energy ofthe electrons leaving the zoom lens. In this way, the focal properties of the zoom lens are maintained over a large energy range.

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be variations in the cathode material and in the preparation of a clean surface prior to activation. GaAsP crystals (24) and molecular-beam-epitaxy-grown GaAs-Al,Ga,, superlattices(25) have been used besides chemically cleaned (100) GaAs (26). Electrons are produced by irradiation of the GaAs surface exhibiting either slightly positive electron affinity (PEA) (2 7, 28) or NEA (22). The PEA surface yields 20-4OYo polarization depending on the energy of the exciting light (27). For a NEA surface at room temperature, the ESP is 32 - 36Yo. The polarization increases by a factor of 1.3 if the sample is cooled to 80 K. Epitaxy-grown cathodes deliver the highest possible ESP of 50%. If the light is left-circularly polarized (a+),i.e., the light angular momentum is in the direction of light propagation, the polarization of electrons photoemitted is antiparallel to the incident-photon angular momentum, and hence ESP is parallel to the electron momentum. For a- light the ESP is in the direction of light propagation and is antiparallel to the electron momentum. The helicity of the light can be modulated at any desired frequency to obtain a spin-modulated electron beam. Since polarized electron sources based on photoemission from GaAs have been described previously in detail (26, 28), only the major aspects were outlined above. The physics of the operating principles are given in Section V.

-

B. Measurement of Spin Polarization Studies of spin-dependent,phenomenain electron spectroscopy require a polarization detector. So far the most widely used polarization analyzers are based on high-energy Mott scattering (29) where the spin component transverse to the scattering plane is measured. Spin-orbit interaction of the incident electron with the scattering center, which is a heavy atom such as gold that is part of a thin foil, creates a left-right asymmetry A of the scattered intensities from which the polarization P is obtained via the Sherman (30) function S : PS = A. The merits and disadvantages of the Mott detector have been described several times (10, 31). It played a dominant role in applications to atomic and solid-state physics. There, however, it meets strong competition from a newly developed device which is discussed below. In high-energy experiments such asp decay (32), its further existence will not be endangered because it eliminates complicated electron- optical coupling between the source and the detector. There are polarization detectors working at low energies. Analogous to the high-energy Mott detector, the beam of polarized electrons may also be scattered at lower energies from an atomic beam (3334). Alternatively, the

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left-right asymmetry in the diffraction oflow-energy(-100 eV) electrons at single crystals has also been used to determine P. This is the so-called PLEED detector (35). A still different proposed method for measuring P makes use of the fact that a target which is bombarded with polarized electrons emits circularlypolarized light; Pis then derived from the degree of circular polarization (36). Various analyzers have been compared (34). The high-energy Mott scatterer has the capability of handling electron beams of poor optical quality, i.e., beams having a large diameter with a large angular or energy spread. Low-energy analyzersare severely affected by the degradation of the beam quality. If I, is the current incident into the analyzer and I the detected current, then I/I, is the sensitivity of the device. It has been shown (10) that, with respect to statistical errors, the figure of merit describing the efficiency of an analyzer is S2Z/Zo.The Sherman function has values 0.2-0.4 for all Mott detectors and the PLEED analyzer, whereas the sensitivity is between and lo+. Therefore, the figure of merit is at best lo4 in these cases. A simple and compact low-energy spin-polarization detector has been realized based on the spin asymmetry in electron absorption (37, 38). It is more efficient than existing detectors, less elaborate,and it can be built to be moveable. We outline the principle of operation in the following text. Electrons scattered at a solid surface are subject to the Coulomb potential of the surface atoms and to the spin - orbit coupling of the electron spin s with its own angular momentum 1as produced during the scatteringprocess. For magnetically ordered materials there is also the exchange interaction with the aligned spins in the surface. The physical and chemical properties of the target material as well as the scatteringgeometry and the electron energy E influence these effects. If the exchange interaction is dominant, the quantization axis in the scattering process is the direction of the target magnetization; otherwise it is the direction of the angular momentum of the electron as it scatters. For diffuse scattering, the latter is the normal of the plane spanned by the momentum of the incident electron and the surface normal n. It is undefined for normal incidence (a= 0). Spin-dependent effects are most prominent if s is along the quantization axis. The total intensity I, diffusely scattered from a target depends on the energy E, intensity I,, and angle of incidence a of the incident beam. The total current collected by the target is given by I, = I, - I,. An unpolarized beam of electrons can hit the target at such an energy that the secondary-electron yield is unity, i.e., I,-, = I,. Then the current absorbed by the target is zero, I, = 0. At lower energies ( E < E,), electrons are predominantly absorbed by the target. For E > E,, more electrons leave the target than are incident on it. At E,, the situation is analogous to a bridge circuit: the incident current I,

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FIG. 2. The current absorbed by a polycrystalline gold target versus the energy of the electrons incident on the target. The incident electrons are fully spin polarized in either direction (lines P = +1 and P = -l), or unpolarized (dashed line): E, = 141.0 eV, a = 35"; A = E o , - E , , = 3 . 4 e V ~ = ( I , - 1 , ) / 1 , = 1.5%.

is exactly compensated by the scattered current I,. If now an electron beam with a degree P of spin polarization strikes the target instead of an unpolarized beam, the bridge is offset because of the spin dependence of the various scattering mechanisms involved. Electrons with spin parallel to the quantization axis are preferentiallyabsorbed (IT)by the target, and those with spin antiparallel are preferentially scattered such that I = IT - IJ is the spin asymmetry of the absorption. A beam fully polarized along the quantization axis shows zero absorption at Eorand for antiparallel spins, zero absorption occurs at Eol # Eot . We denote these two energies by A = Eot - Eol. This is shown in Fig. 2 for a polycrystalline sample of gold (39). The first observation of a spin dependence in electron absorption was made with the ferromagneticglass Ni,Fe,B,, where the spin dependence is caused by the exchange interaction (40); 7 = I/Io was found to be where I is the difference in the absorbed currents for a beam poliarzed completely parallel and antiparallel to the quantization axis. After the observation of a strong spin dependence with 7 = lo-, in absorption of a Au( 1 10) target due to spin-orbit coupling, it became clear that a new polarization detector of high efficiency could be realized (39). In a practical ESP detector one exploits the spin-orbit coupling. It produces higher efficiencies and magnetic fields to align the magnetic domains are not required. Polycrystalline samples are, of course, easier to prepare than single crystals (39). Clean polycrystalline gold targets yield q = 0.59/0 for a = 35" at Eo = 138 eV. This value goes up to 1 .5% for contaminated surfaces (39). Experiments at various Eo values [higher values of Eo are obtained by suppressing the true secondaries by means of a retardation and lower values by depositing minute amounts of cesium onto the surfaces (39)] did not enhance q in the case of Au.

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TARGET

e-

7 h

FIG.3. Schematic diagram of an absorption detector for electron spin polarization.

Since spin - orbit coupling generally increases with 2, experiments have been performed on polycristalline uranium. It is difficult to keep uranium clean because of its chemical reactivity. However, q = 12% was obtained with “stabilized” U surfaces (41). To maximize q, one has to use a material with high 2 and a work function such that E, occurs at an energy where the elastically scattered electrons dominate the secondaries [it is the elastic scattering which produces the spin dependence in absorption (40)]. Various modes of operation of an absorption detector have already been suggested (3 7, 42). Figure 3 illustrates the construction of an absorption detector (43). The electron beam of unknown polarization hits the target under an angle of incidence a.The target and its surroundingsare at such a potential that the absorbed current for an unpolarized beam is zero; I, = Is is obtained by measuring all the scattered electrons. From the current I absorbed in the target, one obtains the degree P of spin polarization along the quantization axis as

p = (2lv)(IlIs) The statistical uncertainty AP is (42)

AP = 2/qz, The analogous expression for the Mott detector (lo)reads

AP = (0s*I,)-’ where Q is the differential cross section for backscattering of 100 keV electrons at a thin target. We see that the absorption detector is superior at least in principle to the Mott scattering detector and, furthermore, much simpler. However, the electrons absorbed in the target cannot readily be counted. Also, the electron beam under investigation must be fairly monochromatic in the case of the absorption detector. Hence, at present, it still depends on the physical situation as to which detector is best.

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C. Various Types of Experiments with Polarized Electrons A natural classification of the experiments involving the spin polarization of electrons arises from the technical requirements, namely, whether one needs a spin-polarizedelectron source or a detector for spin polarization or both. There is some similarity between this classification and the one commonly used in atomic physics, where one speaks of single-, double-, and triple-scattering experiments (20). This can be understood as follows: Consider the scattering of electrons from an object. The scattering is spin selective if one spin state is preferentially scattered into a certain angle. To detect the spin selectivity, one need only measure the intensity of the scattered electrons if one has a polarized source. However, the scattering could also be spin productive. To detect the spin productivity, one may start with unpolarized electrons, but then one needs to detect the spin polarization of the scattered electrons. In the case of elastic scattering of electrons from unpolarized atoms such as gold, the spin dependence arises from spin-orbit coupling. The spin selectivity is then exactly equal to the spin productivity from symmetry reasons (20). Two scattering experiments are needed to detect the spin dependence. In the first scattering, a degree of spin polarization P is generated, and in the second scattering, P is measured. However, solids are generally not as highly symmetric as atoms; crystal structures without mirror symmetry about the scattering plane are quite common. Furthermore, in present solid-state electron sources, spin polarization is not produced any more by elastic scattering of electrons on heavy atoms. Hence the classification in terms of single-, double-, and triple-scattering experiments is not useful here. It is helpful to keep one general requirement in mind: in order for an object to select a spin state or to produce a spin polarization, an axial vector must be defined, either within the object, for instance, through a chiral crystal structure or the direction of magnetization, or the scattering itself must define an axial vector, for instance, by the circular polarization of an absorbed photon. We give an example of how the scattering geometry can define an axial vector in the case of electron scattering from a solid. If k,is the wave vector of the incident electron and k the wave \lector of the electron emerging from the solid, k, X k defines an axial vector as long as k is not parallel or antiparallel to k,. Spin selectivity or spin productivity occurs along the preferred direction parallel to k,X k, which is the direction perpendicular to the scattering plane. However, as opposed to scattering from spherically symmetric atoms, spin-polarization phenomena with solid targets are not necessarily confined to this quantization axis (Section V1,A). Typical experiments that require a source of polarized electrons are cathodoluminescence, in which one observes the intensity and/or circular

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polarization of the light emitted from a solid on which a spin-polarized electron beam is incident. The intensity of the light can depend on spin if the solid is magnetized. This is inversed-spin-polarized photoemission. The circular polarization of the luminescence may also depend on spin if the electrons recombine with appropriate spin - orbit split states. This inverses the principle of operation of the GaAs source of spin-polarized electrons. Further experiments with a source involve elastic and inelastic scattering of electrons from magnetic materials or into a defined angle in the case of nonmagnetic materials with spin - orbit coupling. Typical experiments that require a detector of spin polarization include photo- or field emission of electrons from magnetic materials, photoemission from nonmagnetic solids with circularly polarized light, or angular resolved photoemission. Furthermore, inelastic or elastic scattering of unpolarized electrons on magnetic materials or on nonmagnetic materials into a defined angle is also spin productive. Spin-selective experiments using a source of polarized electrons are formally the inverse of spin-productive experiments using a detector. However, the information obtained is not identical. For instance, the SP of photoelectrons from magnetic materials reflects the SP of the occupied electron states below the Fermi level, whereas luminescence on bombarding with a spin-polarized electron beam yields the SP of the nonoccupied states above EF.There are also experiments that need both a source and a detector for SP. These experiments deal with the detection of the changes of SP that occur in the interaction with a polarized electron beam. As an example, we mention spin - flip scattering of electrons through quantum mechanical exchange or electron - magnon scattering in ferromagnets. This review does not cover the whole field of SP phenomena in solids or at solid surfaces. C . Rau and co-workers (44) have developed a technique sensitive to SP of electrons at the surface of a solid. A beam of fast deuterons is passed by a ferromagnetic surface. The SP of the captured electrons is detected by the hypefine interaction with the nuclear spin moment in a subsequent nuclear reaction. There are also experiments in which the electron source and detector for SP is within one and the same solid, and the electrons are never emitted into vacuum. Meservey and co-workers (45) were the first to actually demonstrate that such experiments are possible. Spin-polarized electrons from a ferromagnet, e.g., Fe, Co, and Ni, tunnel through an oxide layer into superconducting Al. The ferromagnet acts as the source and the superconductor as the detector of SP. Scifres et al. (46) have proposed measuring the SP of electrons injected into a semiconductor by observing the circular polarization of the radiation emitted on recombination with p-type impurities. Another possible way to detect SP may be provided by the Schottky bamer between a fei-romagnetic metal and a

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ferromagnetic semiconductor. Such barriers depend on spin state, and internal photoemission over or tunneling through this bamer must therefore be spin selective (47). Electron scattering in point contacts containing impurities with a spin moment is also spin selective (48). These techniques overcome the necessity of a vacuum and therefore are particularly attractive for future applications of the spin degree of freedom in solid-state electronics. However, this field is only at its very beginning and therefore shall not be treated here. There are combinations of internal photoemission and vacuum electron-beam techniques in which the SP electrons are generated in a substrate acting as a source and travel through an overlayer and escape into vacuum where their SP is measured. These experiments are included in this review and are presented in Section VII1,C. 111. MAGNETISM IN METALS

A . Bulk Electronic Structure in Elemental 3d Ferromagnets

The theory of ferromagnetism in pure 3d metals such as Fe and Ni has been a topic of constant interest. Today, there is confidence that groundstate properties are described by band calculations (49). Even thermic excitations can now be treated with fluctuating-band theories (50) yielding thermodynamic properties such as transition temperatures. Photoemission spectroscopy in the vacuum ultraviolet is capable of directly revealing band-structure features. However, the process of photoemission may leave behind the solid in an excited state. In the case of a narrow-band metal such as the test case Ni, these excitations turned out to be important. The correlation between the 3d electrons is strong and determines the spectral distribution of the holes created in photoemission. Therefore the observed single-particle energies may be different from those of the ground-stateband structure or its thermal excitations. In particular, the observed bandwidth is reduced, and the exchange splitting is about half that of the ground state (51 - 53). Furthermore, the self-energy corrections explain the existence of the satellite structure below the d bands (Section 111,B). It is the spin-, energy-, and angle-resolved measurement of photoelectrons from the valence bands that can yield a quantitative measure of the contributions of many-body phenomena in modifying the one-particle band structures. Spin polarized photoemission from magnetic materials requires a magnetic field at the emitting surface. This magnetic field specifies the z direction along which the spin polarization (a,) is defined and generates a uniform magnetization in the sample in the region of the light spot for

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photoemission. The magnetization may be perpendicular or parallel to the photoemitting surface. The latter geometry allows energy- and angle-resolved SP measurements, but can only be applied to special materials such as atomically flat and homogeneous single crystals magnetized in the easy direction (Section IX). Since s, along the magnetization of the sample is measured and averaged over many atoms, the SP reflects magnetic long-range order. In contrast, the exchange splitting observed in angle-resolved photoemission (54, 55) is an “atomic” property, and its temperature dependence reflects short-range order and does not concur with the magnetization. The interpretation of SP photoemission spectra (i.e., polarization versus photon energy without energy and angle resolution) in general is complex because not only peak position in energy but also emission intensities are measured since the polarization is the differencebetween up- and down-spin emission currents. Full photoemission calculations including photon matrix elements and spin-dependentinelastic mean free paths of hot electrons are thus needed to interpret the spectra. However, a special case is the Photo-ESP with single crystals right at photothreshold where the phase space is restricted and both angular and energy resolution are inherently present. Furthermore the self-energy corrections mentioned above are zero for photoelectrons at threshold since the excitation occurs directly from the Fermi surface. Special attention has to be given to the escape depth of photoelectrons and its possible spin dependence. The inelastic mean free path of electrons near photothreshold ranges from 10to 100A. Spin polarized photoemission data reflect the bulk, since magnetic and electronic surface properties of 3d metals change more rapidly, usually within the first atomic layer (Section II1,C). The spin dependence of the inelastic mean free path is at present under active discussion. Upper limits are established by elastic electron scattering from glasses (Section V1,C). The SP spectrum, notably without energy resolution, of Ni( 100) (56) is presented in Fig. 4. The corresponding spectra for the two remaining low-index faces of Ni have also been measured (5 7,58) and have turned out to look very similar. The polarization always is negative at threshold and turns to positive values at photon energies within a few tenth of an electron volt above photothreshold. These spectra are in qualitativeagreement with a simple initial DOS picture (59) within the Stoner-Wohlfarth model with filled majority bands. Details of the spectra, specificallythe photon energies at which the polarizations change sign, contain information on the value of the exchange splitting A. The spectra along (100) and (1 1 1) were found to correspond to photoemission from bulk bands with a small exchange splitting of A = 0.33 eV (60). Doublet structure in angle-resolved photo-

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS P

13

(%I 30

20

10

0

- 10

-20

-30

FIG.4. Spin polarization of the total photoelectron current versus photon energy for Ni(100): T = 273 K B = 34 kG. [From Ref. (56j.l

emission can also be interpreted as an exchange splitting of A = 0.3 1 eV (54, 55). It later became clear that the reduced A is a consequence of the additional hole in the 3d band left behind in the photoemission process (52). A puzzle still remains for the spin polarization of Ni( 1 10). Kisker and co-workers (3) have studied a transversely magnetized Ni( 110) single crystal using linearly polarized light. They were able to show that optical selection rules can successfullybe used in measurementsof the electron spin polarization as is shown by the two spectra for E//[ 1 101 and E//[ 1001, respectively, in Fig. 5 . For mirror-plane emission (in particular, normal emission), the symmetry of the dipole-allowed initial state is the same as that of the dipole operator causing the optical transition. In the case of Ni( 1 lo), excitation with the electric vector E along [ 1 10J yields emission from C4 bands alone, whereas for E along [loo], the emission is restricted to Z3 bands. Bandstructure calculations show that emission from Ni( 100) at photothreshold comes from the close vicinity of the Xpoint in the Brillouin zone. The large, almost total negative polarization of the Z4 emission at threshold (Fig. 5a) demonstrates that the minority X , point lies above EF,which is in qualitative agreement with self-consistent calculations (49). The fact that the crossover energy from C4is larger than that observed from Ni( 100)indicates that X , lies above X , ,again in qualitative agreement with calculated energy

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t

-20. -40.

-60. -80. -100

P (%)

b)

20 1

.

.'

t:

- 1

FIG.5. Electron s e n polarization of the total photocurrent from Ni( 110) using linearly polarized light: (a) Ell[ 1 lo]; (b) E11[001].The inset (c) shows the sample geometry [from Ref. (3)l.

bands. These statements are sensible only if 3d-electron correlation effects (52) do not invert the order of levels, and we do not see any reason why they should. The emission from X3 bands, on the other hand, exhibits a spin polarization (Fig. 5b) which strongly contrasts with what is expected from bulk band structure. If bulk initial states were responsible for this polarization then it should be identical, at least near threshold, to that observed from Ni( loo), since the Z3bands run into the X5bands at the X point. The two curves of Figs. 4 and 5b do not, however, show any resemblance. Dominant surface-state emission from Ni( 100) (61) could account for the discrepancy, but this is doubtful because of insufficient surface sensitivity of integrated photoemission. Spin-polarized inverse photoelectron spectroscopy provides information complementary to photoemission since it tests the unoccupied states or the density of states of the holes above the Fermi level. In this technique, the surface is bombarded with SP electrons of variable energy, and the photon flux due to radiative transitionsis measured. Again, it is the test-case Ni that was investigated first (62), particularly since the holes in the d band produce ferromagnetism in this case. The first results on Ni( 1 10)are consistent with band theory.

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

15

B. Many-Body Eflects The correlations among 3d electrons can modify the one-electron energies observed in photoemission if the correlation energy U is larger than the bandwidth. In this sense, the term “many-body effects” already applies to some valence-band features discussed in Section II1,A. The valence-band satellite of Ni 6-eV below the Fermi level is the strongest manifestation of a many-body effect, since it occurs if the final state consists of two 3d holes on the same site (53, 63). This satellite exhibits resonant enhancement for a photon energy hv = 67 eV coinciding with the 3p- 3d excitation in Ni (64). Feldkamp and Davis (65) predicted large SP in the resonant part of the satellite based on the following model: At the 3p threshold, 3p electrons are resonantly excited to empty 3d states. The excited 3p53dI0state then decays via a super-Coster- Kronig- Auger transition to a 3p63d8configuration. The two-hole state where the holes are at the same atom rises in energy by the effective hole - hole Coulomb interaction. This determines the apparent binding energy of the satellite electron at resonance. The SP of the Auger electron comes about since only 3pJ (minority spin) electrons can be excited to 3dJ states (the majority 3d bands are full). Transition probabilities of the decay process then lead to a net SP of the emitted electron. Feldkamp and Davis (65) predicted P = +60% for this model. Measurement of the SP of the satellite is the most conclusive technique for discriminating against alternative explanations based on a one-electron band picture or on excitation processes involving 3p 4s,p transitions. The experiment requires an energy resolution better than 1 eV and variable photon energies from a synchrotron source. It was successfully performed by Clauberg et al. (66). In Fig. 6 (see next page), the measured SP of the satellite is shown: (a) the measured intensity at hv = 67.7 eV; (b) the raw data of the SP; and (c) the measured SP after subtraction of a large unpolarized background. The electrons in the satellite are found to be largely spin polarized. The inset in Fig. 6 shows the sample and photoemission geometry. The samples were large single crystals cut like picture frames in order to obtain a fringe field free-transverse magnetization (Section IX,B). Constant initial state spectra show a resonant enhancement not only in the intensity but also in the net SP of the satellite electrons. The maximum value of (57 f 15)% near hv = 67 eV was found to be in very good agreement with the prediction by Feldkamp and Davis (65).

-

-

C. Temperature Dependence of the Surface Magnetization Mean field theory has been highly successful in describing the temperature dependence of the spontaneous magnetization in three dimensional

16

H. C. SIEGMANN et al.

1412-

c=

10 86420-

a N 4

2

0

n

2 100v)

80 60.

40 -

.

20.

OL -;2

hv

'

-h

-;

' Ec=O BINDING ENERGY (%I

I

FIG.6. Energy-resolved photo-ESP of the 6-eV satellite from Ni( 110) measured at

= 67.7 eV: (a) energy distribution curve; (b) ESP correspondingto (a); (c) spin polarization

of the 6-eV satellite after correction for the intensity and polarization of the background. The inset shows the sample and photoemission geometry [from Ref. (66)].

magnetic systems. However, it breaks down if one approaches the transition point closely enough. The relative importance of short-range order is also greatly enhanced by lowering the lattice dimensionality. Spin-polarized electrons offer for the first time the possibility of measuring the magnetization at well-defined surfaces of truly semi-infinite solids. The decrease of the spontaneous magnetization with temperature T as well as the magnetic term in the specific heat is caused by the thermal excitation of magnons. F. Bloch showed that the relative bulk magnetization Mb(T)/Mb(0)decreases according to

Mb(T)/Mb(O)= 1 - CbT3/* if Tis sufficientlylow to neglect magnon- magnon interactions;Mb(0)is the spontaneous magnetization at T= 0; and c b is a constant. Mills and Maradudin (67) found the same law for the relative magnetization p = Ms(T)/M,(O)of the surface of a semi-infinitesolid, except that C, = 2cb

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

17

due to the excitation of additional surface magnons. At low T, the magnons have long wavelength, and there is no difference between the localized and the itinerant picture of magnetism. Hence the result obtained by Mills and Maradudin with the Heisenberg model should also hold for itinerant systems as long as T is sufficiently low. Attempts to test the theory of Mills and Maradudin by specific heat measurements have been inconclusive so far (68). The reason is that the disturbance caused by the surface is confined to the very first layers. Photoemission of electrons, especially close to photoelectric threshold, in general also cannot deliver a clear picture of M,( T) since the probing-depth range 10- 100 A is generally too large. However, the elastic scattering of electrons at energies in the range 50 - 100 eV has the shortest probing depth, correspondingto travel, on the average, one-half the mean free path into and out of the sample. This amounts to little more than one atomic layer in most materials. The spin dependence S of the elastic scattering of spin-polarized electrons has been used successfullyto measurep = Ms(T)/Ms(0)at low Tand at T T, in itinerant ferromagnets.With S = (it - iJ)/(it iJ),where it(J)is the intensity of electrons scattered from the magnetic surface when the incident beam consists of majority (minority) spins, we see that S must change sign when p changes sign. Hence we have

+

s=ap+pp3+yp5+

-

*

It is assumed that the stray magnetic field generated by the magnetization of the sample does not deflect the electrons (Section IX). It is further assumed that 1s coupling does not affect the scattering. In a single crystal the electrons are diffracted and multiply scattered, and it is not clear which term 0 for T -, T, ,the term is dominant in a diffraction spot. However, as p ap becomes dominant. Hence magnetic single crystals are suitable for the measurement of the high-T regime and for determination of critical exponents. When there is only single scattering, we have S = ap at all T. It has been shown that this applies to the case of electron backscattering from metallic glasses (Section V1,C). Therefore, magnetic glasses are ideal for probing the effects of long-wavelength surface magnons. The temperature dependence of the relative bulk and surface magnetization in NiaFeaBZ0 with T, = 700 K very near the crystallization temperature is shown in Fig. 7 for T s 0.4TC.Higher temperatures can usually not be measured with metallic glasses because of the surface segregation and crystallization. The bulk magnetization was obtained from separate measurementswith a moving sample magnetometer. The T3I2law is valid for the bulk with C, = 19.104 deg-312. The relative surface magnetization p( T) was obtained from elastic scattering of 90 eV electrons. Residual asymmetries

-

18

H. C. SIEGMANN et al. 1.0

- 0.8 t-

0.7

I

0

I

50

1

1

I

100 150 200 TEMPERATURE ( K )

I

250

I

300

FIG. 7. Temperature dependence of relative bulk and surface magnetization in the ferromagnetic metallic glass Fe,Ni,B, as measured by elastic backscatteringof spin-polarized electrons at 90 eV [from Ref. (69)]. The solid and dashed lines for the bulk and surface magnetization are the PI2law with constants C,, and C, as given in the text.

introduced by stray magnetic fields or the apparatus have been removed by changing both the spin of the incident beam and the direction of magnetization in the sample and by averaging the results. The T3I2law fits the data very well, confirming the predictions of Mills and Maradudin; however, C,= 3Cb(69). The surface disturbance extends increasingly into the crystal as T, is approached. This is connected with the critical divergence of the spin-spin correlation length near T,. The surface magnetization p( T )is predicted by scaling theory (70, 71) to follow a power law near T, according to p( T ) = const( 1 - T/T,)Ps

where p, is the critical exponent of the surface magnetization. Alvarado et al. (72, 73) determinedp, on Ni( 100)and ( 1 10)surfaces by the spin dependence of elastic electron scattering at energies ranging from 13 to 67 eV. Figure 8 shows results obtained for the ( 1 10)surface with an electron energy of 49 eV where the probing depth is at minimum. The T dependence of the bulk magnetization as measured by neutron scatteringis also shown. Whereas the critical exponent of the bulk is roughly one-third, Alvarado et al. obtained p, = 0.79 k 0.02 for the (1 10) surface and p, = 0.81 f 0.02 for the (100) surface. One might have expected some difference in the magnetic behavior of these surfaces, since (1 10) is believed to be contracted by 5 - 8% of the lattice constant toward the bulk, whereas the more densely packed ( 100) surface is not. Theoretical values forp, depend on the model. The Ising, XY, and Heisenberg models yield p, = 0.776 - 0.8, 0.79 - 0.835, and 0.81 - 0.88, respectively (74). It is not clear to what extent these theoretical results are applicable to an itinerant ferromagnet.

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

19

0.015

0.010

0.005

0

0.90

0.95 T/ Tc

I .oo

FIG.8. The spin dependence S of the elastic backscatteringof electrons at an energy of 49 eV versus reduced temperature T/T, for a Ni( 110) surface [from Ref. (72)]. The T dependence of the bulk magnetization as measured by neutron scattering is shown for comparison.

D. Alloys Based on the recently advanced understandings of photo-ESP from pure Ni (Sections III,A and III,B), photoemission has also been applied to the Ni-based Ni,-xFe&c substitutional alloy. The deviation of the magnetizaFe in tion from the Slater-Pauling straight line at a concentration of 4% these alloys has been ofgreat interest for many years. It is a crucial test of any theory of itinerant electron magnetism in ferromagnetic alloys on the one hand, and it marks the onset of the Invar regime on the other hand. The question is whether the peculiar behavior of the magnetization concurs with the existence of majority holes in the corresponding concentration range of the alloys (75). Spin polarization of photoelectrons at threshold is the difference between majority and minority densities of states near the Fermi energy and thus can answer the question. Photoelectrons at threshold also reflect bulk properties (Section 111,C). The major concern is whether photoelectron final states in the vicinity of the vacuum level contribute to the observed SP. This can be ruled out experimentally as shall be shown. The power of angle-resolvedphotoemission, on the other hand, is reduced in the case of random alloys since the crystal momentum is broadened (76, 77). Due to the simplicity of interpretation, one is particularly interested in features at or near photothreshold. This requires a well-defined work func-

20

H. C. SIEGMANN et al. 100

P

P/o)

I

90-

0070

-

60

-

50

-

40

~

30 20 -

10 0

'

I

a0 --

I

-

u

I

I

I I I

I / I

I

I

I

-

I

I I I I II

I I I 1 I

I

I

a+

a A

I I I I I

I

-

(a) I

1

-

70-

z

r+

-40-

-50-

-

I

@A

I

I

(b) I

I

-

I

tion Q, of the sample which can be achieved using single-crystal surfaces. The work function Q, of a given surface can be lowered by covering the sample with a small amount of alkali. The vacuum level shifts, and different photoelectron final states come into play. Since the SP of emitted electrons is not altered by an alkali overlayer (Section VIII,C), one can investigate experimentally the role of photoemission final states.

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

21

Figure 9 shows polarization spectra (78) of N&.4Feo,(100) and N&.&,z( 100) with various Ws. The spectra appear to be shifted in excitation energy hv, proving that final states do not influence P.Spin polarization at threshold is positive for N&.4Feo,6 and negative for N&,8Feo,2. This implies that the majority bands are not full in N&.4Fe0,6, in contrast to N&,8Feo,2 and pure Ni. The fact that majority holes occur in Ni - Fe alloys at the concentration where the magnetization deviates from the Slater- Pauling straight line was first predicted by Hasegawa and Kanamori (79) who used the coherent potential approximation (CPA) with a very small exchange splitting ANi = 0.35 eV. For a review of other CPA calculations and local environment effects see reference (75). A cluster calculation (80) suggests that for -40% Ni, the presence of strongly antibonding majority spin orbitals and nonbonding minority spin orbitals at the Fermi level is responsible for various Invar anomalies. At higher Ni concentrations the antibonding majority spin level is found to be empty. These results are in qualitative agreement with the sign of the observed polarizations at threshold. Self-consistent band calculations on Fe3Ni representing Invar, fcc Fe, and FeNi in both their para- and ferromagnetic states have been performed (8Z). From comparison of the volume dependence of the local energies it was concluded that Invar is a mixture of para- and ferromagnetic states. The calculated state densities exhibit majority holes in the Fe3Nisystem. The magnitude of the theoretical polarization depends on quantitative details since EF lies close to a very sharp peak in the majority spin-state density. Thus presentday theory can establish only qualitative information. Iv. MAGNETISM IN SYSTEMS WITH LOCALIZED MAGNETIC MOMENTS A . Rare-Earth Materials

The investigation of rare-earth materials has been one of the centers of interest in SP photoemission. A review of the early work is given in Refs. (7, 82). We summarize some of the properties making rare-earth materials attractive for photoemission: ( 1) The localized 4f states have the characteristic features of core levels in that they are largely unaffected by the crystalline environment. In contrast to regular core levels, however, their energy position is close to the Fermi energy (within 1-20 eV), and the 4f shell is only partially filled, according to the position of the element in the periodic table.

22

H. C. SIEGMANN et al.

(2) A direct consequence of the local character of the 4f levels is that rare-earth elements and their compounds exhibit a rich variety of magnetic properties, depending on the type of indirect exchange between the 4f magnetic moments. The insensitivity of the 4f moments themselves to the atomic environment makes them ideally suited to study the effect of indirect exchange. As an example, at T = 4.2 K GdP is paramagnetic if it is structurallydisordered but antiferromagnetic in the ordered, crystalline state (Section IX,A). Another interesting general result is that the bulk magnetic order of polycrystalline antiferromagnetic films [tested materials were EuTe, GdP, GdAs, and GdSb; see Ref. (82)] extends up to the surface. This is in marked contrast with the ferromagnetic semiconductor EuO discussed later. There are magnetic rare-earth compounds where the binding energy of the 4f electrons is sufficiently low that they are photoemitted at convenient photon energies 4 0 eV. To this category belong the europium chalcogenides (83) with the f-shell configuration 4f7. On the other hand, in Gd with identical 4f-shell configuration, the f electrons are more tightly bound, making them inaccessible to photoemission in the near ultraviolet. However, in these materials the effect of the indirect exchange may lead to substantial polarization of the valence electrons (Section V1,D). Due to the strong localization of the 4f levels, the 4fW1final states observed in photoemission are ideally described by the “single ion in the crystal field” model (Section IV,B). The 4f6 final-state multiplet obtained after photoemission from the 4f shell has a width of about 1 eV: The 7FJ(J= 0, ...,6) multiplet is not resolved. The rare-earth compound most extensively studied by spin-polarized photoemission is EuO. A striking observation was reported in Ref. (84): The polarization of the 4f photoelectrons was clearly less than it was before photoexcitation in the bulk. The depolarization mechanism (84, 85) due to spin - flip scattering with disordered surface moments was confirmed in independent experiments (Sections VII1,C and IX,A). The unique energy scheme of EuO produces an anomalously large escape depth of the 4f electrons for hv 5 5 eV, of the order of 100 %, (86). At these photon energies most of the 4f photoelectrons emerge from deep in the bulk. The temperature dependence of the photo-ESP is more complex than expected. The outermost surface layers should exhibit a linear decrease of the magnetization M( T) for T ----* T,, since EuO is a model Heisenberg ferromagnet.The linear decrease ofM( 7‘)is ageneral result ofthe mean field model: It requires nothing more than the breaking of the translational symmetry at the surface (87). Figure 10 shows the Tdependence of the photo-ESP and the magnetization of the bulk. Evidently, P(T) < M ( T ) even at T - T,, showing the

I

I

I

I

I

I

I

-

I

I

-

(a) -

--

I

I

I

I

EuO

I

+

I

2% Gd (b)

I

I

I

I

I

I

I

I

I

-

---

(c)

-

M

M

f

-

24

H. C. SIEGMANN ef al.

-

x = 4.3

01 -

0 ' 0

I

20

'

40

'

60

'

I

80

-

'

1

T(K)

FIG.1 1. Temperature dependence of the total depolarization A = ( M - P)/M as derived from Fig. 1 for trivalently doped E u O EuO x% Gd.

+

effect of depolarization (84). In view of the results presented in Section VIII,C, this points to a number of nonordered moments at the surface, which is clearly below one monolayer otherwise full depolarization would occur. There are strong theoretical reasons for the surface magnetization of EuO to vary linearly with temperature. Although the spin-exchange scattering cross section between the localized 4f moments and the photoelectronsis large, it does not seem to lead to a linear T dependence of the total 4f photocurrent. Still, a clear effect due to spin - flip scatteringwith the ordered surface magnetic moments is evident: It gives rise to the T-dependent part of the depolarization shown in Fig. 11. In this figure, the depolarizaticn A = (P- M ) / M (Pand M are the reduced SP and magnetization, respectively, as shown in Fig. 10)is plotted versus temperature. Disordered surface moments give rise to the T-independent depolarization at T << T,, whereas the additional T-dependent depolarization for T close to T, is due to depolarization by the ordered surface moments. Evidently, doping with trivalent Gd causes the surface moments to couple more rigidly to the bulk, reducing the depolarization. By contrast, the ferromagneticsurface anomaly is evident in the less doped sampleswhere it leads to a strongly T-dependent depolarization. Further details are found in Ref. (88). The spin-polarized photoemission measurements with the rare-earth materials, particularly EuO, have yielded new insights into surface magnetic properties. With respect to surface magnetism, EuO is certainly not the simple prototype Heisenberg ferromagnet which it is considered to be with regard to its bulk magnetic properties. On the other hand, it permits identification of specific surface phenomena more clearly than in other ferromagnetic compounds because of the unique simplicity of the magnetic level scheme. A further interesting feature connected to the ferromagnetism in doped

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

25

0 40 80 120 160 T (K) FIG. 12. Variation of the photothreshold S of 4.30/0Gd-doped EuO as function of temperature; 0 is the paramagnetic Curie temperature of the sample.

EuO is the dependence of the photothreshold on the magnetization (89) (see Fig. 12). Various models have been proposed to account for the observed shift of the photothreshold upon magnetization (90). It seems to be a quite general phenomenon, also occurring for other ferromagnetic semiconductors such as CdCr2S4.The investigation of magnetically induced threshold shifts appears to be an interesting and a still largely unexplored area of surface physics requiring only a modest experimental setup. Threshold shifts are not confined to ferromagnets. In antiferromagneticFe,O, a small decrease of the photocurrent at threshold upon magnetic ordering has also been observed (91).

B. 3d Transition-Metal Oxides Historically,the interest in 3d transition-metal oxides stemmed from the fact that they seemed to be ideal materials in which to study d-band electrons. In the atomic limit we have Me2+and 02-for the simpler oxides such as MnO or NiO; that is, the 4s electrons have been transferred to oxygen, and the problems associated with 3d-4s hybridization in the metals do not arise. Indeed, the magnetic moment localized on Me2+can usually be predicted from the 3dnconfiguration in the crystal field. The attempts to treat the electrons in transition-metalcompounds by the Bloch - Wilson band theory lead to partially filled bands, implying metallic conductivity. This is contrary to the experience, and N. F. Mott pointed out the importance of correlations between d electrons on the band structure.

26

H. C . SIEGMANN er a!.

-

Transport of a d electron from a transition-metal site to the neighboring one 3dnf1.The energy for requires transitions of the form 3dn 3dn 3d"-' this process is the greater the more localized the d electrons or the narrower the band. When the correlation energy U becomes larger than the bandwidth W,transport is impossible. The Hubbard Hamiltonian (92) contains these ideas and is now widely used to investigate the properties of narrowband materials. In photoemission, one measures the process 3dn hv 3d*' e, and in inverse photoemission, 3dn e -, 3d"+l hv. Hence it should be possible to obtain information on U or Wor both from these techniques. The insulating oxides with NaCl structure, e.g., NiO, COO,Fe,O, MnO, and others, have been studied by photoemission (94 - 95), and the following became apparent:

+

-

+

+

+

+

+

(1) 3d states and oxygen-derived 2p states emit photoelectrons at very similar binding energies. According to D. E. Eastman and J. L. Freeouf (94), their relative contributionsto the photoemission spectrum can be separated due to the characteristically different photoemission intensities of p and d states in the photon-energy range 10-90 eV. However, this analysis has been questionned by P. S. Bagus and co-workers (95). (2) Some dominant features of the partial d-state emission spectra are described by ligand field theory of the 3dW1final state (96).This shows that on the fast time scale of photoemission, the interactions of the 3d electrons within one atom (interatomic interactions) are stronger compared to the interactions with a neighbor (interatomic interactions). What one observes then is the excitation spectrum of the ion core left behind. As an example, consider the simple case of a 3d5(Mn2+or Fe3+)initial state in a cubic crystal field. Two lines separated by the crystal field splitting 10 Dq = A constitute the d-state emission; each line corresponds to the emission of an egor a t2g electron from the initial state. One learns very little about the band properties, e.g., the d spectrum of magnetite does not change on going through the metal insulator transition at 1 19 K (97). The natural width of the multiplet lines is given by the lifetime of the hole; it turned out that it is 1-2 eV, which is the same order of magnitude as the separation A of the lines. Hence the multiplets cannot be clearly identified and resolved. Furthermore, the experimental line intensities tend to deviate from the predictions of simple ligand field theory. (3) There are further peaks in the photoemission spectrum appearing at higher binding energies (93,94).Their photon-energy dependence identifies them as states of d parentage, and it is believed that they are manifestations of configuration interaction (95) or other many-body effects (93, 94).

The measurement of photo-ESP has a great potential in helping to

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

27

clarify this complex situation. First, photo-ESP tells readily whether an electron was emitted from the doubly occupied, and therefore essentially unpolarized oxygen 2p bands, or from the highly polarized 3d states. This helps to separate p-state and d-state emission. In the study of the partial d-state emission, photo-ESP is extremely powerful if two adjacent lines in a multiplet have opposite SP. In such a case, the lines can be identified, and their separation can be determined, even if the inherent linewidthsare larger than the line separation. The favorable case of opposite ESP arises for more than half-filled 3d shells aligned in a preferential direction, and for photoemission from two lattice sites A and B with antiferromagneticcoupling, i.e., for the case of A-B antiferromagnets, ferrites, and garnets. It has in fact been shown that the measurement of photo-ESP can be made a diferentiul method comparing the line intensities from one and the same transitionmetal ion on two different cubic lattice sites with high precision (98, 99). Consider the simple case where Fe3+(3d5)is located in the cubic crystal field produced by the oxygen ions in the spinel crystal structure. By photoemission of one 3d electron, the initial spherically symmetric ‘jA, configuration goes into either a 5Eor 5Td2state which is separated by the crystal field energy A. The spinel structure has a tetrahedral A site and an octahedral B site. The magnitude of the crystal field on A and B sites is similar, but the sign is opposite. It follows whereas 5E is the ground state of 3d4on the B site, on the A site the ground state is 5T2.Figure 13 shows an idealized energydistribution curve of photoelectrons expected with a ferrite containing Fe3+ only. Indicated on each line is the state in which the ion core is left behind. The width of the lines accounts for the finite lifetime of the hole and the apparatus resolution. The total emission strength from the A sites is proportional to 1 - S, and from the B sites to 1 S, where 1 - 6 and 1 S are the respective densities of Fe3+on the two sites. The initial state and relaxation energies at the A and B sites might be somewhat different. This is accounted for by a relative shift A of the center of gravity of 3d4. If one measures the sum of all the lines (i.e., the intensity distribution curves of photoelectrons), these multiplets cannot be resolved. The ESP, however, has an opposite sign for electrons emitted from A sites compared to those emitted from B sites, since A and B sites couple antiferromagnetically.One can guess without any numerical calculations from Fig. 13 that P = (n? - nJ)/(nT nJ) will be strongly dependent upon those parameters that introduce differences in the yield of electrons from A sites relative to B sites, but not upon those affecting the yield from both sublattices in the same way. This then establishes the basis for a differentialtechnique. As a general rule one can predict with this model that B sites will emit photoelectrons at photoelectric threshold. This arises because ACG << A and ALA= AB and because the splitting in the crystal field conserves the center of gravity. Since there are 2egelectrons and

+

+

+

28

H. C. SIEGMANN et al.

I

/--,

FIG. 13. Idealized energy-distributioncurves of photoelectrons expected from a spinel lattice containingFe3+(3d5)only; Fe3+at B sites exclusivelyemits majorityspin-up electrons, at A sites minority spin-down electrons. Indicated below each peak is the configuration in which 3d4 was left behind. The center of gravity of 3d4 is shifted by A CG on A relative to B sites. The dashed line is the sum of A- and B-site contributions that would be observed in an energy-analyzed photoemissionexperiment ifthere was no inelastic scatteringof the photoelectronsand if the escape probability over the surface bamer potentials was unity.

3t, electrons, 5Eis shifted further away from the center of gravity compared to 5T2,and an eg electron from the B site will appear first at photoelectric threshold. Figure 14 shows the SP of the photoelectric yield with magnesium ferrite (Fe3+),-s[Mg&Fe:&]04, where the ions in brackets are at B sites, for a sample with 6 = 0.24 [from Ref. (98)]. Note that the ESP of the total yield is plotted; that is, energy selection of the photoelectrons was not performed. Since the total magnetization in this case is parallel to the B-sublattice magnetization, the ESP is positive at threshold, in agreement with the general rule that B sites emit first. It also shows a relative maximum at the photon energy hv = 8.8 eV, due to the emission of T,, electrons from B sites. All this is in perfect agreement with the previous model of a single ion in a crystal field (SICF). At hv > 10 eV, the observed photo-ESP falls below the values predicted by SICF, indicating the onset of emission from the oxygen 2p bands. Figure 15 shows the SP of the photoelectric yield with yttrium iron-garnet (YIG) according to Ref. (99). The magnetization is also exclusively produced by Fe3+located in tetrahedral (A) or octahedral (B) coordination. However, there are more Fe3+ions on the A sites compared to the B sites, and hence the B-site SP is antiparallel to the magnetization. The negative ESP at threshold is then again in agreement with the general rule according to which B sites emit at threshold. The emission from the A sites shows up as two relative maxima at hv = 8.2 and 10 eV, respectively. The onset of emission from the oxygen 2p bands occurs at hv = 10.8 eV. These two examples clearly demonstrate the power of ESP studies with transition-metal oxides. Similar experiments have been performed on a variety of femtes (100). They have led to good estimates of the threshold for

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

P (%: 60 -

(Oh)

50 40 30

0

-

30 20

0

nu"..,

-

cp 0 0

10 -

61

29

7

8

9

10

I1

PHOTON ENERGY (eV)

FIG. 14. Photo-ESP with magnesium femte versus photon energy at constant magnetic field H = 16 kG and at 60 K, 6 = 0.24. The solid line was calculated from the single ion in a crystal field model. The arrow indicates photoelectric threshold [from Ref. (98)].

FIG.15. Photo-ESP with yttrium-iron-garnet versus photon energy at constant magnetic field [from Ref. (9911.

30

H. C. SIEGMANN et al.

oxygen 2p emission and to accurate values for the crystal-field parameters and exchange energies on A and B sites, even in quite complicated cases such as magnetite Fe3+[Fez+Fe3+]0,,where the 3d6and 3d5configurations coexist at B sites, leading to a final-statemultiplet with eleven lines. All these lines occur in an energy range of -4 eV, and cannot principally be resolved in optical absorption or photoelectron intensity studies because of the inherent linewidth determined by the lifetime of the hole. With the parameters obtained from ESP studies, it is possible to understand the optical properties of magnetite (101). Since the transition-metal oxides are of renewed interest in surface adsorption and/or oxidation studies, and since the subtle differences between magnetite and y-Fe203,for instance, play a vital role in the thin-film magnetic recording industry, it is to be expected that finer ESP studies including energy analysis of photoelectrons will be performed unraveling more and finer details of the electronic excitation spectrum in transitionmetal oxides.

C.Actinide Materials Within the periodic table, there is a transition from itinerant electron behavior in transition metals to the localized atom-like character of electrons in rare earths (REs). This transition is encountered in the actinide series alone. Its lighter elements (Pa, p-U, and y-U) are true bulk superconductors and show nonmagnetic transition-metal (TM) behavior. Neptunium compounds display band magnetism and so do those of plutonium. Americium has localized nonmagnetic 5f electrons. Beyond Am the actinides are similar to the REs and show localized 5f electron magnetism; their effective moments are in good agreement with Russel- Saunders values. This delay of magnetism within the actinide series is related to the strong hybridization properties of the 5f electrons and to the broad bandwidths in the light actinides (102). Accordingly, the f bandwidth at the beginning of the series is comparable to that of the 5d electrons in TMs, and the local moments are "diluted" by hybridization. This transition is present even in uranium and its compounds. Figure 16 shows the change in the width of the 6d- 5f bands for a series of uranium compounds, as deduced from photoemission experiments. The bandwidth decreases with increasing anion atomic number and hence with increasing uranium - uranium distance (102). Therefore, one expects that with the right choice of the anion and the crystal structure one can influence the electronic properties of the actinide materials over a wide range. In uranium metal itself the 5f electro,-s have an itinerant behavior, as observed in photoemission spectroscopy (103). The cubic compounds of uranium with chalcogens and pnigogens show mag-

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS 20

-

\

I

5 0

I

I

2

1

m

D

4

‘r,us

\

’h

Use

\

15-

,1 5z : ‘ UN

a

\

-

-

31

\

\

\\ \\

\

-

\

10m -

X UTe \

i‘\,

UAs

“I__

USb I

,

,

I

,

I

,

,

,

,

I

,

,

netic ordering- they have special properties associated with the partially filled 5f shell located at EF (102). The ternary uranium compounds, on the other hand, have localized 5f electrons which display final-state effects in photoemission (104). The SP of electrons photoemitted from magnetically ordered materials reflects their spin orientation before the optical excitation (7). There is no indication of spin-exchange scattering in the escape of the photoelectron. The SP of majority spin electrons will be denoted as positive. Negative SP of electrons photoemitted from magnetic materials has been of considerable interest. It was observed in ferromagnetic nickel (Section II1,A) where it is compatible with both the atomic model of a more than half-full shell as well as with the band model in the case of nearly full bands. The occurrence of negative ESP is restricted to a spectral range of 80 meV from the Fermi level (EF)(56). For ferrirnagnetic magnetite, Fe,O, , the negative ESP was observed also in a relatively small energy range at photothreshold. It originates from Fez+ ions in the octahedral sublattice which is coupled antiferromagnetically to the rest of the crystal (Section IV,B). Hence, it is an atomic property resulting directly from the first Hund‘s rule. The measurements of ESP from ferromagneticuranium monochalcogenides have shown a negative polarization throughout a spectrum of 7 eV below EF(105), as shown in Fig. 17 for US, Use, and UTe. The first attempts (106) to interpret this observation relied on an atomic model. It assumed that the 6d-electron magnetic moments were antiparallel to the crystal magnetization with the 5f’s not being observed at low photon energies (hv < 1 1 .O eV) due to vanishing matrix elements. However, theoretical analyses based on a self-consistent cellular multiple-scattering tech-

32

H. C. SIEGMANN et al.

p 4' -10

T

444

s - -20 z

I

0

I

t

-10

-20

-30

hu

-

0

(eV)

FIG. 17. Photo-ESP versus photon energy hv minus work function (D obtained from ferromagneticallyordered US, Use, and UTe: T < 20 K, H = 8.4 kG.

nique (107) show as a major result that it is not the nature of the 6d electronic states alone that is responsible for the observed negative ESP, but that the 5f resonances located near EFinfluence the 6d-electron density of states (d-DOS)in favor of the minority spins and thus create a trough in the d-DOS of the majority spins near photothreshold (108). By virtue of this unusual f-d interaction, the observed ESP is negative, since the contribution of the 5f electrons to the measured spectra is negligible at photothreshold because of the centrifugal barrier. In Fig. 18 the DOS for both spins is presented for US (107).The f and d characters are shown separately. The bands have a very unique character near EF,but otherwise are typical of transition-metal cubic compounds (109).In fact, without the f-d interaction, the d bands only show a typical splitting into t2gand egparts. The f band induces a further, nonsymmetric splitting of the t2gd band, with the final

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

33

2-

*

I

2 .

3 U

2

3

L 10 LL LL

f

n ul

> 00

LL LL W

m

+ ,Q 1 W

ul

z

0

n u

I-

w

_1

W

2-

+5

EF-O ELECTRON

-5 -10 ENERGY(&')

FIG.18. Local density of states for ferromagneticallyordered US for both spins. States to the right of Ef are occupied.

result shown. The observed spectral exclusion of less localized states coinciding energetically with a narrower band is not new; it was discussed first in the case of the s-d hybridization interaction in transition metals (110). An analysis of the cluster orbitals (108) shows that the f-d interaction requires the presence of the anion s and p orbitals and, therefore, is more closely described as a superexchange rather than a hybridization. Since the unoccupied minority-spin 5f resonance is fairly close to the vacuum level, it is anticipated that, by lowering the work function, it should serve as an additional escape channel for the excited 6d electrons. This would result in an enhancement of the observed 6d polarization. In contrast to this expectation, not an enhancement but a decrease of the ESP is observed (111). It is concluded that the 5f resonance is very narrow; its unoccupied part lies in a not greater than 2-eV-wide interval above EF. The ESP results from uranium monochalcogenides as shown in Fig. 17 are replotted in reduced coordinatesin Fig. 19 where P,, is the polarization near threshold and 4 the work function of the respective compound. The

34

H.C . SIEGMANN et al.

5a a

0.6-

0.81.0 -

u

0

1

2

3

4

5

hu -

Q,

(eV)

6

7

FIG.19. Reduced-spin polarization P/Pm versus (hv - a)for US, Use, and UTe. This comparison shows the differences in the occupied part of the valence bands in each material. Heavy lines are drawn through experimental points for clarity.

choice of these coordinates ensures that for any (hv - 6)value, initial states of the same binding energy are compared (111). The steepest decay of the polarization with increasingphoton energy occurs for UTe, followed by Use and US. It is caused by the onset of unpolarized emission from the s - p part of the valence band. Its occurrence at different photon energies for the three chalcogenidesis due to the differencesin the covalency of their bonding with the uranium atoms. In conclusion, the 5f and 6d electrons in uranium compounds showing opposite spin alignment belong to the same atom and have the same binding energy, as opposed to ferrimagnets. Therefore, the magnetic structure encountered in NaC1-type uranium compounds can be termed interatomic band ferrimagnetism. Spin-polarized photoemission is the only technique that can reveal this feature directly. V. THESYMMETRY OF ELECTRONIC STATES

This section deals with the extraction of polarized photoelectrons from nonmagnetically ordered materials. In the ground state these materials have no preferred direction of the electron spins. Any SP of the photoelectrons must therefore be created by means of the photoexcitation itself. This process is called optical spin orientation. It is governed by the symmetry of the states involved. Because the SP is an axial vector -like magnetization-its direction must also be specified by an axial vector. In all the experiments described hereafter, the quantization axis is provided by the direction of the angular

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

35

momentum of the circularly polarized light used for photoexcitation. The experimental geometry is such that the light falls perpendicularly on the sample surface. The polarization of all the electrons emitted within a cone around the surface normal are collected and their SP measured. The electromagneticfield of the photon acts directly on the orbital part of the electronic wave function alone. Consequently, if SP is to be achieved, the two spin states must be coupled to the orbital part in a distinct manner, otherwise, the spin of the electron would be completely irrelevant for the optical transition, and no polarization would ever be achieved. Therefore a sufficiently strong coupling of the spin to the orbital motion of the electron (i.e., spin-orbit coupling) is indispensable. Taking into account that lifetime broadening in photoemission is usually >0.1 eV, it is recognized that light-element materials are not suitable for optical polarization experiments because the spin-orbit splitting of the electron levels is too small to be experimentally resolved. Any pair of occupied initial and empty final states can be analyzed with respect to the following three features: (1) Is an optical transition allowed by symmetry? (2) If the transition occurs with circularly polarized light, what is the polarization of the excited electrons? (3) In case of symmetry-induced degeneracy of the initial and final states, what are the relative intensities of the simultaneously occurring transitions?

The answer to these questions depends entirely and only on the symmetry of the wave functions involved; no further information on the electronic states is required. Group theory is the powerful theoretical tool to be used. The symmetry of an electronic wave function is expressed by its angular and spin parts. The various symmetries are classified according to the irreducible representations of the relevant symmetry groups. The orbital symmetries of the wave functions (i.e., spin neglected) determine the selection rules because light acts directly on this part of the wave function alone. For a wave function of wave vector k, the symmetry group consists of those operations which transform the crystal and k into itself: for k = 0, it is the point group of the crystal; for k # 0, it is a subgroup called the group of the wave vector. The simple rule which states whether a transition is forbidden by symmetry is the following: Let the irreducible representations according to which the orbital part of the initial and final states and the light operator transform be Ai, Af, and A,. Then a transition is "allowed" if the product representation At 8 Ai contains Af. The multiplication tables can be found

36

H. C. SIEGMANN et al.

in Ref. 112. It is understood that an allowed transition is one which is not forbidden for symmetry reasons. However, it may be suppressed if the explicit forms of the wave functions are considered. The irreducible representations, according to which the total wave functions including spin transform are indicated in the following by suband superscripts. The superscript indicates the irreducible representation without spin, the subscript that with spin. As an example, consider the group C,,(using the tables of Ref. 112).Suppose that the orbital part of the wave function has the symmetry A5which is a doubly degenerateband. A spin 1/2 transforms under C,, according to the representation As. Then the total wave functions including spin derived from A5 transform as A5 8 As = A: A;; i.e., the degeneracy of the band A5 is lifted. To find out the polarization produced by a particular transition it is necessary to know how the spin part is coupled to the angular part of the wave functions involved. For atoms having full rotational symmetry this is done by using the Clebsch-Gordan coefficients. The analogous coupling coefficientsfor the crystal groups with their reduced symmetry are tabulated in Ref. 112. Consider the wave functions belonging to the irreducible representation A$ of the group C,,. Table 35 of Ref. 112gives the total wave function composed of orbital parts belonging to the doubly degenerate representation A5(denoted by u: and u:) and the spin function belonging to the doubly degenerate representation A6 (denoted by vf12and v!LlI2).The two functions belonging to A$ are

+

The relative strengthsof transitions between degenerate levels, belonging to the same representations, are also determined by symmetry. This is shown by an example which is easily generalized to similar situations. Consider the transitions at r in GaAs (point-group symmetry Td)occurring between the top of the valence band and the bottom of the conduction band (see Fig. 20). The wave functions are designed according to the rules described above, using the coupling coefficients of Ref. 112: the valence-band states are of symmetry ri and the conduction-band states of symmetry ri. The light operator transforms according to the representation r5. The relative strengths of the two allowed transitions indicated in Fig. 20 are determined by the square of the absolute magnitude of the two matrix elements Mfi= <(vflOti,&>.

38

H.C. SIEGMANN

el

al.

Up to a constant depending only on the symmetry labels of the representations of the states between which the transition takes place, the matrix elements are entirely determined by symmetry. This is a generalization of the well-known Wigner - Eckart theorem of atomic physics. In order to find the reduced matrix element (neglecting the constant), one proceeds as follows: For transition A, the final state is = UlV51l2

v/f

and the initial state is

The light operator is of the form O,,, = x

+ iy

= u:z

+ iuzz

According to Table 83 of Ref. 112, u1 can be represented in terms of products of basis functions of T5 in the following way: 1 u1 = -u5 0 5

43

yz yz

1 1 +u:zv;z + 43 43

u5 v5 xy xy

Then, the matrix element becomes, using the orthonormality of the basis functions,

~t = -(i/ A)- (i/ &) The intensity IAof transition A is I A

= lMtI2= 4

Similarly, for the second transition B with v/f = U l V L l 2

i

y/ = -u5yzv +1/2 6

one obtains

1 u:zv$1/2 + +-

43

w = (i/J18) + (i/J18)

ig

or IB =

u:yv51/2

= 2/9

Consequently, the polarization of the two competing transitions becomes IPI = (3 - $)/(+ 8) = O.5.This is a well-known result (22) because it is the theoretical value expected for the GaAs source of polarized electrons. The orbital representation of the spin - split valence levels is T5as for the upper valence-band states discussed above. Therefore, in order to determine

+

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

39

the relative strengths of the transitions from the spin-orbit split bands, the generalized Wigner-Eckart theorem may be applied again. It should be noted that the influence of the spin - orbit interaction on the radial matrix elements is neglected, which is correct to first order. With the same arguments as above the intensity of the transition C to the conduction-band edge becomes I, = 4/9. Therefore, in case of vanishing spin-orbit coupling the total polarization of all three degenerate transitions would be zero. This is in accordance with the general argument presented at the beginning of this article. A systematic application of group-theoretical methods to the optical spin orientation in solids has been made by Wohlecke and Borstel(ll3). A. Identijication of Orbitals

An obvious advantage of spin discrimination in photoemission is enhanced resolution. Two narrowly spaced transitions of equal intensity but opposite SP are distinguishable even in cases where non-spin-polarized photoemission is no longer able to resolve the two transitions. This is in fact quite a common situation since, e.g., transitions from spin-orbit split initial-state bands to a single final-state band always produce opposite SP. This follows from the fact that in the absence of any spin -orbit splitting (i.e., if the two initial states coalesce), the polarization is zero. Therefore the optical polarization experiment is especially suited to investigate spin - orbit effects on the band structure. As an example, consider GaAs. Even in the most advanced angular resolved photoemission studies (114) the spin -orbit splitting at r is hardly resolved. On the other hand, it is easily observed in SP photoemission, where it gives rise to the impressive polarization structure at threshold (22). As a further application of the optical orientation technique, transitions along the (1 1 1) direction of gold have been studied near the L point (I 15). The band structurein this kregion is shown in Fig. 2 1. The band structure of gold has attracted great interest (116) because large experimental discrepancies with existing band calculations have been reported. First consider the L point: The symmetry of states 3 - 7 is, in this order Lj+, Lj&, L3-, LA+. The transitions 3, 4 7 are forbidden by parity and 5 7 is not allowed because the direct product of the representation belonging to the operator of the circularly polarized light, r?,with the representation of the initial state r: does not contain the final-state representation rt. Consequently, at the L point all transitions are symmetry forbidden. The L point symmetry is Qd,whereas the A line has C,,symmetry. In the absence of hybridization, the bands 3 - 7 are of the following symmetry

-

-

40

H. C. SIEGMANN ef al.

Fri

r

A

L

6 (A,,&)

FIG. 2 1. Band structure of gold along the (1 1 1) direction [from Ref. (I I7)]. The broken line at 5.3 eV above the Fermi energy EFindicates the position of the vacuum level of the clean gold surface. The table shows the orientation of the spins in the final state band 7 for excitation from the initial state bands 4, 5 , and 6. Note that the transitions 5 7 and 6 7 are not resolved; transition 5 7 is much stronger than 6 7.

-

-

-

-

--

types: A;, A$%,A$, and A:. The light operator transforming according to r3 would then exclude only the transitions A1 A1 ,whereas the other two are not symmetry forbidden; A3% A; (band 5 7) produces “up”-spins and A3 A1 (4 7) “down”-spins. The spectrum of the clean gold(II1) surface (work function, 5.3 eV) is shown in Fig. 22. It presents the firstexample of SP photoemission by optical orientation from a clean surface. In a straightforward explanation of the spectrum the rise of the polarization up to the photon energy of -6.9 eV is attributed to transition 5 7, the plateau corresponds to the width of the spin-orbit splitting of band A3 (the split bands are A:, and A$), and the decrease of the polarization above 7.6 eV occurs because transition 4 7 starts contributingspins of opposite sign. These measurements show that the energy positions of bands 4,5, and 7 are in good qualitative agreement with the relativistic band-structure calculation of Christensen and Seraphin (1 17). Note that the contribution of band 6 to the photocurrent is small. It is due only to hybridization with band 4.

-

- -

-

-

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

21

a

41

n

PHOTON ENERGY (eV)

FIG.22. Polarization spectrum of a clean Au( 1 1 1) surface. The transitions observed are shown in Fig. 2 1.

B. Mixing of Orbitals (Hybridization) Another exciting feature of the optical orientation experiment is that it provides direct insight into the hybridization properties of electronic bands. Transitions in a crystal are subject to selection rules which reflect the symmetry properties of the electronic states. It happens that a transition which should be forbidden if the states involved were of a pure single symmetry type rj shows up nevertheless. This is an indication that at least one of the states has an admixture by spin - orbit interaction of some other band rf,making the transition “allowed.” In the cases encountered so far it was quite evident from the sign of the observed polarization which other band is admixed, or, in other words, which states are hybridized. By observing transitions between the same two bands at different points in the Brillouin zone, the strength of the hybridization can be estimated directly from the value of the polarization. In this context, it should be noted that in the absence of hybridization polarized transitions occur only along high-symmetrydirections of a crystal containing at least a threefold rotation axis. This interesting feature has first been pointed out by Wohlecke and Borstel (1 13). Hybridization is not only able to make transitions “allowed” which are forbidden in single group representation. It may also diminish the polarization of a transition expected if no hybridization would exist. This happens when a band is admixed which produces spins of opposite sign. Good

42

H. C. SIEGMANN et al.

r A H FIG.23. Band structure of tungsten along (100); T, and T2are the two transitions giving

rise to the polarization spectrum of Fig. 25. Note that T , and T2are energetically well separated due to the particular band structure and the position of the Fermi energy EF.

examples of such a situation are the optical spin-orientation measurements on W( 100).These experiments were intended to demonstrate the applicability of optical orientation as a general method to obtain band-structure information (118). Reliable band-structure calculations of W exist (I 19); spin-orbit effects are large and, experimentally, the material is easy to handle. The band structure along the (100) direction is shown in Fig. 23. Prior to the experiment Reyes and Helman (120) derived the polarizations of the various interband transitions within the conduction-band region. The allowed transitions produce either up or down spins, the finalstate polarization being 100 or -100%. The resulting polarization spectrum for a photothreshold of 1.5 eV is shown in Fig. 24. Near threshold two transitions labeled T, (A2 A? in Fig. 23) and T, (A$ A$ in Fig. 23) are predicted, both being fully polarized but of opposite sign. In the experiment two transitions showing the change of sign are indeed observed (see Fig. 25a). However, the peak values of the polarization are only -5 and +8% in marked contrast to expectations. Because these transitions are at or close to the photothreshold, only electrons with momentum along the surface normal [i.e., the (100) direction] are able to escape. Accordingly, the contribution of electrons excited with off-normal wave vectors can safely be assumed to be negligible.

+

-

-

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS W(100)

43

+ cs

100

-d

50

a

z

0

t

o

2 a a

-I

2

-50

- 100 2 3 4 : LIGHT ENERGY (eV)

FIG.24. Theoretical prediction of the polarization spectrum without taking into account hybridization effects [from Ref. (120)]; T, and T2are the transitions indicated in Fig. 23

L 2.0

3.0

4.0

2.0

3.0

4.0

5.0

4

0

4

PHOTON ENERGY

5.0 hv ( e V )

FIG.25. Experimental polarization spectrum of tungsten (100)with photothreshold (a) 0 = 1.5 eV and (b) 0 = 2.4 eV.

44

H. C. SIEGMANN ef al.

Mechanisms which lower the polarization are unpolarized surface emissions, where the final state is not a bulk band state, or depolarization of the escaping photoelectrons at the surface. Surface emission is estimated from the well-known surface density of states and does not amount to more than 50% of the total photocurrent for TIand 75% for T,. This is not enough to explain the low SP. Depolarization of the photoelectrons by alkali atoms deposited on the surface to lower the work function has never been found to be significant in any experiment made so far. This applies to magnetic materials as well as to optical orientation with nonmagnetic materials (Section V111,C). Convincing evidence that none of the above mechanisms (off-normal emission, surface emission, or surface depolarization)is responsible for the strongly reduced polarization values is given by the following experiment. By proper adjustment of the cesium coverage any photothreshold between 1.5 and 4.6 eV (clean surface)is obtained. By increasing the photothreshold from 1.5 to 2.4 eV the electrons excited by transitions T , are not photoemitted any more, whereas T2still lifts the electrons above the vacuum level. At this higher photothreshold the escape cone of the photoelectrons produced by T2is reduced together with the amount of surface emission. At the same time, because the cesium coverage is lower, possible depolarization should be less significant. In spite of this, the polarization of transition T, for the photothreshold 2.4 eV is also 8% (Fig. 25b), exactly as was found for the photothreshold of 1.5 eV (Fig. 25a). This shows that none of the previously mentioned effects masks an in fact larger polarization produced by the excitation process. Quite to the contrary, it shows that the low polarization observed is an intrinsic property of the transitions investigated. It should be noted that the above conclusions are possible only because the transitions TI and T, do not overlap each other. The existence of two completely separate transitions is due to the particular dispersion of the energy bands involved (Fig. 23). There is then only one mechanisms left which can reduce the intrinsic polarization of the transitions: hybridization of the energy bands. This can be stated with certainty because the polarization is given entirely by the symmetry of the electronic states. As transitions between states of a single symmetry type are fully polarized along the (100) direction of tungsten, a reduction can only occur if at least one of the states involved is composed of two parts having different symmetries, one part producing up- the other down-spins. Such a mixing of states of different symmetry is produced by hybridization. The degree of hybridization depends on the details of the band structure and cannot be determined by group theory. The hybridization of the states involved in the transitions T, and T2is as follows: The fourth band denoted by A: in Ref. 120 also contains part of A?

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

45

and A:; the fifth band, except AT, also contains A# and A?. Then, the transition TIfrom band 4 to band 5 produces both kinds of spins: A?, AT

--

A#

produces up-spins

produces down-spins A# A?, AT The mixture of the symmetries in the initial and final states results in a polarization of less than 1OYo. This indicates that hybridization is very strong in this part of the conduction band of tungsten. For transition T2, the hybridization in the initial state takes place between states A; and A: :

A; A:

-

A;

produces up-spins

A?

produces down-spins

This example shows that SP is a quantity which is sensitiveto hybridization. The effect of hybridization on the polarization spectrum of a clean Au( 1 1 1) surface has been mentioned in Section V,A. It presents an example A:) becomes allowed by the admixin which a forbidden transition (A: ture of band A: to the initial state. Polarization spectra of Au( 1 1 1) surfaces with a lower work function have been obtained by slight coverages with potassium. The results are discussed in Ref. 121. The third and last example showing the effect of hybridization concerns transitions near r in germanium (122). The relevant part of the level structure is shown in Fig. 26. Figures 27 and 28 show polarization spectra taken with photothreshold 1.6 and 2.6 eV. The spectra are independent of crystal orientation, which is an unambiguous indication that the transitions are excited near r, where the band structure is rather isotropic with parabolic energy surfaces. From energy considerations it is clear that the 1.6 eV transition of Fig. and the 27, which is 50% polarized, occurs in a k region around flT r;Z. Two features are surprising: 3.05 eV transition of Fig. 28 near flT The transition E$’ ry- is exactly 50%polarized. However, this transition occurs at hv = 0.9 eV and not 1.6 eV, where Fig. 27 shows the maximum polarization at photothreshold. The conclusion is necessarily that the photoelectrons measured are not excited exactly at r but in a neighborhood close to it. However, a problem arises, namely, that away from r the polarization should be zero in the absence of hybridization. In order to show this, attention is focused on the k line along (loo), i.e., along the A direction. Due to the isotropic nature of the band structure around k = 0, this line is representative for all transitions around r. becomes a state A: and A:., and r?Without hybridization the state goes over into A?, as follows from the compatibility relations and indicated

-

-

-

- v-,

P

P

(r;?-r;.) (ri?-rr.)

= 50% = 16.70~

FIG.26. Sequence of energy levels of germanium at r (schematic). The vacuum level Q cannot be lowered below 1.5 eV, which is about 0.6 eV above the conduction band level p-.

PHOTON ENERGY (eV)

FIG. 27. Spectrum of spin polarization of Ge(100) with photothreshold 1.6 eV at T = 30 K.

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

47

I

PHOTON ENERGY (eV)

FIG.28. Spectrum of spin polarization of Ge(1 1 1) with photothreshold of 2.4 eV at T = 300 K. There is no temperature dependence of the spectrum for T < 300 K.

in Fig. 29. Transitions excited along A would yield P = 0, since

AZ-AT,

AG-AT

yield spins of opposite sign with equal intensity. This is no longer true if the states are hybridized. In the initial state the only possibility is for state A$ to hybridize with AT. This will leave the matrix element A: $’ unchanged; AT is a forbidden transition, it will remove strength however, since A? from the nonhybridized transition A$ A?, thereby leading to a final-state polarization. Using the physically appealing argument that the polarization along A should match that at r continuously for A r,the strength of the hybridization is immediately derived. The A$ initial states obtain the weight whereas the AT states have This results in P = 50%also along A, as experimentally observed and indicated in Fig. 29. Although the 3.05 eV transition of Fig. 28 exactly fits the energy difference FA?, there is strong evidence that even in this case the transition does not take place at k = 0 exactly and that hybridization effects have to be taken into account. The point is that the transition riF: r:? is 16.7% polarized, whereas the measurements invariably produce a higher value, P = 23 f 1%, for photothresholds 2.4 < @ < 2.9 eV. Again, hybridization has caused this phenomenon, this time in the initial state, as discussed above as well as in the final state. It can be shown that, due to hybridization near r, the polarization can become as high as 40% (123).

-

m,

c:-

-

m.

-

-

-

48

H. C. SIEGMANN et al.

A (a)

A (b)

v-

FIG.29. Hybridization of the levels near rjr,Qr, and (see Fig. 26) in Ge along the A direction:(a) symmetry ofthe wave functions without hybridizationresultingin P = 0 along A; (b) symmetry of the wave functions with hybridization(P# 0). Subscripts u and d indicate upand down-spin, respectively. By choosing appropriate hybridization parameters, the polarization at r can be matched continuously.

The investigation of hybridization effects seems to present one of the most rewarding purposes of the optical spin-orientation technique. It is already clear that a rich variety of phenomena can be expected which will give insights into important properties of electronic wave functions in solids which have been hitherto barely accessible to experiment. C. The 100% Polarized-Electron Source It would be useful to have a polarized-electronsource of high brightness with the capability of inverting the sign of the polarization without changing other beam parameters. The latter point is very important because otherwise apparative, systematic errors are introduced which severely limit the range of applications. This is the case for polarized-electronsources operated in an applied magnetic field. In contrast, the decisive advantage of a source based on optical orientation is that the polarization of the photoelectrons is inverted by merely changing the direction of the circular polarization of the light, which does not affect the electron optical adjustment of the gun. The feasibility of such a source was first proved with gallium arsenide (Section 11,A). The source was later perfected in various laboratories (124). Inp-GaAs, by excitation with circularlypolarized light of energy hv =EG (where EG is the gap energy), a polarization of 50% is theoretically calculated and, somewhat less, namely, 48Y0,experimentally observed. The only conceivable improvement of the source is the replacement of GaAs by a material which produces a fully polarized-electron beam but retains all the

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

49

other useful properties of negative electron affinity and a convenient gap energy for excitation with laser light. From the transition scheme shown in Fig. 20, it is apparent that the 50% polarization in GaAs arises because of two competing transitions, one producing up- and the other down-spins. The removal of the initial-state degeneracy could therefore lead to a level configuration where only one type of spin is created by excitation across the band gap. To remove the degeneracy of the energy levels the symmetry of the system has to be lowered: compounds of lower symmetry than the cubic zincblende structure of GaAs must be found. An interesting possibility is offered by the chalcopyrite-structure semiconductors. Among these tetragonal materials is a group of compounds which is closely related to the 111-V compounds in the sense that the group I11 cation is alternatively replaced by a group I1 or group IV cation. The formula unit is then of the form I1- IV- V, ;i.e., it contains four atoms as compared to two atoms of the zincblende compounds. The lower symmetry of the chalcopyrite structure causes a crystal-field splitting of the valence bands at r (Fig. 30). In the cubic case, without ZINCBLENDE

CHALCOPYRITE without

with

TRANSITIONS WITH CIRCULARLY POLARIZED :+I Y:

IP>

Y ? IP>

Y-; IP>

FIG.30. Level scheme of a direct gap chalcopyrite semiconductor at r. At the left-hand side, and r, denote the states at the upper valence-band edge and the lower conductionband edge of a zincblende semiconductor without spin-orbit interaction. The tetragonal distortion in the chalcopyrite semiconductor together with the spin- orbit interaction removes the orbital degeneracy of the valence levels completely;Ac,,denotesthe crystal field splitting. At the right-hand side the symmetry properties of the wave functions are indicated in terms of spherical harmonics, permitting application of the selection rules as for atoms. The circularly polarized light is incident along the c axis of the crystal.

50

H. C. SIEGMANN er al.

spin - orbit interaction the electronic states at the top of the valence band are of threefold orbital degeneracy and transform as r,5.The compatibility tables show that reduction to the D,, chalcopyrite symmetry splits this level into a nondegenerate r4and a doubly degenerate r, . The introduction of the spin -orbit interaction lifts all orbital degeneracy. The r4state becomes r;.,and Ts goes over into rz and Ej,all these new states being only twofold spin degenerate. In order to use the tables of Ref. (112) it should be borne in mind that the z axis is defined by the c axis of the tetragonal lattice. For circularly polarized radiation incident along the z axis, the operator is still of the form x f iy. It transforms according to the irreducible representation r5,x as -S, = -u: and y as S, = uz. Following the procedure discussed at the beginning of this article, one finds that the transition from the uppermost valence level rj to the lowest conduction band Q is not excited at all by circularly polarized light. For x iy - polarized light, the first allowed transition is Q Q producing only p spins. Increasing the light energy by the amount of the spin-orbit splitting, the r5-r; transition is induced, producing only a spins. It should be noted that the order of the valence energy levels at r is the same for all I1- IV -V, chalcopyrite-structure semiconductors (125). Evidently, the transitions at r are fully polarized, as anticipated. The preparation of these ternary semiconductors is not trivial (126). Optical orientation experiments have been made with ZnGeAs, and ZnSiAs, (12 7). Various polarized transitions have been observed. However, due to the unfavorable crystal parameters (gap energy, spin - orbit splitting) and the insufficient size of the crystals, the relevance of the data is limited. With ZnSiAs, an additional problem arises. There, the lowest conduction-band level is not of orbital rlsymmetry, but r, .This peculiarity is due to the fact that the binary zincblende analog of ZnSiAs, is not a direct gap semiconductor,as explained in detail in Ref. (125). As a consequence of the smaller size of the chalcopyrite-structure Brillouin-zone parts of the corresponding zincblende band structure lie outside the first Brillouin zone and have to be reduced by a reciprocal lattice vector to fall inside of it. By this procedure the conduction-band state of r3symmetry giving rise to the indirect gap of the zincblende analog of ZnSiAs, is mapped onto the point k = 0 of the chalcopyrite. The energy gap at r is then called pseudodirect. Transitions across a pseudodirect gap are about one order of magnitude weaker than for the case of a direct gap (125). Therefore pseudodirect materials are not good candidates for a highly polarized electron source. In order to get 100%polarization from chalcopyrite-structure semiconductors it seems most important to solve the material problem. This consists in obtaining a good-quality crystal of sufficientsize which belongs to the

+

-

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

51

“direct-gap’’ class with energy gap 1.5 eV (to obtain negative electron affinity), is p type, and has a spin-orbit coupling large enough to separate the up- and down-transitions (0.2eV). Then the prospects are indeed promising for obtaining a source of polarized electrons with all the useful features of GaAs but with P = 100%.

D. The Efect of Lattice Disorder Symmetry is a parameterlessquantity, independent of all the hazardous assumptions entering the electronicband structure. Because the SP obtained in optical orientation is a consequence of symmetry, it does not depend on numerical features of the electronic structure. The question arises as to how sensitive the polarization is with respect to a disturbance of the ideal crystal lattice. The very existence of a surface is a break in the crystal symmetry. However, in metals as well as in semiconductors the bulk band properties are generally reached within a few angstroms of the surface (a notable exception is silicon). Due to this circumstance, photoemission has become the unique tool for exploring bulk band structures. No evidence has been found so far that the situation is different with the SP obtained from optical orientation in the photon energy range up to 9 eV where the escape depth of the electrons is 10- 100 A. The polarization appears to be that expected for perfect periodicity of the crystal. In order to investigate the effect of disorder by thermal motion, the polarized transition at hv = 7.8 eV along Au( 1 1 1) (Section V,B) has been measured as a function of temperature T (122). The polarization at T = 300 K equals exactly that at T = 70 K, although the Debye temperature is To= 180 K. We do not understand this behavior, since photoemission is a very fast process compared to vibrational frequencies and one should see a frozen lattice distorted by the influence of thermal motion. With the present limited amount of experimental evidence we conclude that the spin orientation is not sensitive to phonon-induced disorder. Recently optical spin orientation has been attempted with amorphous germanium. Although amorphous, the atomic arrangement is not at all random. Each Ge atom is in an almost perfect tetrahedral environment (228). The difference to the crystalline solid is that neighboring tetrahedra are rotated with respect to each other. If the symmetry of the wave functions were completely determined by a cluster of nearest neighbors, no difference between the polarization spectra of amorphous and crystallineGe should be observed. The result of the experiment on amorphous Ge, namely, P = 0, is shown in Fig. 3 I. The polarization spectra of crystalline Ge with the same pho-

52

H. C. SIEGMANN et al.

1

2 1

3 I

PHOTON ENERGY (eV)

L I

FIG.3 1 . Polarization spectra of amorphous germanium taken at room temperature: (a) photothreshold 2.6 eV, (b) photothreshold 1.7 eV.

tothresholds are displayed in Figs. 27 and 28, Section V,C. Upon annealing the amorphous gemanium film, the full polarization as observed with single crystals reappears. This is in agreement with the fact that the polarization spectra of Ge in the photon-energy range 1.4 < hv < 4.0 eV are independent of crystal orientation. The experimental situation is clear: nearest neighbors do not determine the symmetry of the wave function. Neither is perfect periodicity required, since photoemission from surfaces shows no significant effect of the break of three-dimensional symmetry. The intriguing problem is to find out at what critical size an ordered agglomerate of Ge atoms exhibits the SP of the bulk crystal. Possibly, SP photoemission will contribute here to the well-known and difficult problem of the transition from the physical properties of atoms to those of the solid (129). VI. THESPINDEPENDENCE OF THE ELASTIC SCATTERING OF ELECTRONS FROM SOLIDS

Only as late as 1960 did low-energy electron diffraction (LEED), an experiment based on the wave nature of electrons, emerge as a technique to study the geometry of crystal surfaces. The observation of electron spin polarization in elastic scattering of low-energy electrons at W, Pt, and Au

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

53

polycrystalline targets by Eckstein and Loth (130) was the beginning of experimental investigations combining the concept of electron spin polarization with scattering of electrons from solid surfaces. The first successful spin-polarized LEED (SPLEED) experiments were performed on W( 100) and on Au( 1 10) (131 - 133). The following mechanisms lead to a spin dependence in the scatteringof electrons from solids: spin- orbit coupling, which is strong for surfaces containing heavy atoms (Section VI,A), and the exchange interaction in the case of magnetically ordered materials (Section V1,C). The component P of a polarization vector P(k,,, k,g) for a LEED beam g in an arbitrary direction is given by

+

P = (NT - NJ)/(NT NJ)-l where NT(NJ)is the number of diffracted electrons with spins parallel(antiparallel) to this direction. The incident unpolarized electrons have the wave vector k,, .The diffracted beam is characterized by the wave vector k and the surface reciprocal net vector g. The component A of the intensity asymmetry vector A&, k, g) is observed in the scattering of SP electrons with the initial degree of polarization Po along a direction in space. It is given by A = lpol-l(~(Po) - Z(-P0))(Z(Po) + ~(-P0))--'

where Z(po)(Z(-pol) is the scattered intensity if Po is parallel(antiparalle1)to the direction of quantization; A is a measure of the strength of the spin-dependent interaction. A . Surface Structures in Nonmagnetic Materials (SPLEED)

Surface-structure analysis in SPLEED has been performed by several authors. The observed variation of A or P with electron energy or scattering angle ( A or P profile) is compared to calculations for assumed surface structures. Such procedures are also used in the analysis of conventional LEED data. However, surface reconstruction and relaxation or contraction of the top-layer spacing with respect to the bulk spacing is found to produce more drastic changes in the polarization or asymmetry profiles compared to the intensity profiles (134). An iterative calculation is performed until the experimental results are reproduced to reveal structural parameters of the crystal surface, the inner potential, and the surface barrier, as well as the Debye temperature of the surface. The accuracy with which such parameters can be determined is greatly improved if both the spin polarization and the intensity are taken into account.

54

H. C . SIEGMANN et al.

Of particular interest is the (110) surface of Au because of a structural phase transition which manifests itself as a transition from a (2 X 1) pattern at low temperatures to a (1 X 1) pattern at high temperatures (135). Comparison of SPLEED measurements at the high-temperature phase with theoretical results for an unreconstructed Au( 1 10) surface yields an inner potential of 14 eV which changes slightly as the electron energy is varied (136). Although the surface Debye temperature is not uniquely inferred, a surface contraction of less than 5% is obtained. Further, a nonreflecting surface bamer yielded results which were closer to the experimental data (137). Application of this procedure to the W(OO1) surface showed that the experimental results lie closer to those calculated for a surface contracted by 10%(138).However, the results for W(O0 1)as well as for Au( 1 10)are not yet very satisfactory, since both surfaces exhibit considerable disorder and remnants of a superstructure even at elevated temperatures. More conclusive results are obtained from the Pt( 11 1) surface, which is geometrically unreconstructed. In the calculations, real and imaginary potentials V, = 12 eV and Vi = 4 eV are used with energy-dependent exchange terms (139, 140). Also, a slight outward relaxation of the surface atoms is found with a surface Debye temperature very close to that of the bulk (140). Asymmetry profiles of the Ni(OO1) surface have been measured at temperatures above the Curie point to avoid the exchange interaction. They agree with numerical calculations, assuming a 2.5% expansion of the topmost interlayer spacing (141). This is a remarkable result since it shows that even low atomic number materials are accessible to SPLEED; polarization effects of up to 159/0have been observed in some reflexes. This indicates that even at low Z , the omission of spin - orbit coupling can produce some errors. Temperature effects in SPLEED were been studied for the (2 X 1) reconstructed Au( 1 10)surface (133, 137). This study is of particular interest, since for the Au( 1 10) surface a structural phase transition occurs. A (2 X 1) room-temperaturesuperstructuretransforms into the (1 X 1) bulk structure for T, > 700 K. The variations of the polarization profiles with increasing temperature are displayed in Fig. 32. The relative hights of the negative polarization maxima near 8 = 78" and 96" can be seen to change drastically with increasingtemperature. Muller found a drastic drop in the polarization of fractional order spots near the phase-transition temperature T, (1 33). For certain scatteringconditions,Pincreased with increasingtemperatures up to 1 120 K for the (00) beam. N. Muller (133) attributed this increase to lattice expansions both in the bulk and at the surface and to additional multiple scattering effects due to enhanced lattice vibrations. There is interesting behavior of the polarization (Z33)and the asymmetry (142) as a function of temperature for the (00) beam (0 = 90"; C$ = 90"; E = 50 eV). They both

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

55

SCATTERING ANGLE 8

FIG.32. Spin polarization of the (00) beam versus scattering angle at 50 eV for crystal temperatures of 320,420, ..., 830 K. The scattering plane is normal to the 170 direction (133).

oscillate with an amplitude of AP =1.5% and a period of T = 20" between room temperature and T,. There are certainly several competing effects acting on the polarization simultaneously, as pointed out earlier (134): reduction of the effective ion - core scattering amplitudes due to increased lattice vibrations, and lattice expansions in the bulk and at the surface. Thermal motion is expected to decrease and expansion is expected to increase the polarization (134). This might explain the oscillations;P(r) has also been studied for the W(OO1) surface (143). Also in this case, an enhancement of P with increasing T is observed. In electron -atom scattering, the experiments are often perfectly repro-

56

H. C. SIEGMANN et al,

duced by the theory (10). If the atomic beam is unpolarized, only the componentsA, and P,,of A and P normal to the scatteringplane are nonzero and are always equal to each other. In the case of electron scattering at solid surfaces, multiple scattering occurs which results in P # A and P, # IPI and A , # IAl (Section 11,C). However, for the same Scattering condition, /PI = ]A!.These aspects make the analysis of the SPLEED data difficult, and successful work has been performed only on ideal, nonreconstructed surfaces so far. On the other hand, because of multiple scattering, the observables P and A sample the crystal-surface properties. Therefore, to exploit SPLEED for surface-structureanalysis, one makes use of the properties of an axial vector under spatial symmetry operations such as rotation and reflection and time reversal (9, 144, 145). Some general results can be obtained for special cases due to spatial symmetries either in the diffraction geometry or in the crystal surface. One special case occurs when the surface normal s of the crystal is a twofold or fourfold rotation axis of the crystal. Then, time reversal should change the sign of the A and P components parallel to the surface for the case of the (00) beam and conserve the normal components (9, 144). In Fig. 33, P,(8) profiles, measured at fixed energy E = 50 eV are shown for two (00) beams time reversed to each other, and with the scattering plane not a mirror plane of the crystal (azimuth, 4 = 35") (133, 146). With the positive sign referred to n, P,(8) should be identical for both beams if the surface has

SCATTERING ANGLE

0

FIG.33. Pn(6)profiles for (00) LEED beams from Au(ll0) time reversed to each other;

-

4 = 35"; E = 50 eV. The scattering plane is not a mirror plane of the bulk. Note that in the laboratory system, Pnchanges sign under time reversal (n

-n) (133, 147).

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

57

the twofold rotation axis of the bulk. Indeed, both profiles are in good agreement, and therefore P,(@ and A,(@ should also be identical. These results support theoretical predictions and show that the (2 X 1) surface reconstruction of Au( 110) has the two-dimensional surface symmetry derived from the bulk (1 10) planes (146). Further, if the scattering plane coincides with a mirror plane of the crystal, polarization, and asymmetry vectors are equal and normal to the scattering plane, as in the case of electron-atom scattering. Therefore, time reversal changes the sign of the component of A and P normal to the scattering plane (146). These symmetry operations applied to the Au( 110) surface yield the results displayed in Fig. 34 for a set of 01/07 beams at E = 50 eV. Here, the scattering plane is a mirror plane of the crystal. The insets show each scattering condition for which the P,(B) terms are obtained. Operations (a) into (c) and (b) into (d) represent a reflection at the plane [170] X k.

SCATTERING

ANGLE

8

FIG.34. Pn(6)profiles for the (01) and (07) LEED beams from Au( 110). The scattering plane is the (170) mirror plane of the bulk, perpendicular to the close-packed chains of the ( 1 10) plane (133, 147).

58

H. C. SIEGMANN et al.

Therefore, in the laboratory system, for (c) and (d) n is antiparallel to that for (a) and (b). A combined operation, consisting of a time reversal, a reflection at the plane [ 1101 X k, and a rotation around [ liO] transforms (a) into (b) and (c) into (d), as seen from the insets (133). The excellent reproduction of the P,(S)profiles under all these spatial symmetry operations and under time reversal confirms the theoretical results and does not show a broken bulk-derived symmetry at the (1 X 2) reconstructed Au( 1 10) surface. For the same scattering conditions, A,(@ profiles of the Ol/Oi beams reproduce the P,(@ results shown in Fig. 34 (147). Like A,,(@ and Pn(@ for 01 and Oi beams, those for the 0 1/2 and 01/2 beams are related to each other by a time reversal and a reflection at the plane [ liO] X k. In fact, one obtains identical results for A,(@ and P,(S)from half-order LEED beams belonging to the reconstructed surface of Au( 1 10) (146). We have noted that the special relationsrelating the normal components of A and P for the mirror-plane case are identical to those in electron- atom scattering (lo). The first measurements of the in-plane component Pk were performed on Pt(ll1) (148, 149). The authors show that LEED also produces polarization components in the scattering plane, Pk and p,, as a consequence of multiple scattering. This emphasizes directly the major difference between electron - solid and electron - atom scattering. In a solid, for a primary electron beam with the wave vector k,, ,there are many multiple-scattering events which lead to k. Each partial-scattering process occurs with a finite probability and with its own spin state. The diffracted electrons then are a coherent superposition of these partial multiple-scattering processes resulting in an SP vector observable in the experiment. Whenever P,or Pk occurs, then partial multiple-scatteringevents out of the scattering plane play an important role. The component P,,normal to the scattering plane is invariant under reflection of the scattering event at a symmetry plane of the crystal where the components in the scattering plane change sign under reflection (9, 43). Therefore, the components of the polarization vector in the scattering plane, P, and Pk,must be zero if the scattering plane coincides with a mirror plane of the crystal. This is a direct consequence of the conservation of parity under reflection. Only for these special cases, the normal component P,,carries the full information about the electron spin polarization. Figure 35 shows rotation diagrams for P, and Pk of the (00)beam from Pt( 1 1 1 ) (148). Since the mirror-symmetry planes of the (1 11) surface are separated by 60", Pk is zero at every 60". Because the component of an axial vector parallel to the mirror plane changes sign under reflection and the normal component is invariant, P,,is symmetricwith respect to 4 = 60" and 120" and Pk is antisymmetnc. However, unlike the spin-averaged LEED data, there is no mirror or antimirror symmetry with respect to 4 = 90" and

59

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS 30

60

90

120

150

180

60

90

120

150

180

E = 80 eV

-

20

5 0 ac

0 la N [L a

-20 -LO

J

2

-60

- 80

5

La

30

I

ax

f

2C

z

0

G

N rr a _I

C -2c

I

0

a

-LC

30

60

90

-

.

120

150

180

AZIMUTH ANGLE ( d e g )

FIG.35. Rotation diagrams for P,,and Pkfor the diffraction of 80 eV electrons at Pt( 1 1 1) under a scattering angle of v = 47" (149).

150". Therefore, for the Pt(111) surface the P(4)profiles show threefold rotational symmetry about the surface normal. The LEED intensity rotation diagrams display higher symmetry (sixfold) due to the reciprocity theorem. Therefore, the real symmetry of the surface is not apparent in spin-averaged LEED. The example of Pt( 11 1) constitutes a beautiful demonstration of how SPLEED can provide additional information about the surface symmetry. Such rotation diagrams are generally preferred to P(0) and P(E) profiles because P(4)displays the crystal symmetry. Figure 36 illustrates results of measurementsfor both components of the polarization vector, P,,and P,,for E = 100 eV obtained from Au( 1 10) as a function of the azimuth alignment 4, where 4 is the angle between the mirror-symmetry planes of the fcc bulk and the trace of the scattering plane in the surface. The scattering angle is 0 = 139". Also shown (top) is the intensity distribution of the (00) reflex.

60

H. C. SIEGMANN et al.

AZIMUTH

ANGLE

(deg)

FIG.36. (a) The intensityI, (b) P, (normal component),(c) and P,(in-planecomponent) for the (00) LEED beam from Au( 1 10) as a function of the azimuth angle 4. The scattering angle (0 = 140"), as well as the scattering energy ( E = 100 eV), are constant. The error bars give the uncertainty in the measurement of polarization and in the determination of 4 (43).

Throughout the spectrum,P,,displays negative values, whereas P, shows interesting behavior. It is zero for 8 = 0" and 90". In the first orientation the (OOi)plane of the crystal, containingthe close-packed chains, coincideswith the scatteringplane, and in the second case, it is the ( li0) mirror plane of the bulk. For other azimuth orientations of the crystal, P, has positive and negative values. It even assumes much larger values than the normal component P,,. The results of the measurementsof the in-plane component of the transversal ESP vector from Au( 1 10)are therefore in accordance with the symmetry properties of the fcc lattice of Au and show interesting multiple-scattering properties asymmetric to and away from the scattering plane (43). Experimental values for Pcan change drastically if the surface is covered with adsorbates. This can be due to adsorbate-induced reconstruction of the host material and/or due to additional Scatteringof electrons at the adsorbed

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

61

layer. For the W(O0 1) surface significant changes in P occur after adsorption of disordered CO and 0, overlayers (150). However, there is no systematic trend in the experimental data to draw a clear conclusion. For the ordered CO overlayer on W(OO1) (151), the authors find distinct PiE, profiles corresponding to the 4 2 X 2) overlayer. It is concluded that PiE)is a very sensitive indication of the tightly bound p3 phase of CO. Similar changes in the magnitude and in the sign have been observed in PLEED from W(OO1) covered with nitrogen overlayers (152). This similarity suggests that both N, and CO are responsible for a reconstruction of the W(OO1) surface producing the observed changes in P; H, on W(OO1) induces a reconstruction observed in LEED and SPLEED (153). Therefore these techniques are superior in detecting H, to those methods which rely on core-level excitation or deexcitation mechanisms.

B. Surface Resonances Surface-resonancescattering implies the capture of an incident particle by the target to form a compound state in which the particle is bound in a discrete energy level of the potential perpendicular to the surface. The effect is observable in the form of abrupt minima in the specularly reflected intensity,which is otherwise a smoothly varying function of incident energy. The resonant state can be excited in a narrow range of incident energy and momentum characteristic of the bound state. These temporary states are called surface resonances. The first observations of surface resonances were made in atom scattering (154) and in high-energy electron-diffractionexperiments (155). Also in LEED one has observed resonant states bound between the topmost layer and the surface potential barrier. Here, the electrons travel parallel to the surface subject to their own image charge potential. If the bound-state energy lies below the beam-emergence condition, it is called a surface-barrier resonance (156). If the electrons are trapped in the eigenstates of the topmost layer of the crystal, one encounters in-plane resonance (157). In the case of threshold resonance, the threshold for the beam emergence is reached, and the bound state lies above the vacuum level (158). All these observations can be made if either the scattering energy or the scattering geometry is varied. This technique has been used several times to study the electronic surface resonance band structures, like for W(O0 I), Al(00 I), Ni(OOl), and Ni(OOl)42 X 2)O (159), by plotting the resonance energy of the elastic reflection coefficient as a function of the surface-parallelmomentum. It is also suggested that one tests three-dimensional models of the effective potential at the surface and outside of it (159). High-resolution

62

H. C. SIEGMANN et al.

LEED experiments on Cu(001) have been interpreted in terms of an interference between the directly reflected wave and a wave internally reflected at the surface potential barrier, rather than in terms of a resonance phenomenon (160). The authors were able to determine that the image potential acting on an electron saturates to a linear form on approaching the surface and assumes a value much smaller than the inner potential at the surface, otherwise being Coulomb-like. They also found that the translation of the image plane outside of the surface is larger than calculated with the jellium model [e.g., 1-2 a.u. for A1 (16l)l. Muller measured large SP effects near the LEED intensity resonance minima for Au( 1 10) near 50 eV (133). Assuming that the spin-orbit interaction of electrons with the gold atoms produces a splitting and a shift in the elastic reflection near resonances, he estimated the spin - orbit energy to be around 3 eV. Pierce et al. (162) observed the spin dependence of a threshold interference mechanism at low energies for W(OO1). It becomes apparent that spin - orbit coupling produces shifts and large splittings ( 1.3 eV) of the resonances for certain scattering conditions (163). These data make it possible to refine the existing surface-resonance band structure of W(O0 1) (159). Some of the observed features must be associated with interferences between direct and indirect reflection processes. Calculations by P. J. Jennings and R. 0.Jones (164) establisheda best fit to the experimental data for W(OO1) using a barrier with an image plane 3.3 bohrs from the outermost atomic layer and with a value of 70%of the bulk inner potential at that layer.

C. Exchange Scattering on Magnetic Surfaces Elastic scattering of electrons from atoms or ions with a magnetic moment depends on the orientation of the electron spin with respect to the atomic spin. The spin dependence is relatively weak since the exchange energy is generally small compared to the Coulomb energy. The energy-dependent exchange interaction can be calculated rigorously in only simple cases, e.g., the scattering of two electrons on each other (Section VI1,A). Exchange scattering of slow spin-polarizedelectrons from magnetic surfaces is the most promising technique for studying surface magnetism. One important aspect, the temperature dependence of the surface magnetization, was treated in Section II1,C. Loss of symmetry at the surface can also cause new types of magnetic order such as antiferromagneticor ferrimagnetic arrangement of the spins at the surface of a ferromagnet. Such transitions may be connected to or caused by a rearrangement of the geometrical position of the surface atoms known as surface reconstruction. Due to multiple scattering, LEED data are difficult to interpret even with nonmag-

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63

netic materials. If one now superimposesthe complexitiesof surface magnetism, it is evident that SPLEED with magnetic surfaces will need some time do develop. The feasibility of SPLEED was first demonstrated by Celotta and coworkerson Ni (165). The asymmetries produced by exchange scattering are of the order of only yet this can easily be detected using the GaAs source. Spin-dependent atomic scattering and electron attenuation can, within reasonable approximations, be separated from effects of spin-dependent crystal diffraction and multiple scattering. The key idea is to use a ferromagnetic glass as a target and to measure the elastic backscattering of electrons, with electron spin parallel or antiparallel to the magnetization. The advantages of using a glass are the following: (1) The ease with which it can be magnetized due to lack of crystalline anisotropy. This minimizes the stray magnetic field outside the sample surface, as pointed out in Section IX,B. (2) Glasses are sufficiently disordered to neglect effects of crystal diffraction. (3) Contributions from multiple scattering are weak under certain conditions.

J. S. Schillingand M. B. Webb (166) have shown that atomic Scatteringis dominant in liquid metals in the backward-scatteringdirection. This due to the very strong attenuation of low-energy electrons in a solid. Although several successive atomic scatterings by small angles taken by themselves would yield a stronger intensity in the backward direction, these multiplescatteringprocesses require a longer path of the hot electron in the solid and therefore are more attenuated than one large angle atomic scattering. By analyzing the angular dependence of the scattering, Pierce and co-workers (69) have shown that the contribution of multiple scattering to the total intensity backscattered from a metallic magnetic glass is below 30%. The intensity i scattered in the backward direction is given by i = Acr, where cr is an atomic elastic cross section and A is the mean free path determined by inelastic scattering. The spin dependence S of this scattering is given by

s = (&o+

- hcr-)/(A+&

+ A-0-)

where +(-) represents the case where the spin of the incident electron is parallel or antiparallel to the majority spin direction in the sample. Figure 37 shows data obtained by Pierce and co-workers (69, 16 7) on a crystalline Fe(001) surface and on surfaces of the metallic ferromagnetic glasses Fesl,5B,4,5Si4 and Fe,Ni,B,O. The electron beam is incident along the surface normal in the case of the glasses and 7" off surface normal in the case of Fe( 1 10). The electrons scattered by 166" with respect to the incident

64

H. C. SIEGMANN ef a/.

a? 3

a

2 I

0 -I

0

40

120

80

180

200

E (eV)

FIG.37. Spin asymmetriesA (%) from Fe( 1OO)(---)and two metallicferromagneticglasses versus electron energy: (0)FeaNiaB,; (-) Fe,,,.,B,,,Si,. The spin-polarized electron beam from a GaAs source is incident near the surface normal, and the electronsemergingat an angle of 166" with respect to the incident beam are measured. The spin polarization in the scattering plane is such that effects of spin-orbit coupling are minimal [from Refs. 69, 167)].

beam are measured. The spin dependence S of this scattering is plotted against electron kinetic energy in eV. We see a complex structure in the case of the beam reflected specularly from the crystalline Fe surface. By comparing the liquid-like glasses one understands that most of this is due to effects of diffraction. In comparing the two glasses it becomes clear that most of the spin-dependent scattering is due to the Fe atom. The Ni atom contributes only at energy 6 1 eV and beyond. Furthermore, S produced by Fe changes sign at 50 eV. These energies happen to be the excitation energies of a 3p core electron to a 3d state in Ni and Fe, respectively. Because S is the normalized difference of terms proportional to la, positive contributions are produced either by selective elastic scattering of majority-spin electrons or by selective inelastic scattering of minority-spin electrons. The fact that S changes sign with energy conflictswith the energy dependence expected from the singlet absorptive part of a complex optical potential as suggested by Feder (9),which implies positive S for all energies. Rendell and Penn have computed the spin asymmetry of 1for crystallineFe, Co, and Ni (168). Only in Fe do they find sizable spin dependences of 1, with a positive A = (4 ' gl)decreasing monotonically with

+

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

65

increasing electron energy up to 80 eV. This cannot explain the observations either. S. W. Wang (169) investigated the spin-dependent elastic scattering in the framework of a one-electron potential, whereas R. K. Nesbet (I 70) points out that effects of electron scattering are associated with excitation processes involving localized 3p- and 3d-hole states. The latter model can explain the observed energy dependences of S and especially the fact that the structure is related to the excitation energy of a 3p-core hole. We see that glassy ferromagneticmaterials are best suited to obtain a first insight into the single-atom exchange scattering and the spin dependence of the inelastic processes. The theory is not sufficiently developed at present. This is not surprising, since even the electron- hydrogen collision problem is not fully understood at present, at least as far as the exchange term is concerned (171). Once the correct atomic exchange scattering factors are known, one can proceed to crystalline materials and determine magnetic surface structuresand other surface magnetic data such as the restoration of the bulk magnetization with distance from the surface. First steps in SPLEED on magnetic materials have been taken by G. Waller and U. Gradmann (172) in collaboration with E. Tamura and R. Feder (173) on Fe and by S. F. Alvarado et al. (174) on Ni. It is found that the magnetization is enhanced by 30% at the (1 10) surface of Fe, but remains essentially constant at the surface of Ni. The physical models on which these conclusions are based are described in a review by Feder (175). It is noteworthy that an energy-dependent attenuation of the type proposed by Nesbet (170) is needed to obtain a good fit to the experimental data in the case of Fe.

D. The Special Case of Gadolinium Gadolinium was predicted to exhibit strong spin-dependent scatteringin a narrow energy range, namely, at resonance with the empty 4f configuration level (176). Theoretically, Gd is a simple case, since the atom is in the 4f ground-state configuration(8S,,2). Any additional electron in the 4f shell must be a down-spin and causes the configuration to rise in energy because of correlation. The empty 4f8 configurationallevel lies about 2 eV above the vacuum level (1 77). The reflection coefficient of electrons with this kinetic energy is expected to be strongly spin dependent: only down-spin electrons are absorbed in the 4f8 state and, because of isotropic decay, are lost from the coherent backscattering. Consequently, electron reflection produces positive SP. The spin- flip scattering is also enhanced (Section VII1,C). Experimentally, scattering of polarized electrons is difficult because the

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20

-

15 -

10 -

3

4

5

6

7

8

9

10

hv (eV)

FIG.38. Spin polarization of the total photocurrent versus photon energy for magnetically ordered polycrystallineGd films: He,, = 25 k 2 kOe; T = 220 K.

large magnetic moment of gadolinium may produce stray fields that deflect low-energy electrons. Spin-polarizedphotoemission in the longitudinal field configuration (Section IX,A) avoids this problem. Valence electrons can or cannot be excited into the quasi-bound 4f8 state depending on the photon energy. The one-electron decay of the 4f configuration into emitting-band states produces negative ESP of the photoemitted electrons. Figure 38 shows the polarization spectrum of photoelectrons from a magnetically ordered gadolinium film (I 78). It exhibits a pronounced minimum around 6.5 eV. The polarization of the exchange-split 5d conduction electrons is expected to decrease monotonically with increasing photon energy based on calculated state densities (I 79). The occurrence of the minimum is ascribed to down-spin electrons emitted from the photoexcited 4f state. Width and position of the minimum agree well with the convolution of the occupied part of the 5d band (I 79) and the 4f8 states obtained from Bremsstrahlungs- Isochromat spectra (I 77). The relative change in polarization implies that the current in the one-electron decay channel is greater than 8% of the total integrated photocurrent at 6.5 eV. This shows that 4f-5d resonant scattering is strong in Gd producing a large spin dependence in the scattering of low-energy electrons. We note that Auger decay of the 4f state yields an SP corresponding to the 5d polarization and thus does not contribute to the observed structure. Furthermore, the ordered 4f7 electrons lie about 12 eV below the vacuum level (I 77) and thus do not directly show up in the spectrum of Fig. 38.

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VII. SECONDARY ELECTRONS When a beam of primary electrons impinges onto a metal surface, it interacts with ion cores and with electrons of the solid. Those events are called inelastic where some part of the primary energy Epis transferred to electrons or quasi-particlesof the solid (180). The inelastic collisions can be classified into direct excitation of core electrons, collisions with conductionband electrons, and plasmon excitations. The spectrum of secondary-electron emission (SEE) contains the by-products of these excitations either directly or after further decay processes. Auger-electron emission or plasmon decay are examples of the latter. The elastic interaction with ion cores shows up as an intense peak at the secondary energy E, = Epaccompanied by structures due to discrete energy losses in the form of surface and bulk plasmon excitations. At the low kinetic energy end of the spectrum the “true” secondaries are emitted. They originate from the decay of the plasmons and from cascade processes resulting from repeated inelastic collisions in the conduction bands. Between these two extremes in energy, the spectrum contains a nearly homogeneous emission as a result of electron -electron collisions and core - electron excitations. A comprehensive treatment of SEE phenomena is given in Ref. (180). A . Emission of Secondary Electronsfrom Nonmagnetic Metals

As is common in photoemission from solids, SEE has also been thought of as a three-step process. In this sense, the spectra contain information about the excitation, the transport, and the escape of electrons. In conventional spin-averaged measurements, the transport and escape processes obliterate the strong anisotrophy (181, 182)in the excitation spectrum such that the observed SE seems to be homogeneous in energy and angular distribution. However, by measuring the SP of SE, specific information can be obtained about various mechanisms responsible for SEE. The strongest mechanism for SE excitation is the collision of a primary electron with the electrons of the Fermi sphere. This collision can be described by a probability function which is restricted in space by cos 5 cos 8 5 cos 02, where 8 is the angle between wave vector of the primary electron and the wave vector k of a secondaryelectron to which an energy E, is transferred during the collision (180). If the target electron has initially Ef and kf, then

cos

= (k2

- ki f k(&

- k2

+ k#)1/2)(bk)-1

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H. C . SIEGMANN et al.

For kf= 0, this formula reducesto the classical one for a noncentral collision and still applies reasonably well for cases where the energy transfer during the collision is much larger than the binding energy Ef.This process of electron - electron collisionsresults in an incoherent excitation of secondary electrons with energies 0 5 E, 5 Ep. Depending on the energy transfer, the distribution of secondary electrons is highly anisotropic. The excitation cross section is large for small energy transfer to a recoil electron, i.e., for e = 900. Plasmons decay by exciting an electron-hole pair in the Fermi sea; electrons from this decay may escape over the surface bamer. They are expected to be unpolarized in the case of a nonmagnetic solid. The matrix elements for electron excitation by plasmon decay is identical to that for absorption ofphotons of the same energy (183). The plasmon-excited SE are limited to an energy range below the plasmon energy minus the work function. The spatial electron distribution is close to isotropic (180). SE can also be produced by the primary electron colliding with core electrons. The intensity of this excitation mechanism depends on the overlap of the plane-wave functions with those of the core states and hence on the binding energy of the core electrons. The spatial distribution of SE thus excited does not depend appreciably on the energy transfer during the collision in the range of Ep considered here (180). The elastic electron-atom interaction, on the other hand, has a large cross section in the forward direction in which the electron spin polarization (ESP) created via spin-orbit coupling is negligibly small. The ESP can generally have sizable values for large-angle scattering with a smaller cross section. Therefore the scattering angle used in an electron-scatteringexperiment is a crucial parameter that determines the strengths of different SE excitation mechanisms and the ESP observed in the experiment. Figure 39 shows the experimental setup used in the study of SEE from an Au( 110)target (184). With the GaAs source emitting unpolarized electrons with Ep = 500 eV, the SP of SE are measured as a function of E, for 50 5 E, 5 300 eV after an angular resolved energy analysis. The scattering angle is 90". The results are displayed in Fig. 40. The ordinate shows the component of ESP normal to the scattering plane P,,; the abscissa is the secondary energy E,. Since the measurements are made well above the plasmon energy and the core-electron excitations are rather weak, the SEs in the energy range considered here are mostly produced by screened electron-electron collisions. At low-energy transfer to a SE, they are excited mostly in a direction perpendicular to $. Since the detector is placed at 8 = 90", it can directly collect the excited electrons. During the transport and escape process, the electrons can still elastically scatter at gold atoms in the forward direction. However, for this condition, no ESP will be produced

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

‘s

69

‘a

FIG.39. Apparatus for studying the secondary-electronemission from metals. The GaAs electron gun and the absorption detector for ESP are described in Sections II,A and II,B. Not shown is an electron gun for unpolarized electrons at 0 = 139”.

50

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Experiment

- Calculated

40 -

30 -

-

20 -

-

-

-

10

0

- 10

I

I

I

I

0.1

0.2

0.3

1

0.4

I

0.5

I

I

0.6 E,/Ep

FIG.40. The spin polarization of the secondary electrons versus the relative energy transfer E$E,, with E, = 500 eV. For the calculation it was assumed that electrons have equal masses and that the secondary electrons acquire the change of the momentum necessary to reach the detector in one elastic scattering from a single gold atom.

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via spin-orbit coupling (20). This argument is valid for E, 5 100 eV, as manifested by the vanishing ESP shown in Fig. 40. As E, is increased, the excitation by electron- electron collision is no longer perpendicular to the momentum of the primaries, and the excited electrons must be scattered elastically at gold atoms in order to change their direction so that they can reach the detector. Since the electron -gold atom scattering is no longer in the forward direction, ESP will be produced via spin - orbit coupling. Therefore, in the simplest case, one needs to adopt a two-step model for the SEE. First, the primary electrons make a deep inelastic scattering with the conduction-band electrons of gold to produce an anisotropic SE distribution in the solid. This process acts as an incoherent internal source of electrons with energies 0 5 E, 5 Ep. Following this excitation process, the electrons are scattered at gold atoms where an ESP can be produced with values depending on E, and the scattering angle. Note that, once E, is fixed, the spatial distribution of the excited electrons, and hence the scattering angle in the electron-atom scattering, is determined for a given angle 8 at which the detector is set. Also plotted in Fig. 40 as a continuous curve are results calculated on the basis ofthe two-step model (185). At a given E,, the spatial distribution of SE in the solid is taken from Ref. (280). For the subsequent interaction of the excited electrons with the gold atoms, tables of scattering amplitudes and polarizations for single electron - atom collisions are used (286). The agreement between the experimental and calculated results is surprisingly good despite some deviations. The following observations can explain the deviations. The calculations are very sensitive to even minute variations in the scattering angle. Other possible causes for the deviation of the calculations from the measured results could be due to plasmon creation before the first collision and after the elastic scattering. Further, the atomic data are not very reliable at low energies, and we do not have isolated gold atoms in the solid. The two-step model has its limitations. If 8 > 90", a sequence of elastic and inelastic scattering events is likely. Results of such a case with 8 = 139" are shown in Fig. 4 1. Both components of the ESP, P, and P,,normal to the emitted electron momentum have been measured as a function of E, (187). We note that the two-step model cannot account for the polarization components lying in the scatteringplane. Hence, the occurrence of P,shows that multiple-scattering events are present. If 8 = 90", the SE are mostly excited perpendicular to the incomingbeam direction for small energy transfer, and the following elastic scattering at gold atoms is in the forward direction. As seen in Fig. 40, in the energy range of 0.1 5 E,/Ep 5 0.25,the effects of spin-orbit coupling in elastic scattering can be neglected. Excitation by plasmon decay cannot contribute to SE emission since E, lies above the plasmon energy. Therefore, this

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50

70

90

110

71

130

SECONDARY-ELECTRON ENERGY E,(eV)

FIG.4 I . The measured values of the transversal components of the ESP of secondary electrons P, and P,, emitted from Au( 1 10) at 0 = 139”; P, is the component normal to the scattering plane: (a) Pe = P e; (b) P,,= P n; E, = 600 eV.

-

-

situation allows the study of electron - electron interactions. For this purpose, primary electrons with initial polarization Po are directed onto the gold target, and the SP of SE is measured. Since P = 0 for Po = 0, the measured ESP is due to the polarization dependence of the electron-electron scattering in the excitation process. It reflects the transfer of primary electron spin onto a secondary electron, which is emitted. This is a direct observation of the quantum mechanical exchange of electrons in an electron -electron scattering process (184). As was shown by Bincer (188), at low-energy transfer, the triplet scattering dominates over the singlet scattering, favoring the emission of SE with an ESP close to Po. As the energy is increased, the cross section of the singlet scattering becomes stronger, and the observed exchange polarization is reduced. The exchange and direct amplitudes If1 and lgland the relative phase angle betweenfand g are all energy dependent; this can generate negative SP up to -33% and may explain the negative excursion at E, = 0.2Epobserved in Ravano et al. (184). At higher energies, the secondary electrons are not any longer ejected perpendicular to b,and an ESP is created via spin - orbit coupling in the elastic scattering, making it difficult to extract the exchange information from the data. Such experiments are promising and must be repeated with low-2 materials where spin -orbit coupling cannot produce any polarization that

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masks the exchange. Generally, these experiments are of great value for the study of electron-electron interactions in a solid. B. Secondary Electronsfrom Ferromagnets

The motivation to study the SP of SEs from ferromagnetsarose from the demand for an efficient and simple surface magnetometer. True secondaries at low kinetic energy, so-called cascade electrons, are emitted with high intensity, typically two orders of magnitude higher than elastically scattered electrons or valence-band photoelectrons. Since SEs production is not spin dependent (40),they are expected to carry a polarization proportional to the average magnetization at the surface. At present, surface magnetic studies utilizing secondaries have not yet been published however, SE polarization from a ferromagnet was reported to exist (189) and the technique is rapidly developing. The SE can be divided into three classes each of which constitutes a separate regime of investigation: ( 1) Low-energy cascade electrons. The SP for different materials such as ferromagnetic glasses (190, 191) or single-crystal transition metals (I 92, 193) exhibits rather universal dependence on the kinetic energy of SEs. The highest SP occurs at zero kinetic energy, decreases within the first -5 eV to approximately half its initial value, and then remains roughly constant throughout the energy range of cascade electrons (E, < 20 eV). Energy-dependent variation of the escape-depth probing bulk versus surface contributions (189) must be ruled out as an explanation since the effect persists down to low temperatures (190). It was suggestedthat the inelasticmean free path for minority carriers is strongly reduced because of the excess of minority holes available for absorption (191, 192). This explanation, however, contradicts what was found in the elastic scattering of polarized electrons from a ferromagnetic glass. The asymmetry with respect to incident SP was found to be below 1% and strongly depends on kinetic energy at very low kinetic energies (Section V1,C). Furthermore, it strongly conflicts with the interpretation of SP photoemission spectra based on bulk band structures (Section 111,A). The SP of the true secondariesbears information on decay mechanisms of hot electrons, band features near the surface of a ferromagnet, and surface magnetism. (2) Inelastically scattered electrons. Exchange scattering is the key feature in the energy range where electron-electron scatteringwith nonzero energy transfer (called inelastic scattering)is dominant. Studying the SP of electrons scattered from a polarized target (ferromagnet)using unpolarized primaries is complementary to the experiment with polarized electrons

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

73

FIG.42. Spin-polarization P and intensity I versus kinetic energy of secondary electrons from Fe,,B,,, excited by electrons of E, = 2900 eV. Each data point represents the average of two consecutive runs. The statistical error is AP = H.2%.

impinging on an unpolarized target (Section VI1,A). From measurements of the SP of secondaries excited from a ferromagnetically ordered material with polarized primary electrons the energy-dependent exchange, direct, and triplet cross sections can be determined separately. Scattering angle and energy must then be matched in order to discriminate against large-angle elastic scattering events (Section VI1,A). (3) Core excitations, Auger electrons. High-resolution Auger spectroscopy, in particular LMM spectra of 3d metals with partly filled d bands, yields rich information on electron and hole interactions (193). Measuring the SP of the Auger electrons opens new perspectives in both the Auger spectroscopy of 3d transition metals and in the understanding of ferromagnetism of pure metals, compounds, and alloys. The information is manifold depending on the particular Auger transition. As an example, spin-polarized Auger spectra from a ferromagnetic glass of composition Fes3B,,are presented. In Fig. 42, intensity Iand polarization P versus secondary-electronkinetic energy in the vicinity of the three prominant Auger lines of iron are shown (194). Each transition has a different final-state hole configuration. In L3M4,M4,two additional holes in the 3d valence band are left behind. In the case of iron where the 3d effective Coulomb interaction is small compared to the bandwidth, the L3M4,M4, spectrum is given by the self-convolutionof the local one-particle density of states. In L3MZ3M4,a 3p and an additional 3d hole are generated. The

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spectrum then reflects the local valence-band density of states in the presence of a 3p hole. In L,M,,M,, the 3d valence band is not directly involved. The final state consists of two holes in the 3p shell. Therefore the observed SP reflects the coupling of holes in a core subshell to an unfilled valenceelectron shell. The coupling is to the unpaired spin or magnetic moment at the Fe site. Since (s,) along the magnetization of the sample is measured and averaged over many atoms, the signal reflects long-range order. The L3Mz3Mz,SP thus contains information on the magnetization or, due to its local nature, on the sublattice magnetization in the case of a composite system. The Auger electrons from the boron KLL transition which leaves behind two holes in the 2s2p valence band at the boron site were observed to be unpolarized (I 94). This agrees with the fact that the magnetization is zero at the boron site and clearly illustrates how spin-polarized Auger spectroscopy can be a powerful technique in revealing local magnetic features in magnetic alloys and compounds. MAGNETOCHEMISTRY VIII. SURFACE A. Surface Magnetization and Segregation

Surface segregation or adsorbate-induced decomposition is likely to occur in many intermetalliccompounds or alloys. It can be accompaniedby magnetic effects if at least one component is magnetic. Spin-polarized photoemission may then be used as a surface magnetometer to monitor surface segregation and chemical reactions at the surface. Two examples involvingintermetalliccompounds with large capacity for hydrogen storage shall be discussed. It has been recognized that surface catalytic effects are important for the hydrogen-uptake kinetics (195). In particular, oxygen-induced surface segregation produces transition-metal clusters near the surface on which H, dissociates by chemisorptionsuch that it can subsequently enter into the bulk. The growth of ferromagnetic Fe clusters that occurs upon exposing paramagnetic FeTi surfaces to oxygen manifests itself by the emission of SP photoelectrons (196).Figure 43 shows Pversus Hcurves at constant photon energy together with the oxygen dosage in langmuirs (1 L = 1 X lod Torr sec). At constant photon energy and temperature, P is proportional to the average magnetization M, within the escape depth of photoelectrons (-50 A). One finds that M, increases with increasing oxygen exposure. The nonzero polarization observed on the initially sputtered surface is caused by segregation due to initial oxidation as detected with Auger spectroscopy.

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

--z z

50

I--

75

1

1

40

0

tN

30

a 4

&

a

20 10

0 0

2

4

6

MAGNETIC

-

10

8 FIELD

1 2 1 4

(kOe)

FIG.43. Spin polarization versus external magnetic field of 0,-exposed FeTi surfaces: (0) sample A, T = 296 K, (0)sample B, T = 253 K. Oxygen dosage (L)

Curve

Approximate particle size (k40%p ~

A

B

C D E

3000 I000 300 Sputtered(A13, 1 kV) Sputtered (Art, 1 kV)

~~

2800 3200 3600 1100 2000

Fe atoms.

The increase of M, upon oxygen exposure signals the precipitation of fresh metallic ferromagnetic Fe clusters, with the formation of Ti oxide. The magnetization (i.e., spin polarization) versus magnetic field curves exhibit superparamagnetic behavior. Langevin curves (solid lines in Fig. 43) were fitted to the curves using the magnetic moment of p of a cluster as a parameter, where p gives a rough estimate of the average number of Fe atoms per cluster. The resulting approximate particle sizes are indicated in Fig. 43. The intermetallic compound ErFe, is chosen as the second example. It behaves quite differently, demonstrating the rich variety of possible phenomena (197). In contrast to FeTi, Pdecreases to zero upon oxydation. The SP of the in situ freshly broken samples is small and negative. Exposure to hydrogen at room temperature causes P to become even more negative. Figure 44 shows the spectra of SP for two different runs. The striking feature is the occurrence of P < 0. The compound ErFe, is ferrimagnetic with a

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0

-10

-20 4.0

4.5

5.0

-

5.5

hv ( e V )

FIG.44. Spin polarization versus photon energy of the ErFe, surfaces: shaded rectangles -freshly broken in UHV, open rectangles-after exposure to 100 L H, at room temperature. The two sets of curves correspond to two different runs.

-

compensation temperature T, 500 K. At T < T,, the Er 4f moment dominates, and the net Fe 3d moment points in a direction opposite to the external magnetic field. At photon energies <5 eV, the Er 4f electrons are not photoexcited to an escape level; hence the observed polarization reflects the Fe 3d signal only. The negative SP is then characteristic of the presence of ErFe, near the surface. We conclude that metallic ferromagnetic Fe is not formed in large amounts by oxygen-induced segregation of ErFe, since ferromagnetic Fe exhibits a large positive P (I98). In a recent X-ray photoemission study it was shown that minute amounts of oxygen on clean ErFe, produce surface segregation with the formation of metallic Fe, but that already small oxygen doses (
SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

77

emission proves to be more sensitive compared to X-ray core-level spectroscopy since the latter does not detect any effect of hydrogen exposure (199).

B. Surface Magnetism Induced by Surface Chemical Reactions Surface magnetism at the vacuum interface of homogeneous bulk systems has been the subject of numerous investigations. Some results of experimental investigations are discussed in Sections 111,C; IV,A; V1,C; and IX. Very little is known yet, however, about the magnetic properties of systemswith chemicallyinhomogeneoussurfaces, where the inhomogeneity may be produced by adsorbates or surface chemical reactions. The chromium( 100) surface reacts readily with oxygen and other gases and is therefore not easy to clean. It exhibits surprising changes of the magnetic properties depending on the location of small amounts of oxygen (200). The behavior is entirely different for oxygen adsorbed on top of the surface or for oxygen embedded in the crystal below the outermost surface layer. This latter type is termed incorporated oxygen. In the experiments (200) the nonreconstmcted Cr( 100) 1 X 1 surface was stabilized by less than a monolayer of adsorbed nitrogen. Its location on top of the surface is determined by observing that it is easily sputtered off by mild A+ bombardment. Incorporated oxygen is recognized by the fact that it does not appreciably affect the work function due to efficient screening of the charge located on the negative oxygen ions (201). Incorporated oxygen may be produced by heating the crystal after exposure to oxygen gas. The incorporation is detected by Auger spectroscopy and work-function measurements. Adsorbed oxygen increases the work function by virtue of its dipole moment (see Fig. 4 of Ref. 201); upon incorporation, oxygen still produces an Auger signal, but the work function is reduced to its bulk value. Photoemission of electrons with the full spectrum of a Hg lamp (hv < 5.5 eV) reveals that a small amount of incorporated oxygen-of the order of a few atomic percent of the total volume sampled by Auger spectroscopy-is sufficient to produce a substantial electron polarization (Fig. 45). Chromium forms a ferromagnetic compound CrO, , but even if all the oxygen is supposed to be in the form of CrO,, the photo-ESP would be ten times smaller than observed (200). Therefore, ferromagnetic CrO, does not cause the observed magnetic ordering. One of the possibilities is that oxygen induces redistribution of the electronic charge such that local moments are formed. Also, the distortion of the crystal lattice upon oxygen incorporation could change the sign of the magnetic interaction, since the exchange integral depends critically on distance.

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H. C. SIEGMANN e? al

l0I P(%)

FIG.45. Spin polarization of electrons emitted from a nitrogen-stabilized nonreconstructed Cr( 100)surface by illumination with the full spectrum of a Hg-Xe lamp, T = 300 K. The abscissa displaysthe content of incorporated oxygen as determined by Auger spectroscopy.

From extrapolation of the data displayed in Fig. 45 to zero oxygen coverage, we conclude that the oxygen free surface is not ferromagnetic. This is in contrast to the results of Rau obtained by electron capture (202). In electron capture, however, the polarization of the outermost tail of the electron distribution extending into the vacuum is measured, whereas in SP photoemission, the probing depth is about 15 A (203). It has long been believed that both the nonreconstructedCr( 100)and the V( 100)surfaces are ferromagnetic,either due to the enhanced density of states at the Fermi level

FIG. 46. Temperature dependence of the spin polarization of a sample containing 3.3 at.% oxygen. The antiferromagnetic ordering temperature of bulk chromium is indicated by an arrow.

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

79

in the surface (204), or due to the occurrence of a surface charge density wave (205). Figure 46 shows the temperature dependence of the polarization. The linear decrease is typical for ferromagnetic surfaces (87). The extrapolated ordering temperature of -450 K shows that the magnetic ordering of the surface is not related to the antiferromagnetic ordering of the bulk with TN= 314 K. These findings suggest several further questions: Is oxygen the only element causing magnetic order? To which depth is it able to induce magnetism, i.e., how important is the presence of the surface? Are there other metallic surfaces [e.g., vanadium (206)] turning magnetic if in sufficient contact with oxygen or a different chemical? The case of chemically induced surface magnetism on a nonmagnetic substrate is contrasted by the better known demagnetization of a previously ferromagnetic surface upon chemisorption. The case of Ni has been studied in some detail. Spin polarization of electrons field emitted from the (1 10) and (100) faces of Ni was reduced upon chemisorption of H (207,208). This suggests that chemisorbed H demagnetizes these Ni faces. Conventional magnetization measurements had shown much earlier that the magnetic moment of a dispersed Ni catalyst is reduced by - 0 . 7 ~for ~ every absorbed H atom (209).This shows that surface magnetic measurementscan detect H that is very difficult to measure in other electron spectroscopies. The detection of surface magnetism does not depend on ultrahigh vacuum conditions. From a practical point of view, interest is more likely to focus on the magnetic behavior of surfaces under ambient conditions. If the surface - bulk ratio is large enough, surface magnetism may be detected by conventional techniques such as static magnetization measurements. A good example presents the oxygen-induced segregation (Section VII1,A) of ferromagnetic nickel particles on the surface of paramagnetic LaNi, (210). C. Spin - Flip Scattering on Paramagnetic Surface Atoms Ideally, electron spectroscopy yields information on the energy of the electron, its k vector, and the spin orientation. This information is not generally available in the case of photoemission. During the photoemission process, the excited electron may lose energy by inelastic collisions. The k vector perpendicular to the surface is certainly not conserved because of the surface potential. Phonon or impurity scattering may change all k components. However, since the pioneering work of Allen and Gobeli (211) it is known that a sizable fraction of the excited electrons reach the vacuum without energy loss and with the k component parallel to the surface conserved. In angle-resolved photoelectron spectroscopy interest is focused

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on these primary electrons. Clearly, for SP photoemission it is crucial to know to which extent the spin is conserved during the escape process. In the case of ferromagnetic EuO at low temperatures, P i s considerably below the expected 100%(Section IX,A). This was taken as evidence that spin-exchange scattering at the outermost disordered surface atoms depolarizesthe photoelectrons (SectionIV,A). One sees the interesting possibility of detecting adsorbates with a spin moment. Quantum mechanical exchange in the scattering of electrons is a very fast process, even on the time scale of photoemission, and may thus lead to depolarization of slow electrons. The rare earths are ideal candidates for studying depolarization because the intraatomic exchange is large, e.g., -0.5 eV for the 4f-6s exchange in Eu or Gd. Depolarization by the paramagnetic 4f moments of Gd has been demonstrated (212). Spin polarization photoelectrons with P = 23 f 1% are excited in germanium by circularly polarized light with hv = 3.05 eV. It was found that slight amounts of Gd produce a noticeable reduction of the polarization (Fig. 47). The photothreshold of Ge is adjusted to lie between 2.4 and 2.8 eV by codeposition of potassium. One obtains -3.8 A for the spin-flip scattering length of Gd; this is much shorter than the inelastic mean free path of hot electrons at low electron energies (203). On the other

i

5

10 THICKNESS

15

(1)

FIG.47. Spin polarization of photoelectronsfrom Ge versus thickness of Gd overlayer.

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81

hand, potassium coverages of 20-A thickness did not change the P value of 23%within the experimentalerror (&I%). This shows that the photocurrent at high coverages is still dominated by emission from Ge. Furthermore, the quantum yield did not depend on the amount of Gd deposited; i.e. no repulsive potential is built up at the interface Ge -Gd, impeding the polarized Ge electrons to escape. This experiment showsclearly that spin depolarizationin photoemission does occur. However, as pointed out in Ref. (212),it is, at the present level of experience, a rarely observed phenomenon. We believe that this type of measurement is a unique tool for investigatingthe spin - flip scattering cross sections of hot electrons with many materials, thereby giving insight into the strength of the exchange interaction with various types of atomic or molecular spin moments. For instance, paramagnetic, molecular oxygen should depolarize electrons, whereas the chemisorbed, diamagnetic species 02should not. The information obtained from this type of SP photoemission experiment could also be acquired from an experiment involving the scatteringof a polarized electron beam on a paramagnetic target. However, at low energies (
IX. SURFACEMAGNETIZATION CURVES A solid acquires a magnetization M in an external field according to M = xH, where x is the magnetic susceptibility.Due to the very short mean free path of slow electrons, the measurement of spin-dependentphenomena may be used to determine such magnetization curves in a very thin sheet at the surface. Elastic or inelastic scattering or photoemission of electrons from a magnetized surface has been used to determine M(H). However, M can create a stray magnetic field outside the sample in which the electrons experience an unwanted deflection due to the Lorentz force. There are basically three solutions to this problem: (1) The Lorentz force is minimized by letting the electrons travel parallel to the stray field; M is choosen perpendicular to the surface under investigation. (2) The stray field is minimized by choosing M parallel to the surface and by applying H along directions of easy magnetization in materials with flat surfaces.

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(3) The stray field is minimized by employing a sample in the demagnetized state. This requires an incident electron or photon beam focused to a spot of diameter smaller than the diameter of the Weiss domains. A . Magnetization Perpendicular to Surface

The sample is located in the bore of a (superconducting) coil with iron shield, as shown in Fig. 48.A primary beam of electrons or photons strikes the surface of the sample thereby causing the emission of photo- or secondary electrons. The electrons emerging near the axis of the coil can be extracted from the external magnetic field by suitable electrical acceleration parallel to the axis of the coil, and an electron beam can be formed for the measurement of SP. Those electrons that emerge off-center spiral away along the field lines and cannot be extracted. This configuration has the disadvantagethat angular resolved SP measurement of electrons cannot be performed. Energy analysis is also difficult (213). However, it has the advantage that the sample may be exposed to very high magnetic fields. Also, the sample can have any shape, and its surface must not be perfectly

t

BEAM IN /OUT

FIG.48. The measurement of surface magnetization curves with magnetization perpendicular to the surface. A light beam or a primary-electron beam excites photon- or secondary electrons, which may be extracted from the magnetic field region by electrical acceleration parallel to the axis of the coil for the measurement of SP if they originated close to the center of the sample surface. The meter connected to the sample indicates the spin-dependent current absorbed in the sample if a spin-polarizedelectron beam is incident.

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P(B1A

15 -

10 -

/

FIG.49. The field dependence of the photo-ESP with a polycrystalline film of antiferromagnetic GdP at T = 4.2 K. The photoelectrons are excited with the full spectrum of a Xe high-pressure arc.

flat. It is the only configuration to investigate hard magnetic materials such as permanent magnets or para- and antiferromagnets. Most experiments reported so far have been photoemission experiments in which the photon energy was close to photoelectric threshold, and the SP of all photoelectrons regardless of their angle of emission and energy has been measured. The SP of these electrons is proportional to the surface magnetization M,. The effectivearea of the sample is approximately 1 mm2, the probing depth being relatively large, ranging from 10 to 100 A depending on the electronic structure of the material, and the mean free path for conservation of spin. The primary beam could also be a spin-polarized electron beam, and the signal proportional to M, could be the spin dependence of the absorbed current (40) measured with a meter connecting the sample to ground potential. Figure 49 shows the photoelectric magnetization curve (PMC) taken at 4.2 K with GdP, which is antiferromagnetic with a Nkel temperature of 15 K. Sizable photo-ESP is observed because the 4f moments of Gd are partially forced into the direction of the external field. However, the observed photoelectrons are not emitted from the 4f7shells but from higher lying Gd-derived electron states. These states are strongly coupled to the 4f electronsby the intraatomic exchange,and therefore their SP is proportional

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0

I

I

I

10

20

30

I 40

1

50

I

c

60 B (kG)

FIG. 50. Same as Fig. 50, but with disordered GdP obtained by evaporation onto a substrate kept at 4.2 K (215).

to the SP of the 4f7 shell. The PMC of GdP is identical to the bulk magnetization curve M,(H) within the accuracy of the SP measurement. If, however, GdP is evaporated onto a substrate kept at 4.2 K, structural disorder is introduced in this compound which has a simple NaCl lattice (214). The PMC changes from a straight line to a Brillouin function for S = 7/2 (corresponding to 4f7) as shown in Fig. 50. This indicates that the structural disorder, or new states introduced by the structural disorder, have broken the antiferromagnetic coupling and that disordered GdP is paramagnetic (215), in agreement with the theoretical notion that antiferromagnetic order is “frustrated” in glassy material (compare Section IV,A). Figure 5 1 shows the PMC of the ferromagnetic insulator EuO doped with 4.3% of Gd (Section IV,A). Electrons at photoelectric threshold stem directly from the 4f7 shell, apart from a smaller contribution of impurity states or the states introduced on doping with trivalent Gd. Since the half-filled 4f7 shell is in a pure S state, the SP of the 4f electrons can be calculated from the magnetization by P = M(T, H)/Mo,where Mo = 24 kG is the saturation magnetization at T = 0. From Fig. 5 1 one obtains M(43 K, 5 kG) = 0.28 X 24 = 6.7 kG. On the other hand, it has also been shown (216, 217) that the absolute magnitude of the surface magnetization may be obtained from the PMCs if the demagnetizing factor N is known. The field acting inside the sample is

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FIG.5 1. Spin polarization of photoelectronsemitted from the 4f7-statesin fresh (100) surfaces of Gd-doped single crystals of ferromagnetic EuO versus the external magnetic field strength (88): EuO 4.3%Gd; T = 43 K.

+

H = Hex- NM, where Hexis the external field generated by the coil. If x, is the intrinsic susceptibility in weak fields for a closed-ring sample (N = 0), one has M = x,H. This yields M = ( I&, - N)-'-Hex= (NHeX)-'for soft magnetic materials such as EuO where 1/x, << N. The initial susceptibilityxi= l/Ncan be read from Fig. 5 1. It isx =M( T, Hix)/Hix,where HLx is the external field at which the straight line approximating the magnetization curve in small Hexintersects the almost horizontal straight line at large Hex.One obtains M( T, Hlx)= HLx/N.The crystal had approximately the shape of a cube in which Nis not constant. In the middle where the electrons emerge, the sample may be approximated by a sphere yielding N = 1/3. From Fig. 52 one obtains Hix = 2.5 kG, yielding M(T, Hix)= 7.5 kG, in reasonable agreement with the first estimate from the degree of ESP. Better values for Mare, of course, obtained for thin-film samples magnetized perpendicular to the surface with N = 1. However, one has to be careful because magnetic anisotropy may be introduced by stress or by the presence of the surface, and the condition l/x, < Nmay not hold. M = 7 kG obtained with doped EuO from the photoelectric measurements is much lower than the bulk saturation magnetization at T = 43 K. The reason for this reduced surface magnetization becomes apparent on inspecting the PMCs taken at much lower T. Figure 52 shows data at T = 10 K for EuO and Eu,-xGdxO (218). With N = 1/3, the bulk saturates at Hex= 8 kG. However, there is no magnetic saturation in the PMCs and, correspondingly, P is much smaller than the bulk value of almost 100%. This and the large slope of the PMCs at large Hexindicates the existence of uncoupled, quasi-paramagnetic 4f moments at the surface. The total field aligning the surface moments against the thermal motion is the sum of Hex, the field produced is the underlying magnetized bulk crystal and possible rests of the ferromagnetic exchange field. The latter contribution can be

86

H. C. SIEGMANN et a/ P (To)

70

60

50

40

30

H (k(

FIG.52. Same as Fig. 52 but at T = 10 K, and for two surfaces with different n-type impurity concentrations (84).

increased by introducingextra electrons on n-type doping with trivalent Gd. This is why the PMC of Eu,-xGdxO lies above that of pure EuO. Spin-exchange scattering of electrons is very efficient in EuO (85), which enhances the surface sensitivity of threshold photoemission. This is why the reduced coupling of the last layer surface moments becomes dominant in determining the shape of the PMCs despite the fact that the threshold photoelectrons have a large escape depth of 100 A in EuO (Section IV,A). The energy arising from the free magnetic poles at the surface with perpendicular magnetization may be reduced by the formation of closure domains. However, the formation of such domains costs anisotropy and magnetoelastic energy. Therefore, closure domains form at some surfaces, whereas they do not in others. This is readily detected by measuring surface-magnetization curves and comparing them to those of the bulk. Pescia et al. (219) found closure domains at the surface of Fe30, magnetized in the easy (1 1 1) direction, but in US with a very large anisotropy energy these domains did not occur. Alvarado (21 7) determined the surface anisotropy constant in Fe30, by measuring PMCs.

B. Magnetization Parallel to Surface It is clear that for minimal stray field H(x), where x is the distance from the surface, the sample must be magnetizedparallelto the surface. Figure 53

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS DETECTOR

87

J

FIG. 53. The measurement of surface magnetization curves with magnetization parallel to the surface. A light beam or a primary-electron beam excites photo- or secondary electrons the SP of which is measured in the detector. Alternatively, a spin-polarized primary electron beam can be scattered elastically or inelastically from the sample and the spin dependence of the absorbed or scattered current can be measured. The stray field H(x) is parallel or antiparallel to the surface magnetization and must be kept minimal.

shows the experimental setup. The horse-shoe electromagnet generates a magnetic field which aligns the Weiss domains in the sample. Symmetry shows that H(x) in the middle of the sample at the point of incidence of the primary electron or photon beam must be parallel or antiparallel to the magnetization M. It is assumed that the sample is magnetically homogeneous and has an atomically flat surface. The effect of the Lorentz force is readily estimated by assuming H(x) = const for 0 5 x 5 d, and H(x) = 0 for x > d. Figure 54 shows a cross section perpendicular to the plane of Fig. 53 through the point of incidence of the primary beam. In elastic electron scattering, the incident and scattered beam are shifted by 22. This showsthat spin -orbit coupling can contribute to exchange scattering even when the primary beam is polarized in the scattering plane of Fig. 53 and even when the crystal has mirror symmetry about this scattering plane. Namely, the spin is then perpendicular to the plane of Fig. 54, and H(x) produces a deflectionthat introduceseffects of 1s coupling. Careful analysis of SPLEED

IN CTRON EAM OUT

FIG.54. Effect of a stray field H(x) = const for 0 5 x 5 don the path of electrons scattered elastically from the sample. Plane of drawing is perpendicular to that of Fig. 54; R is the curvature of the electron path in H(x).

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data is necessary, since H(x) changes sign with M, and the effects of 1s coupling may look like the effects of exchange scattering. In photoemission or secondary emission, the slow electrons that emerged in the direction of the surface normal will reach the detector at an angle (b. For small 4 one obtains 22 = d2/Rand (b = d/R, where R is the curvature of the electron path in H(x) = const. Measurements with a Hall probe showed H(x) = H,exp(-x/d). With very high susceptibilitymaterials such as well-annealed single-crystalline Fe or Ni magnetized in the easy direction, one finds 22 = 1 mm and (b = 20" just at the point of magnetic saturation for electrons of 0.1 eV kinetic energy (69). Electrons emitted off surface normal experience a larger deflection since they travel a longer distance in the region where H(x) persists. This shows that angular resolved measurements with electron energies below 1 eV are difficult. In summary, we see that (1) Generally, only high x materials can be used, since only those materials are effective in screening the dipole field of the electromagnet. (2) The coercivity and remanence observed in the configuration of Fig. 54 may have contributions caused by the electromagnet and the gap between the sample and the electromagnet. (3) Picture-frame single crystals such as those used in Ref. (72) are ideal because they yield minimum H(x) and unperturbed hysteresis loops.

As an example, Fig. 55 shows surface-magnetization curves taken by elastic electron scattering on a continuous loop of Fe8,.5B,4,,Si,magnetic

-2

t

-100

-50

0

50

100

H (mOe)

FIG.5 5 . Surface hysteresis curves measured on Fe81,5B14,5Si4 by the spin dependence (%) of the elastic backscattering of 110 eV electrons. The upper curve is for an ion-bombarded surface with the bulk composition and some additional C, and the lower curve after annealing this surface to 120°C for 1 min [from Ref. (220)].

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glass ribbon according to Ref. (220). The open ends were mechanically clamped, and insulated wire was wrapped loosely around the ribbon to provide the magnetic field. The electron energy was 110 eV, yielding a probing depth of -3 A. The surface composition was monitored by Auger spectroscopy. Most of the oxide is removed from the surface by Ar-ion bombardment. The surface composition is approximately that of the bulk plus some residual C, and yields the upper hysteresis loop. Mild annealing to 120°C for 1 min yields the lower square hysteresis without changing the surface composition. We see that the magnetic properties are altered dramatically in this very mild heat treatment, demonstrating the power of surface magnetic measurements for detection of probably minute structural changes. Hysteresis curves have also been measured by using the magnetooptic Kerr effect having a probing depth of - 150 A. The optical measurement, however, could not detect any changes of the hysteresis loops on heating to 1 10"C, and square loops such as the lower curve in Fig. 56 have been obtained for all surfaces even before ion bombardment. The surface hysteresis loop of the well-annealed sample, although generally quite square, still exhibits rounded edges. This shows that surface magnetization reverses gradually as the external field is reversed. Bulk hysteresis loops of soft magnetic materials are known to exhibit sharp edges (221).The round edge displayed in the surface hysteresis loop may indicate that the magnetization reversal nucleates at the surface, as has been postulated theoretically (222). Whereas the reversal of M starts gradually when the applied field approaches the coercive field, the reversed saturation magnetization is reached instantaneously with the annealed sample. This shows that the applied field lies in the easy direction parallel to the direction of melt spinning. For the freshly bombarded sample however, no such easy direction seems to exist in the surface, since the magnetization reaches the reversed state only gradually. The greatest promise of polarized-electron techniques lies in the possibility of viewing magnetic domains with unprecedented resolution. For instance, a primary-electron beam may be focused into a spot having a diameter of 10 nm, and the spin dependence of the absorbed current or the SP of the secondary electrons may then be used to detect small magnetic bubbles (223) or even the variation of magnetization across a domain wall and its various dynamic responses to external disturbances. If the sample is in the demagnetized state, the stray magnetic field is at minimum. Furthermore, the small size of the magnetic domains of typically 1 pm automatically leads to a significant reduction of H(x), since it is proportional to the magnetic dipole moment produced by the saturated sample. This is why electron spectroscopies have been performed on demagnetized or very thin

-

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(1 72) ferromagneticmaterials without any difficulty.Hence a primary beam

of photons or electrons focused into a spot of diameter smaller than the diameter of the Weiss domains represents the ideal way to measure magnetization with polarized-electron techniques. It is much superior, at least in principle, to Lorentz microscopy or even electron holography (224) for viewing magnetic domains.

X. CONCLUSION The reader is perhaps surprised at the rich variety of spin-dependent phenomena in various areas of solid-state and surface physics. In fact 15 years ago, no one would have predicted this many-sidedness. Spin-polarized electrons seemed an elusive rarity, and the effects of exchange and spinorbit coupling appeared to be a small, mostly negligible correction to the dominant effects produced by the Coulomb field of the electrons. It was a common belief in the 1930s that the effects of spin-orbit coupling could be neglected with slow electrons, since this term decreases with v/c. Furthermore, theoretical arguments seemed to show that the scatteringof electrons on the periodic potential of a crystal is independent of spin state even at high electron energies. Both suggestions proved erroneous. First, at energiesbelow a few keV, there are marked diffraction effects in the scattering of electrons from an atom. At certain scattering angles, the interference may be destructive for one spin state but constructive for the other. This produces large spin dependences despite a relatively small spin - orbit interaction. Second, if the periodic potential in a solid is approximated by the long-wavelength terms of the Fourier expansion, one loses sight of precisely those terms that produce spin -orbit coupling, namely, the terms with a high gradient of the electric field. Such computational restrictions, of course, do not exist any more. The exchange interaction, on the other hand, was believed difficult to observe with electron-beam techniques because it has been anticipated to decrease rapidly with increasing electron energy. The notable exception was Marller scattering in which spin-polarized electrons from the p decay of a nucleus are scattered on magnetized iron. However, the spin asymmetry is small because the scattering occurs on all the 26 electrons of the Fe atom of which only two are spin polarized, yielding an average electron SP in the Fe target of only 8%. However, with present-day electron spectroscopies, one has angle and energy resolution, and one can tune in to specific and sometimes resonant excitations. This technical progress and the much

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improved spin sensitivity achievable with spin-modulated electron-beam sources makes the effects of exchange readily accessible to experimental investigation over a large range of energies. Furthermore, conservation of electron spin polarization in optical excitations establishes spectroscopy of photoemitted electrons as an ideal tool for studying the effects of exchange and spin - orbit interactions on the electron states within the solid. In the field of itinerant magnetism, the exchange splitting between spin-up and spin-down subbands has been determined by spin-polarized photoemission. The role of many-body effects in modifying the one-particle band structure of nickel has been quantitatively ascertained. Scattering of spin-polarized electron beams on well-defined surfaces has permitted accurate observation of the surface-layer magnetization and its temperature dependence. In systems with localized magnetic moments, spin-polarizedphotoemission detects the multiplets generated by the magnetic levels even in very complex cases. It is a differential technique in which the multiplets of one magnetic ion in two different lattice sites can be compared with high precision. Spin-polarizedphotoemission is also unique because it allows one to measure the magnetization of states of p, d, or f parentage separately, due to the characteristic photon-energy dependence of the emission intensity, even if these states are degenerate in energy. Nonmagnetic solids may emit spin-polarizedelectrons if irradiated with circularly polarized light. Transitions from spin - orbit split initial-state bands to a single final-stateband produce opposite SP of the photoelectrons. Hence, spin-orbit splittings may be determined even in cases where conventional spectroscopy is no longer able to resolve the transitions due to inherent broadening effects. An additional unique feature of this application is that it provides direct information on the hybridization of electronic bands. In most cases, it is directly evident from the sign of the observed SP which subband is admixed. The SP obtained in photoemission with circularly polarized light is a consequence of symmetry, independent of all the hazardous assumptions entering the determination of the electronic band structure. Exciting prospects for this technique arise therefore in the study of lattice disorder. The elastic scattering of electrons from solid surfaces is spin dependent as a result of spin - orbit coupling and/or the exchange interaction in the case of magnetically ordered solids. The effects of spin-orbit coupling can be very large with surfaces containing heavy atoms such as W or Au; however, with lighter atoms, e.g., Ni, it is also readily observed. The accuracy with which surface structure parameterscan be determined is greatly improved if the SP produced by spin-orbit coupling is taken into account. To fully

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exploit SPLEED (spin-polarized low-energy electron diffraction) for surface-structure analysis, one makes use of the properties of the axial SP or asymmetry vector under symmetry operations such as rotation, reflection, and time reversal. The spin dependence of elastic electron scattering from magnetized surfaces is of the order of only lo-*; yet this can easily be measured by using the spin-modulated beam from a GaAs source. This technique yields detailed determination of magnetic surface structures, analogous to the use of neutrons for measuring bulk magnetic structures. Inelastic scattering of electrons from a solid surface is also spin dependent no matter whether the surface is magnetic or not. The measurement of the SP of secondary electrons produced in an electron - electron collision allows one to probe directly the screened electron - electron interaction in solids, via the transfer of SP by the quantum mechanical exchange of electrons in the collision. Ultimately, one may obtain the singlet and triplet scattering amplitudes separately. Electrons produced in the decay of a spin-polarized core hole via Auger transitions show SP carrying important information about the detailed mechanism of decay or magnetism or both in alloys. Magnetism at the surface is the finest sensor of the chemical state. The various spin-polarizedelectron-beam techniques promise to become practical tools in surface magnetochemistryas, e.g., in the study ofsegregationand oxidation, and in distinguishing adsorbates with a paramagnetic moment from the diamagnetic ones. Chemicals can induce ferromagnetism at a metallic surface depending on their specific position above or below the first layer, or they can demagnetize a previously magnetic surface. Surface magnetization curves are obtained with the external magnetic field applied parallel or perpendicular to the surface. The latter enables one to study even very hard magnetic materials and to force antiferromagnetic and paramagnetic moments into the field direction. Surface magnetization curves respond, for example, to minute structural changes in the surface undetectable by any other technique. Magnetic domains can be viewed with unprecedented resolution. For instance, a primary unpolarized electron beam may be focused into a spot of 100 A, and the very high SP of the emerging low-energy cascade electrons may be employed to determine the magnetization direction. At present, we are still mostly in the era of vacuum-beam techniques where electrons have to escape, at one point or another in the experiment, over the surface barrier into the vacuum. The necessity of a vacuum may be overcome in the future by the development of practical integrated solid-state sources and detectors of SP. Therefore, we predict further rapid expansion of this field.

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REFERENCES 1. D. E. Eastman, J. Appl. Phys. 40, 1387 (1969). 2. U. Enninger, G. Busch, M. Campagna, and H. C. Siegmann, Phys. Rev. Lett. 25,585 ( 1970). 3. E. Kisker, W. Gudat, E. Kuhlmann, R. Clauberg, and M. Campagna, Phys. Rev. Lett. 45, 2053 (1980). 4. E. Garwin, D. T. Pierce, and H. C. Siegmann, Helv. Phys. Actu 47, 343 (1974); D. T. Pierce, F. Meier, and P. Zurcher, Appl. Phys. Lett. 26, 670 (1975). 5. H. C. Siegmann, Europhys. News 14, 2 (1983). 6. D. T. Pierce and R. Celotta, J. Vuc. Sci. Technol. At, 1 1 19 (1983). 7. S. F. Alvarado, W. Eib, F. Meier, H. C. Siegmann, and P. Zurcher, in “Photoemission and the Electronic Properties of Surfaces” (B. Feuerbacher, B. Fitton, and R. F. Willis, eds.), Chapter 18. Wiley, New York, 1978. 8. D. T. Pierce and R. J. Celotta, Adv. Electron. Electron Phys. 56, 219 (1981). 9. R. Feder, J. Phys. C 14, 2049 (1981). 10. J. Kessler, “Polarized Electrons.” Springer-Verlag, Berlin and New York, 1976. 11. P. S. Farago, Adv. Electron. Electron Phys. 21, 1 (1965). 12. K. Jost and J. Kessler, Z. Phys. 195, 1 (1966). 13. U. Heinzmann, J. Kessler, and J. Lorenz, Z. Phys. 240, 42 (1970). 14. R. L. Long, Jr., W. Raith, and V. W. Hughes, Phys. Rev. Lett. 15, I (1965). 15. M. V. McCusker, L. L. Hatfield, and G. K. Walkers, Phys. Rev. Lett. 22, 817 (1969). 16. P. Lambropoulos, Phys. Rev. Lett. 30, 413 (1973). 17. N. Muller, W. Eckstein, W. Heiland, and W. Zinn, Phys. Rev. Lett. 29, 165 1 (1972). 18. E. Garwin, F. Meier, D. T. Pierce, K. Sattler, and H. C. Siegmann, Nucl. Instrum. Methods 120,483 (1974). 19. M. R. ONeill, M. Kalisvaart, F. B. Dunning, and G. K. Walters, Phys. Rev. Lett. 34, 1 167 (1975). 20. J. Kirschner, R. Feder, and J. F. Wendelken, Phys. Rev. Lett. 47,614 (1981). 21. M. S. Lubell, At. Phys. 5, 325 (1977). 22. D. T. Pierce, F. Meier, and P. Zurcher, Phys. Lett. A 51,465 (1975); D. T. Pierce and F. Meier, Phys. Rev. B 13, 5484 (1976). 23. R. C. Eden, J. L. Moll, and W. E. Spicer, Phys. Rev. Lett. 18, 579 (1967). 24. D. Conrath, T. Heindorff, A. Hermani, N. Ludwig, and E. Reichert, Appl. Phys. 20, 155 (1979); E. Reichert and K. Zahringer, Appl. Phys. A 29, 191 (1982); J. Kirschner, H. P. Depen, and H. Ibach, Appl. Phys. A 30, 177 (1983). 25. S. F. Alvarado, F. Ciccacci, and M. Campagna, Appl. Phys. Lett. 39,6 15 ( 198 I). 26. D. T. Pierce, R. J. Celotta, G.-C. Wang, W. N. Unertl, A. Galejs, C. E. Kuyatt, and S . R. Mielczarek, Rev. Sci. Instrum. 51,478 (1980). 27. M. Erbudak and B. Reihl, Appl. Phys. Lett. 33, 584 (1978). 28. B. Reihl, M. Erbudak, and D. M. Campbell, Phys. Rev. B: Condens. Mutter 19, 6358 ( I 979). 29. N. F. Mott, Proc. R. Soc. London, Ser. A 135,429 (1932). 30. N. Sherman, Phys. Rev. 103, 1601 (1956). 31. W. Eckstein, IPP Rep. 7/1. Institut fur Plasmaphysik, Garching, 1970. 32. H. F. Schopper, “Weak Interactions and Nuclear Beta Decay.” North-Holland Publ., Amsterdam, 1966. 33. H. Deichsel, Z. Phys. 164, 156(1961). 34. K. Jost, F. Kaussen, and J. Kessler, J. Phys. E 14, 735 (1981).

94 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51.

52. 53. 54.

55.

56. 57. 58. 59.

60. 61. 62. 63. 64. 65. 66.

H. C. SIEGMANN et al. J. Kirschner and R. Feder, Phy. Rev. Lett. 42, 1008 (1979). P. S. Farago and J. Wykes, J. Phys. B 2,747 (1969). M. Erbudak and N. Miiller, Appl. Phys. Lett. 38, 575 (1981). R. J. Celotta, D. T. Pierce, H. C. Siegmann, and J. Unguris, Appl. Phys. Lett. 38, 577 (I98 1). M. Erbudak and G. Ravano, J. Appl. Phys. 52,5032 (1981). H. C. Siegmann, D. T. Pierce, and R. J. Celotta, Phys. Rev. Lett. 46, 452 (1981). G. Ravano and M. Erbudak, Proc. J. Actinides, Ilth, p. 242 (1982). D. T. Pierce, M. S. Girvin, J. Unguris, and R. J. Celotta, Rev. Sci. Instrum. 52, 1437 (1981). M. Erbudak, G. Ravano, and N. Miiller, Phys. Lett. A 90,62 (1982). C. Rau, Comments Solid State Phys. 9, 177 (1980). R. Meservey, P. M. Tedrow, and V. R. Kalvey, Solid State Commun. 36,969 (1980), and references cited therein. D. R. Scifres, B. A. Huberman, R. M. White, and R. S. Bauer, Solid State Commun. 13, 1615 (1973). H. C. Siegmann, F. Sanches-Sinencio,and J. S. Helman, Bull. Am. Phys. Soc. [2] 18,553 (1973). N. d’Ambrumeni1 and R. M. White, J. Appl. Phys. 53,2052 (1982). C. S. Wang and J. Callaway, Phys. Rev. B: Solid State 15, 298 (1977); J. Callaway and C. S. Wang, ibid. 16,2095 (1977);V. L. Moruzzi, J. F. Janak, and A. R. Williams, “Calc. Electronic Properties of Metals.” Pergamon, Oxford, 1978. C. S. Wang, R. E. Prange, and V. Korenman, Phys. Rev. B: Condens. Matter 25, 5766 (1982), and references cited therein. L. A. Feldkamp and L. C. Davis, Phys. Rev. B: Condens. Matter 22, 3644 (1980). A. Liebsch, Phys. Rev. Lett. 43, 1431 (1979); Phys. Rev. B: Condens. Matter 23, 5203 (1981). G. Treglia, F. Ducastelle, and D. Spanjaard, Phys. Rev. B: Condens. Matter 21, 3729 (1980); 22,6472 (1980). D. E. Eastman, F. J. Himpsel, and J. A. Knapp, Phys. Rev. Lett. 40, 1514 (1978); F. J. Himpsel, J. A. Knapp, and D. E. Eastman, Phys. Rev. B: Condens. Matter 19, 2919 (1979); D. E. Eastman, F. J. Himpsel, and J. A. Knapp, Phys. Rev. Lett. 44,95 (1979). C. J. Maetz, U. Gerhardt, R. E. Dietz, A. Ziegler, and R. J. Jeliotto, Phys. Rev. Lett. 48, 1686 (1982). W. Eib and S. F. Alvarado, Phys. Rev. Lett. 37,444 (1976). E. Kisker, W. Gudat, M. Campagna, E. Kuhlmann, H. Hopster, and I. P. Moore, Phys. Rev. Lett. 43, 966 (1979). W. Gudat, E. Kisker, E. Kuhlmann, and M. Campagna, Phys. Rev. B: Condens. Matter 22,3282 (1980). E. P. Wohlfarth, Phys. Lett. A 36, 131 (1971); Phys. Rev. Lett. 38, 524 (1977). I. D. Moore and J. B. Pendry, J. Phys. C 11,46 15 ( 1978). L. Kleinmann, Comments Solid State Phys. 10, 29 (1981). J. Unguris, A. Seiler, R. J. Celotta, D. T. Pierce, P. D. Johnson, and N. V. Smith, Phys. Rev. Lett. 49, 1047 (1982). D. R. Penn, Phys. Rev. Lett. 42,921 (1979). C. Guillot, Y . Ballu, J. Paignt, J. Lecante, K. P. Jain, P. Thiry, R. Pinchaux, Y. Petroff, and L. M. Falicov, Phys. Rev. Lett. 39, 1632 (1977). L. A. Feldkamp and L. C. Davis, Phys. Rev. Lett. 43, 151 (1979). R. Clauberg, W. Gudat, E. Kisker, E. Kuhlmann, and G. M. Rothberg, Phys. Rev. Lett. 47, 1314 (1981).

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

95

67. D. L. Mills and A. A. Maradudin, J. Phys. Chem. Solids 28, 1855 (1967); D. L. Mills,

Comments Solid State Phys. 4,28 (197 1); 4, 95 (1972).

68. D. L. Mills, in “Surface Excitations” (V. M. Agramovich and R. Loiidon, eds.). NorthHolland Publ., Amsterdam (in press). 69. D. T. Pierce, R. J. Celotta, J. Unguris, and H. C. Siegmann, Phys. Rev. B: Condens.

Matter 26,2566 (1982).

70. K. Binder and P. C. Hohenberg, IEEE Trans. Magn. MAG-l2,66 (1976). 71. H. W. Diel and S. Dietrich, Z. Phys. B 42, 65 (1 98 1). 72. S. F. Alvarado, M. Campagna, and H. Hopster, Phys. Rev. Lett. 48,5 1, 1768 (1982). 73. S. F. Alvarado, M. Campagna, F. Ciccacci, and H. Hopster, J. 1ntermagn.-MMM Conf, 3rd, 1982 (1982). 74. H. W. Diel and S. Dietrich, Phys. Lett. A 80,408 (1980). 75. D. M. Edwards, Nato Adv. Stud. Inst. Ser., Ser. B 42,283 (1979). 76. P. Heimann, H. Neddermeyer, and M. Pessa, J. Magn. Magn. Muter. 7, 107 (1978). 77. P. J. Durham, J. Phys. F11,2475 (1981). 78. M. Landolt, P. Niedermann, and D. Mauri, Phys. Rev. Lett. 48, 1632 (1982). 79. H. Hasegawa and J. Kanamori, J. Phys. SOC. Jpn. 31,382 (1971); 33, 1599 (1972). 80. J. Kaspar and D. R. Salahub, Phys. Rev. Lett. 47, 54 (1981). 81. A. R. Williams, V. L. Moruzzi, C. D. Gelatt, Jr., J. Kubler, and K. Schwarz,J.Appl. Phys.

53,2019 (1982). H. C. Siegmann, Phys. Rep. C 17,38 (1975). D. E. Eastman, F. Holtzberg, and S. Methfessel, Phys. Rev. Lett. 23, 226 (1969). K. Sattler and H. C. Siegmann, Phys. Rev. Lett. 29, 1565 (1972). J. S. Helman and H. C. Siegmann, Solid State Commun. 13, 89 1 (1973). D. E. Eastman, Phys. Rev. B: Solid State 8,6027 (1973). D. L. Mills, Phys. Rev. B: Solid State 3,3887 (197 1). F. Meier, P. Ziircher, and E. Kaldis, Phys. Rev. B: Condens. Matter 19,4570 (1979). F. Meier, J. Phys. CoNoq. C(Orsay, Fr.) 5, 5 (1980). D. T. Vigren, Phys. Rev. Lett. 41, 197 (1978); F. Meier, Phys. Rev. B: SolidState 15,4537 (1977). 91. S. F. Alvarado, M. Erbudak, F. Meier, and H. C. Siegmann, Phys. Rev. Lett. 39, 219 (1977). 92. J. Hubbard, Proc. R. SOC.London, Ser. A 276,238 (1963). 93. S. Hufner and G. K. Wertheim, Phys. Rev. B: Solid State 8,4857 (1973). 94. D. E. Eastman and J. L. Freeouf, Phys. Rev. Lett. 34, 395 (1975), and references cited therein. 95. P. S. Bagus, C. R. Brundle, T. J. Chuang, and K. Wandelt, Phys. Rev. Lett. 39, 1229 (1977), and references cited therein. 96. S. Sugano, Y. Tanabe, and H. Kamimura, “Multiplets of Transition Metal Ions in Crystals.” Academic Press, New York, 1970. 97. S. F. Alvarado, W. Eib, F. Meier, D. T. Pierce, K. Sattler, H. C. Siegmann, and J. P. Remeika, Phys. Rev. Lett. 34, 319 (1975); S. F. Alvarado, M. Erbudak, and P. Munz, Phys. Rev. B: Solid State 14,2740 (1976). 98. S. F. Alvarado, W. Eib, H. C. Siegmann, and J. P. Remeika, Phys. Rev. Lett. 35, 860 (1975). 99. S. F. Alvarado, F. Meier, and W. Tolksdorf, Solid State Commun. 28, 107 (1978). 100. S. F. Alvarado, W. Eib, H. C. Siegmann, and J. P. Remeika, J. Magn. Magn. Muter. 3, 121 (1976). 101. A. Schlegel, S. F. Alvarado, and P. Wachter, J. Phys. C 12, 1157 (1979). 102. M. Erbudak, F. Meier, Physica B (Amsterdam)102, 134 (1980), and references therein. 82. 83. 84. 85. 86. 87. 88. 89. 90.

96

H. C. SIEGMANN et al

103. Y. Baer, Physica B (Amsterdam) 102, 104 (1980). 104. J. Brunner, M. Erbudak, and F. Hulliger, Solid State Commun. 38, 841 (1981). 105. F. Greuter, W. Eib, M. Erbudak, F. Meier, and B. Reihl, J. AppI. Phys. 50,7483 (1979).

106. W. Eib, M. Erbudak, F. Greuter, and B. Reihl, Phys. Lett. A 68,391 (1978). 107. M. Erbudak and J. Keller, Z. Phys. B32,281 (1979). 108. M. Erbudak and J. Keller, Phys. Rev. Lett. 42, 115 (1979). 109. P. Weinberger, Ber. Bunsenges. Phys. Chem. 81, 804 (1977). 110. E. C. Snow and J. T. Waber, Acta Metall. 17,623 (1963). 111. M. Erbudak, F. Meier, and D. Pescia, Phys. Lett. A 83, 449 (1981). 112. G . F. Koster, J. 0.Dimmok, R. G. Wheeler, and H. Statz, “Properties ofthe Thirty-two Point Groups.” MIT Press, Cambridge, Massachusetts, 1963. 113. M. Wohlecke and G. Borstel, Phys. Rev. B: Condens. Matter 23, 980 (1981); 24, 2857, 2321 (1981). 114. T.-C. Chiang, J. A. Knapp, M. Aono, and D. E. Eastman, Phys. Rev. B: Condens.Matter 21, 35 13 ( 1 980). 115. F. Meier and D. Pescia, Phys. Rev. Left.47, 374 (1981). 116. N. E. Christensen, Solid State Cornrnun.37,57 (198 1); R. Laser, N. V. Smith, and R. L. Bembow, Phys. Rev. B: Condens. Matter 24, 1895 (1982);P. Heimann, H. Miosga, and H. Neddermeyer, Solid State Commun. 29,463 (1979);R. Rosei, R. Liisser, N. V. Smith, and R. L. Benbow, ibid. 35,979 (1980). 117. N. E. Christensen and B. Seraphin, Phys. Rev. B: Solid State 4, 332 1 (197 1). 118. P. Ziircher, F. Meier, and N. E. Christensen, Phys. Rev. Lett. 43,54 ( 1 979). 119. N. E. Christensen and B. Feuerbacher, Phys. Rev. B: Solid State 10,2349 (1974). 120. J. Reyes and J. S. Helman, Phys. Rev. B: Solid State 16,4283 (1977). 121. D. Pescia and F. Meier, Surf Sci. 117, 302 (1982). 122. R. Allenspach, F. Meier, and D. Pescia, unpublished. 123. R. Allenspach, Diplomarbeit ETH Zurich (1982) (unpublished). 124. C. K. Sinclair, E. L. Gamin, R. H. Miller, and C. Y. Prescott, AZP Conf:Proc. 35, 424 (1976); M. Campagna and S. F. Alvarado, Int. Symp. High Energy Spin Physics, 5th, 1982 (in press). 125. U. Kaufmann and J. Schneider,Adv. Solid State Phys. 14,229 (1974). 126. J. L. Shay and J. H. Wernick, “Ternary Chalcopyrite Semiconductors: Growth, Electronic Properties, and Applications.” Pergamon, Oxford, 1975. 127. P. Zurcher and F. Meier, J. Appl. Phys. 50, 3687 (1979). 128. D. Weaire and M. F. Thorpe, Phys. Rev. B: Solid State 4,2508 (1971). 129. J. Perenboom, P. Wyder, and F. Meier, Phys. Rep. 78, 175 (1981). 130. W. Eckstein, Z. Phys. 203, 59 (1967); R. Loth, ibid. p. 66. 131. M. R. ONeill, M. Kalisvaart, F. B. Dunning, andG. K. Walters, Phys. Rev. Lett. 34, 1167 (1975). 132. N. Muller and D. Wolf, Bull. Am. Phys. SOC.[2] 21, 944 (1976). 133. N. Miiller, Rep. 9/23. MPI fur Plasmaphysik, Garching, 1979. 134. R. Feder, Surf Sci. 63,283 (1977). 135. D. G. Fedak and N. A. Gjostein, Acta Metall. 15, 827 (1967); Surf Sci. 8,77 (1967). 136. R. Feder, N. Miiller, and D. Wolf, Z. Phys. B 28,265 (1977). 137. N. Miiller, D. Wolf, and R. Feder, Con$ Ser.-Int. Phys. 41,281 (1978). 138. M. Kalisvaart, M. R. ONeill, T. W. Riddle, F. B. Dunning, and G. K. Walters, Phys. Rev. B: Solid State 17, 1570 (1978). 139. P. Bauer, R. Feder, and N. Miiller, Surf Sci. 99, L395 (1980). 140. R. Feder, H. Pleyer, P. Bauer, and N. Muller, Surf Sci. 109,419 (1981). 141. S. F. Alvarado, H. Hopster, R. Feder, and H. Pleyer, Solid,State Commun. 39, 1319 (1981).

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

97

142. M. Erbudak and N. Miiller, unpublished. 143. J. Kirschner and R. Feder, Surf Sci. 104,448 (198 1). 144. R. Feder, Phys. Lett. A 78, 103 (1980). 145. B. I. Dunlap, Solid State Commun. 35, 141 (1980). 146. N. Miiller, M. Erbudak, and D. Wolf, Solid State Commun. 39, 1247 (1981). 147. N. Miiller and M. Erbudak, unpublished. 148. P. Bauer, Rep. 9/34. MPI fur Plasmaphysik, Garching, 1980. 149. P. Bauer, R. Feder, and N. Miiller, Solid State Commun. 36,249 (1980). 150. T. W. Riddle, A. H. Mahan, F. B. Dunning, and G. K. Walters, Surf Sci. 82,5 I 1 1979). 151. T. W. Riddle, A. H. Mahan, F. B. Dunning, and G. K. Walters, Sur$ Sci. 82,5 17 1979). 152. A. H. Mahan, T. W. Riddle, F. B. Dunning, and G. K. Walters, Surf Sci. 93,550 1980). 153. G.-C. Wang, J. Unguris, D. T. Pierce, and R. J. Celotta, Surf Sci. 114, L35 (191 !). 154. R. Frisch and 0. Stern, Z. Phys. 84,430 (1933); R. Frisch, ibid. p. 443. 155. S. Kikuchi and S. Nakagawa, Sci. Pap. Inst. Phys. Chem. Res. (Jpn.) 21,256 (1933). 156. K. Hirabayashi, J. Phys. SOC.Jpn. 25, 856 (1968). 157. E. G. McRae, J. Chem. Phys. 45, 3258 (1966). 158. J. I. Gersten and E. G. McRae, Surf Sci. 29, 483 (1972). 159. E. G. McRae, Rev. Mod. Phys. 51, 541 (1979), and references therein. 160. R. E. Dietz, E. G. McRae, and R. L. Campbell, Phys. Rev. Lett. 45, 1280 (1980). 161. J. A. Appelbaum and D. R. Hamann, Phys. Rev. B: Solid State 6, 1122 (1972). 162. D. T. Pierce, R. J. Celotta, G.-C. Wang, and E. G. McRae, SolidStateComrnun. 39, 1053

(1981).

163. E. G. McRae, D. T. Pierce, G.-C. Wang, and R. J. Celotta, Phys. Rev. B 24,4230 (198 I). 164. P. J. Jennings and R. 0. Jones, Solid State Commun. 44, 17 (1982). 165. R. J. Celotta, D. T. Pierce, G.-C. Wang, S. D. Bader, and G. P. Felcher, Phys. Rev. Lett.

43,728 (1979).

166. J. S. Schilling and M. B. Webb, Phys. Rev. B 2, 1665 (1970). 167. D. T. Pierce, R. Celotta, and J. Unguris, J. Magn. Magn. Muter. 35, 30 (1983). 168. R. W. Rendell and D. R. Penn, Phys. Rev. Lett. 45,2057 (1980). 169. S. W. Wang, Bull. Am. Phys. SOC.[2] 27, 147 (1982).

170. R. K. Nesbet, private communication. 171. G. D. Fletcher, M. J. Alguard, T. J. Gay, V. W. Hughes, C. W. Tu, P. F. Wainwright, M. S. Lubell, W. Raith, andF. C. Tang, Phys. Rev. Lett. 48, 1671 (1982). 172. G. Waller and U. Gradmann, Phys. Rev. B Condensed Matter 26,6330 (1982). 173. R. Feder and H. Pleyer, Surf Sci. 117,285 (1982). 174. R. Feder, S. F. Alvarado, E. Tamura, and E. Kisker, Surface Sci. 127, 83 (1983). 175. See R. Feder in Ref. 9 176. Y. Baer and R. Monnier, Bull. Am. Phys. SOC.[2] 25,237 (1980). 177. J. K. Lang,Y. Baer,andP. A.Cox, J. Phys. F l l , 121 (1981). 178. D. Mauri and M. Landolt, Phys. Rev. Lett. 47, 1322 (1981). 179. B. N. Harmon and A. J. Freeman, Phys. Rev. B Solid State 10, 1979 (1974). The binding energy has been scaled by a factor 2.2 to fit XPS-data from Ref. 177. 180. M. Rosler and W. Brauer, Phys. Status Solidi B 104, 161, 575 (1981). 181. H. W. Streitwolf, Ann. Phys. (Leipzig) [7] 3, 183 (1959). 182. H. Puff, Phys. Status Solidi 2, 1699 (1962). 183. P. A. Wolff, Phys. Rev. 92, 18 (1953). 184. G. Ravano, M. Erbudak, and H. C. Siegmann, Phys. Rev. Lett. 49, 80 (1982); ibid., 50, 1022 (1983). 185. M. Erbudak and G. Ravano, Phys. Lett. A 91,367 (1982). 186. M. Fink and A. C. Yates, Tech. Rep. 88. Plasma and Quantum Electronics Lab., University of Texas, Austin, 1970.

98

H. C. SIEGMANN et al.

187. G. Ravano and M. Erbudak, Solid State Commun. 44,547 (1982). 188. A. M. Bincer, Phys. Rev. 107, 1434 (1957). Later theoretical work by D. R. Penn [Phys.

Rev. B: Condens. Matter 22, 2677 (198O)l has used different approximations of the screening function in the electron-electron scattering. 189. J. Unguris, D. T. Pierce, A. Galejs, and R. J. Celotta, Phys. Rev. Lett. 49,72 (1982). 190. D. Mauri and M. Landolt, Bull. Am. Phys. SOC.28,298 (1 983). 191. E. Kisker, W. Gudat, and K. Schriider, Solid State Commun. (to be published). 192. H. Hopster, R. Raue, E. Kisker, G. Guntherodt, and M. Campagna, Phys. Rev. Lett. 50, 70 ( 1983). 193. For a review see J. C. Fuggle, in “Electron Spectroscopy” (C. R. Brundle and A. D. Baker, eds.), Vol. 4, p. 85. Academic Press, New York, 1981. 194. M. Landolt and D. Mauri, Phys. Rev. Lett. 49, 1783 (1982). 195. L. Schlapbach, A. Seiler, F. Stucki, and H. C. Siegmann, J. Less-Common Met. 73, 193 (1980). 196. A. Seiler, P. Zurcher, M. Landolt, and L. Schlapbach, Vide, Couches Minces 201, Supp., 1064 (1980). 197. M. Landolt, F. Meier, P. Zurcher, H. Oesterreicher,K. Ensselen,J. Hoenigschmid,and E. Bucher, Solid State Commun. 32, 1009 (1979). 198. G. Busch, M. Campagna, and H. C. Siegmann,Phys. Rev. B: SolidState4,746 (197 I); W. Eib and B. Reihl, Phys. Rev. Lett. 40, 1674 (1978). 199. A. Seiler, L. Schlapbach, and H. R. Scherrer, SUP$Sci. 121,98 (1982). 200. F. Meier, D. Pescia, and T. Schriber, Phys. Rev. Lett. 48,645 (1982). 201. J. C. Peruchetti, G. Gewinner, and A. Jaegle, SUP$Sci. 88,479 (1979). 202. C. Rau and S. Eicher, Phys. Rev. Lett. 47,939 (1981). 203. B. Feuerbacher, B. Fitton, and R. F. Willis, in “Photoemission and the Electronic Properties of Surfaces” (B. Feuerbacher, B. Fitton, and R. F. Willis, eds.), Wiley, New York. Chapter 1, Fig. 1.7. 204. G. Allan, Su$ Sci. 74, 79 (1978); G. Allan, Phys. Rev. B: Condens. Matter 19, 4774 (1979); D. M. Edwards, in “Trends in Physics” (M. M. Wolfson, ed.), pp. 150ff. Adam Hilger, Ltd., Bristol, 1979. 205. A. J. Freeman, private communication. 206. H. Akoh and A. Tasaki, J. Phys. SOC.Jpn. 42,791 (1977). 207. M. Landolt and M. Campagna, Phys. Rev. Lett. 39,568 ( I 977). 208. M. Landolt, Y. Yafet, B. Wilkens, and M. Campagna, Solid State Commun. 25, 1141 (1978). 209. R. E. Dietz and P. A. Selwood, J. Chem. Phys. 35,270 (1 96 1). 210. L. Schlapbach,J. Phys. F 10,2477 (1980). 211. G. W. Gobeli, F. G. Allen, and E. 0. Kane, Phys. Rev. Lett. 12,94 (1964). 212. F. Meier, D. Pescia, and M. Baumberger, Phys. Rev. Lett. 49,747 (1982). 213. D. T. Pierce, C. E. Kuyatt, and R. J. Celotta, Rev. Sci. Znstrum. 50, 1467 (1979). 214. M. Campagna, D. T. Pierce, and H. C. Siegmann, in “Disordered Solids” (J. Stuke and W. Brenig, eds.), Vol. 2, p. 1379. Taylor & Francis, London (1974). 215. G. Busch, M. Campagna, and H. C. Siegmann, Znt. J. Magn. 4,25 (1973). 216. S. F. Alvarado, H. C. Siegmann, and M. Campagna, Ned. Tijdschr. Vacuumtech. 16 (2-4), 102 (1978). 21 7. S. F. Alvarado, Z. Phys. B 33, 5 1 (1979). 218. K. Sattler and H. C. Siegmann, Z. Phys. B 20,289 (1975). 219. D. Pescia, M. Erbudak, F. Meier, and 0. Vogt, Vide, Couches Minces, 201, Suppl., 1056 (1980). 220. D. T. Pierce, R. J. Celotta, J. Unguris and H. C. Siegmann,J. Magn. Magn. Muter. 35,28 ( 1983).

SPIN-POLARIZED ELECTRONS IN SOLID-STATE PHYSICS

99

221. R. Becker and W. Doring, “Ferromagnetismus.”Springer-Verlag, Berlin and New York, 1939. 222. R. Carey and E. D. Isaac, “Magnetic Domains and Techniques for their Observations.” English Univ. Press, London, 1966. 223. T. H. Di Stefano, ZBM Tech. Discl. Bull. 20,4212 (1978). 224. A. Tonomura, T. Matsuda, H. Tanabe, N. Osakabe, J. Endo,A. Fukuhara,K. Shinigawa, and H. Fujiwara, Phys. Rev.B: Condens. Matter 25,6799 (1982).