PHYSICAL REVIEW B VOLUME 53, NUMBER 18 1 MAY 1996-II Magnetic linear dichroism in spin-resolved Fe 2p photoemission F. U. Hillebrecht, Ch. Roth, H. B. Rose, W. G. Park, and E. Kisker Institut fu¨r Angewandte Physik, Heinrich-Heine Universita¨t Du¨sseldorf, D-40225 Du¨sseldorf, Germany N. A. Cherepkov* Universita¨t Bielefeld, Fakulta¨t fu¨r Physik, P. O. Box 10 01 31, D-33501 Bielefeld, Germany Received 11 August 1995 Linear magnetic dichroism is studied for the Fe 2p level by angle- and spin-resolved photoemission with high energy resolution. The dichroism occurs in angle-resolved experiments for a geometry as in the transverse magneto-optic Kerr effect, i.e., on reversal of sample magnetization in the direction normal to the plane defined by light polarization and electron emission. The large spin-orbit splitting allows us to investigate the j 1/2 and j 3/2 states separately. Spin analysis allows differentiation between polarization effects related to ex- change and spin-orbit interactions. The results are discussed in the framework of an atomic model, where the exchange interaction between the magnetic d shell and the core hole lifts the degeneracy of magnetic sublevels of the core hole spectrum. The model is able to explain the general trend in the spectra, but does not fully account for the observed shapes of the j 3/2 peaks. The analysis shows that the dichroism is governed by the spin polarization parameter which determines the spin-orbit-induced spin polarization. This shows that if there is a magnetic dichroism then there is a finite spin-orbit-induced spin polarization. The rich structures observed in our complete experiment are evidence for the influence of many-electron effects in the Fe 2p spectrum. S0163-1829 96 01718-3 INTRODUCTION has been performed in x-ray absorption using circularly po- larized radiation.2­4 In such an experiment the core electron The electronic structure of magnetic materials, which pro- is excited to an unoccupied state near the Fermi level EF . vides the key for understanding their properties in general, Circular dichroism in x-ray absorption can be understood as and the basis of their magnetic properties in particular, is resulting from a spin-dependent excitation of core electrons being studied by numerous electron spectroscopic tech- into spin-polarized final states immediately above the Fermi niques. Spectroscopies involving explicitly those states level.2 The spin dependence comes about due to the coupling which carry the magnetic moment, i.e., the d states of tran- of the angular momentum of the photon to the total angular sition metals, or the f states of rare earths, are photoemis- momentum of the electron, which is reflected in the dipole sion, x-ray absorption, and emission, etc. Apart from such selection rule mj 1 for or light, respectively. techniques, core level spectroscopies which do not directly Since the spin and orbital angular momenta of the electron involve the magnetic states, e.g., x-ray photoemission, are are coupled by spin-orbit interaction, the spin polarization of useful since these spectra also are influenced by the interac- photoelectrons is coupled to photon helicity. Spin and orbital tion between the localized core hole generated by photoemis- moments of the incompletely filled valence shell can be sion and the magnetic valence states. The earliest example of probed by comparing excitation cross sections for different a magnetic effect of this type in core level photoemission relative orientations of light helicity and sample spectra is the occurrence of a satellite in the 3s photoemis- magnetization.6,7 sion spectrum of 3d transition-metal magnets, which is When comparing photoabsorption to photoemission, there caused by the exchange interaction between the remaining, are two important differences. The first difference is that in a unpaired 3s electron and the 3d electrons.1 Since this inter- photoemission experiment, the photoelectron is excited to a action is comparatively large, the associated difference in state far above the Fermi level, where one can usually ne- binding energy is several eV 4.5 eV for Fe , and can easily glect exchange and spin-orbit interactions.5 In other words, be measured. This splitting and intensity ratio have been the continuum final states available for the photoelectron are used in numerous examples as an indicator for the presence of equal density for both kinds of spin; there is no spin and size of a magnetic moment.2 For other core levels, the polarization in this continuum of empty states. Secondly, it is core-valence exchange interaction is much smaller, so that close to impossible to perform a truly angle-integrated pho- the influence of exchange can only be studied by spin- toemission experiment on solids, so any experiment has a resolved photoemission. As an alternative to spin-resolved finite angular acceptance. Consequently, the angular depen- photoemission, one may make use of magnetic dichroism in dence of the excitation cross section has to be taken into photoemission: core level spectra show under certain condi- account, whereas in photoabsorption one measures the angle- tions changes of line shapes and/or intensity upon change of integrated excitation cross section. To stress the angle- the relative orientation of the light polarization and resolving nature of photoemission experiments, one may magnetization.2­5 characterize the effects discussed here as magnetic dichroism To date, the largest number of experiments of this type in the angular distribution MDAD . 0163-1829/96/53 18 /12182 14 /$10.00 53 12 182 © 1996 The American Physical Society 53 MAGNETIC LINEAR DICHROISM IN SPIN-RESOLVED Fe 2p . . . 12 183 In general, magnetic dichroism is associated with the peaks for j 32 and j 12. Preliminary accounts of this work combined influence of spin-orbit and exchange interactions. have been presented earlier.23 In the present comprehensive It is known from experiment that both effects by themselves report we include a discussion of the results in the frame- are large enough to cause significant spin polarization in core work of an atomic model.24 The exchange interaction be- level spectra; the influence of exchange interaction is known tween magnetic d states and the core hole is important for from spin-resolved photoemission on core levels which be- magnetic materials. In the model used here, it is assumed gan a couple of years ago with experiments on the Fe 3p that the effect of the exchange interaction is to lift the mj level.8 Since then, the 3s Refs. 9 and 10 and 3p Refs. 11 degeneracy of the core hole state with j 12 or 32, like the and 12 core levels of the 3d ferromagnets have been studied magnetic field in the Zeeman effect. No other structure due using synchrotron radiation. Studies of the Fe 2p core levels to the core-valence interaction is considered. The theory is have been performed recently using unpolarized Mg K ra- discussed in more detail separately.24,25 Here we apply this diation, where 1.6 eV total energy resolution was reached.13 theory primarily for the qualitative discussion of the features Spin-orbit-induced spin polarization14 has been known for a observed in experiment. In principle, the type of magnetic long time from experiments on noble gases, adsorbates, dichroism considered here is expected to occur, and has in etc.15 This phenomenon is expected for any subshell with fact been observed with excitation by unpolarized nonzero orbital angular momentum l provided the spin-orbit radiation.26,27,13 splitting is resolved. Recently, this polarization has been ob- Since magnetic linear dichroism comes about because of served for Cu 3p and 2p Ref. 16 and W 4 f Ref. 17 the combined influence of spin-orbit and exchange interac- emission excited by linearly polarized light. For circularly tions, its basic properties can be derived from the effects polarized light the spin polarization may have finite compo- generated by each of these interactions on its own. The early nents in all three directions in space15 while for linear polar- study of the spin-orbit-induced spin polarization in Ar and ized light the electron polarization is normal to the plane Xe photoemission spectroscopy PES showed a vanishing defined by the light polarization the electric field vector of polarization in the angle-integrated intensity.14 The experi- the light and the direction of electron emission.14 In the ments on Cu 3p and 2p Ref. 16 show that there is a suf- latter case, the polarization is caused by an interference be- ficiently large l 1 cross section for the levels and energy tween the different continuum final states accessible for the range of interest here. For the Fe and Co 3p level, the photoelectron from an initial core state with angular momen- angular dependence has been studied, revealing the influence tum l 0. In a naive picture, magnetic dichroism occurs if of photoelectron diffraction, and showing a vanishing di- the spin polarization due to spin-orbit interaction is collinear chroism in the angle-integrated signal,28 in analogy with the with the axis of magnetization. This is consistent with the disappearance of the integrated spin polarization for non- reports on magnetic circular dichroism MCD in non-spin- magnetic materials. Kuch et al. confirmed the angular depen- resolved photoemission by Baumgarten et al.5 and Schneider dence expected from atomic theory in an experiment de- et al.18 for bcc Fe, by Pappas et al.19 for fcc Fe on Cu, and signed to avoid the influence of diffraction by the crystal by van der Laan et al.20 for Ni 3p. Also, the observation of lattice29 by fixing the emission direction with respect to the circular dichroism for helicity and magnetization perpen- crystal while varying the angle of light incidence. dicular to each other18 with the electron emission in the plane A number of authors have presented theoretical models spanned by these two directions is consistent with this pic- relevant to the experiment discussed in this work. Thole and ture. van der Laan30 analyzed the origin of spin polarization and In this publication we report on magnetic dichroism in Fe dichroism in core level spectra in the context of an atomic 2p photoemission excited by linearly polarized light. This model. Atomic means that the magnetic d states are charac- dichroism occurs in angle-resolved experiments for a geom- terized by their spin and total angular momentum, and as a etry as in the transverse magneto-optic Kerr effect, i.e., on consequence the spectra show strong multiplet features reversal of sample magnetization in the direction normal to which are common for spectra of ionic compounds. The the plane defined by light polarization and electron theory is highly successful for describing the 4 f spectra of emission.21 The magnetization is parallel to the spin-orbit- rare earths which are localized. Also, Ni circular dichroism induced spin polarization in nonmagnetic materials in this could be well described by modeling the electronic structure geometry. Linear magnetic dichroism for the Fe 3p level of Ni as a linear combination of localized d8, d9, and d10 was recently reported by us,21 and has been confirmed by a configurations.20 Imada and Jo31 performed calculations number of other groups,22 also for other core and valence similar to the atomic model. An analysis of the dichroism in levels. As will be discussed below, the angular dependence general terms with an emphasis on the angular dependence of the dichroism is the same as that of the transverse was presented by Venus et al.,32,33 and also Thole and van magneto-optic Kerr effect. In the context of this publication, der Laan refined their model with respect to angular we only address linear dichroism in transverse geometry as resolution.34 Venus et al. placed special emphasis on the described above, which has to be distinguished from the lin- possible influence the crystal symmetry may have on the ear dichroism occurring for magnetization either parallel or magnetic dichroism. Sum rules,6 which have proved so use- perpendicular to the polarization.21 ful in x-ray absorption,7 exist also for photoemission. How- Analysis of the 3p level is complicated by the fact that ever, for photoemission out of filled inner shells of transition exchange and spin-orbit interactions are of comparable size, metals, integration of, e.g., the dichroism spectrum over en- such that the validity of LS coupling is questionable.22 For ergy should yield zero, as also the moment in the filled core the Fe 2p level, the spin-orbit interaction is much larger than shell is zero. Recently, it was shown that analysis of the that of the 3p level, leading to two well-separated final-state statistical moments of the spectra yields information on 12 184 F. U. HILLEBRECHT et al. 53 ground-state properties.35,36 Similar relationships were de- rived some time ago in the context of the 3s spectra of Fe and other 3d magnetic systems by Kakehashi.37 The impor- tant feature of the statistical moment analysis is that it allows one to extract ground-state properties from photoemission spectra without the necessity to choose between a localized or delocalized description of the system. It is of interest to explore the potential of such an analysis, as this would pre- sumably be free from variation of the matrix elements through the relevant part of the spectrum, which may be a source of uncertainty in the sum rules for x-ray absorption. Fully relativistic calculations using multiple-scattering formalisms38 were performed by Ebert et al. for Fe 2p MCD,39 and recently also for MLDAD,40 and by Tamura et al.41 for Fe 3p. This approach has the advantage that it does not contain any adjustable parameters or input from experiment, and promises to provide a detailed account of the variation of the magnetic dichroism with emission direc- tion which is caused by scattering from the solid state envi- ronment. The close relationship between the type of linear dichroism studied here and circular dichroism became appar- ent from experimental42 as well as from theoretical work.31,33,35,56 EXPERIMENT The experiments were performed at the new undulator beamline43 BW3 at HASYLAB, Hamburg, shortly after the Doris ring became a dedicated synchrotron radiation source. Synchrotron radiation is generated by a device equipped with three different magnet structures to cover the range from 15 to 1800 eV with the first harmonic. To allow for quick changeover from one to another magnet structure during op- eration of the storage ring, the magnet structures are mounted on two revolving supports. The monochromator is a modified SX700 plane-grating type, complemented by a tor- FIG. 1. a Fe 2p photoemission spectra taken with 879 eV oidal refocusing mirror behind the exit slit.43 The samples linearly polarized photons for magnetization up full line and down were thin films of Fe grown epitaxially on W 110 by elec- dashed . Inset shows the experimental geometry: linearly tron beam evaporation, following the procedures described p-polarized radiation is incident under 15° measured to the sur- by Gradmann et al.44,45 The evaporation rate was about 0.5 face , electrons are collected in normal emission. b Asymmetry. Å/s. During growth of the first monolayer the substrate was c Normalized intensity difference see text . heated to about 100 °C.44 The thickness of the Fe film was chosen larger than 70 Å, so that the easy axis for magneti- ever, due to the retardation of the photoelectrons from about zation was along the in-plane 100 direction of the W 110 100 eV kinetic energy to the pass energy 10 eV of the surface. The low-energy electron diffraction LEED patterns spectrometer, the effective angular acceptance was smaller, of the W 110 substrate and the Fe film were of similarly and depends on the kinetic energy. Around 100 eV kinetic high quality. The experimental geometry is sketched in the energy we estimate an angular acceptance of the order of 2° inset in the top panel of Fig. 1. Due to the thin-film nature of full cone for 10 eV pass energy. The total energy resolution, the magnetic sample, the magnetic state can be assumed to including the finite energy spread of the photons, was about be single domain after applying field pulses of 80 Oe. All 0.7 eV. data were taken in remanence. The light was incident under The spin polarization of the photoelectrons was analyzed 15° measured to the surface, along the 110 direction of the by very-low-energy VLEED scattering off a magnetized W surface. In previous experiments performed at BESSY,21 Fe 100 surface.46,9 In spin-resolved electron spectroscopy there was an angle of 5° between the direction of light inci- an apparent spin polarization may occur due to apparatus dence and the 110 direction of the substrate. Since this asymmetries. In experiments on magnetic materials, these angle was very small, the geometries can be regarded as can be excluded by reversing the sample magnetization. identical. This is also demonstrated be Fe 3p spectra taken in However, in measurements under excitation conditions lead- the present geometry at 90 eV photon energy being identical ing to magnetic dichroism the spectra obtained for opposite to the ones reported earlier.21 Photoelectrons were collected sample magnetizations are no longer equivalent, so that the in normal emission with a geometrical angular acceptance of apparatus asymmetry cannot be removed by averaging data the spectrometer entrance lens of about 8° full cone. How- taken with opposite sample magnetizations. For our spin de- 53 MAGNETIC LINEAR DICHROISM IN SPIN-RESOLVED Fe 2p . . . 12 185 tector one may take data with a scattering energy for which sity should be proportional to the primary intensity. How- there is no spin dependence; remaining intensity differences ever, the intensities in primary peaks are very similar to each should then reflect the apparatus asymmetry. Alternatively, other, since the increased width of the peak for magnetiza- one may analyze the spin polarization for spectral regions tion up compensates the higher peak intensity of the line for away from the main peaks where the dichroism should van- magnetization down. Consequently, the finite dichroism in ish, so that the spin polarization should not depend on the region between the two peaks cannot be due to second- sample magnetization. This should, for example, be the case aries. A finite asymmetry between the 3 on the low-binding-energy BE side of the Fe 2p 2 and 12 lines has also 3/2 photo- been found in circular dichroism for the Fe 2p level.5,18,19 emission peak, since the photoemission peaks of the 3p shell In order to reduce the influence of the secondary back- are far away in energy, and the total intensities are usually ground on the quantitative dichroism result, one may con- the same for both sample magnetizations. Consequently, the sider the difference between the spectra for the two magne- apparatus asymmetry can be fixed by requiring the spin po- tizations, rather than the asymmetry. To allow a quantitative larizations on the low-BE side of the Fe 2p3/2 peak to be the comparison, the spectra for the two magnetizations were same for both sample magnetizations. The two procedures added, and the intensity on the high-binding-energy side of yield consistent results. For the measurements considered in the Fe 2p this publication the apparatus asymmetry was smaller than 3/2 line was subtracted as a constant background. The difference spectrum was then normalized to the peak 1%. intensity of this spectrum. The difference spectrum obtained For experiments depending on the light polarization, it is in this way is shown in the lowest panel of Fig. 1. It is important to address the possibility of a change of light po- similar to the asymmetry spectrum; however, for obvious larization by the material under investigation. Lately, a num- reasons the scatter of the data in regions of low intensity is ber of reports have appeared on Faraday rotation in the soft- reduced. x-ray regime by ferromagnetic Fe.47 However, in all those Qualitatively, the observed linear dichroism has a similar experiments the rotation is only appreciable for photon ener- appearance to the circular dichroism for bcc Fe,18 and for fcc gies close to core level thresholds. Since in photoemission Fe on Cu.19 A detailed comparison is, however, difficult due one uses photon energies well above the binding energy of to the improved energy resolution in the present experiment. the level to be investigated, the polarization state of the light By applying a suitable broadening to our data, one finds that will not be affected. Such effects will, however, be a serious the dichroic asymmetry decreases by a factor of 2­3 when problem in resonant photoemission, where one measures the resolution changes from 0.7 to 3 eV. This indicates that photoemission from a shallow core level, tuning the photon the linear magnetic dichroism is of the same order of mag- energy to the binding energy of a deeper core level. nitude as the circular dichroism observed for fcc or bcc Fe.18,19 For the Fe 3p level it was shown that the line shapes SPIN-INTEGRATED LINEAR DICHROISM of the circular and linear dichroisms are virtually identical.42 Figure 2 shows a detailed view of the dichroism in the Figure 1 shows spin-integrated Fe 2p spectra taken with neighborhood of the Fe 2p3/2 photoemission peak for three photons of 879 eV for a magnetized Fe film. The spectrum different photon energies for a different sample. The maxi- shows the j 32 and j 12 final states, separated by 13 eV due mum of the difference occurs at 706.5 eV, at slightly smaller to spin-orbit interaction. The spectrum averaged over both binding energy than the photoemission peak 706.8 eV . In sample magnetizations agrees with earlier reports, as do the all cases, the positive lobe is weaker than the negative one. binding energies for the two final states. The magnetization Although the data cover only a limited photon energy range, direction was normal to the reaction plane, as indicated in the they show a decrease of the dichroism from 10% for energies inset in Fig. 1. Comparing the spectra for the two magneti- within 100 eV of threshold to about 7% at 879 eV. An in- zation directions, one finds that they change when the sample teresting feature can be seen in this graph, namely, that the magnetization is reversed: For magnetization up the j 32 dichroism shows a structure 2­3 eV away from the main peak intensity is reduced, and the peak has slightly higher photoemission peak, although there is no strong feature in binding energy than for magnetization down. For the j 12 the original data at this energy. This feature is reproducible, final state, the situation is reversed: for magnetization up the and was found in all spectra; it is also recognizable in Fig. 1. 12 peak is higher and at lower binding energy than for mag- Since the original spectra do not show a clearly recogniz- netization down. This difference in line shape and/or inten- able structure at this energy, one may attribute this feature to sity is the magnetic linear dichroism discussed here. different line shapes of the lines for the two magnetization A common representation of the changes associated with directions. Core level photoemission line shapes of metallic the magnetic dichroism is the asymmetry, which is the dif- solids are affected by excitation of electron-hole pairs in the ference of the spectra for the magnetization up and down, vicinity of the Fermi level.48 The number of such excitations divided by the sum. Figure 1 b shows this asymmetry. Start- depends on - among other things - the combined density ing at low binding energy, the 32 state first shows a negative of states around the Fermi level. In a ferromagnetic solid, the asymmetry, changing to positive, while for the j 12 state the densities of states for majority and minority spins at the asymmetry is positive at low binding energy, and changes to Fermi level are different. From our spin-resolved measure- negative. Apart from that, the asymmetry does not go to zero ments to be shown below we also know that the spin polar- between the two peaks. This is also apparent in the original ization of the Fe 2p photoemission peak changes when the spectra in Fig. 1 a . In principle, this behavior may be caused magnetization is reversed. If also the cross section for exci- by the background of secondary electrons, which is generally tation is spin dependent, the line shapes of majority- and associated with photoemission from solids, and whose inten- minority-spin portions of a photoemission peak will be dif- 12 186 F. U. HILLEBRECHT et al. 53 expect a larger dichroism since spin-polarized LEED SPLEED experiments have shown that at room temperature the magnetic moment at the 110 surface of Fe is 30% en- hanced over the bulk moment.45 Clearly, the change of di- chroism does not reflect - or at least not primarily - a change of the magnetic moment at the surface, but demon- strates the influence of photoelectron diffraction. This effect has to be taken into account for any detailed quantitative comparison between theory and experiment when the emis- sion angle is varied. We note that the line shapes of the Fe 2p lines averaged over both magnetizations are virtually identical for both angles. A recent detailed study of the in- fluence of photoelectron diffraction on the magnetic linear dichroism28,49 has shown that large effects are quite com- mon, but in agreement with the present observation no strong effect was observed in the spectral shape averaged over both magnetizations. The angular dependence of the magnetic circular dichro- ism in Fe 2p photoemission was studied by Venus et al.32 They also find quite dramatic changes of the dichroism with geometry; however, their data do not show a sign change. The results are analyzed by expanding the photoelectron wave into spherical harmonics, chosen such as to reflect the crystalline symmetry. For emission along high-symmetry di- rections, e.g., normal emission in our experiment containing two mirror planes, only some of the expansion coefficients are finite, so that at least the spectral dependence of the di- chroism is not affected by the solid state environment. This means that sum rules should also be transferable from angle- integrated theory to an angle-resolving experiment. In con- trast, for the emission in low-symmetry directions, i.e., the non-normal 75° emission in our case, all final-state waves FIG. 2. Detail of the magnetic linear dichroism at the Fe 2p3/2 allowed by dipole selection rules may contribute. In our level for 796, 816, and 879 eV photon energy top to bottom . 75° data, we note, however, that for the spin-integrated Lowest panel shows dichroism for normal light incidence, and elec- dichroism the deviation from the sum rule stating that the tron emission at 75° to surface normal. total intensities should be the same for both magnetizations ferent. For Doniach-Sunjic-type48 line shapes this would re- is small. Furthermore, in this picture32 no diffraction effects sult in different asymmetry indices. Also, the lifetime widths are included. For the Fe 3p and Co 3p levels it is known that of majority and minority core holes may be different. These photoelectron diffraction does affect the dichroism strongly, circumstances together may affect the line shapes such that and may even lead to a sign reversal.28,49 the extra feature in the magnetic dichroism is generated. Since the linear dichroism as studied here is similar to the SPIN-RESOLVED MAGNETIC DICHROISM circular one, it is meaningful to compare to the circular di- chroism spectrum calculated by Thole and van der Laan.30 Before discussing the spin-resolved data, some remarks They find, in fact, a feature reminiscent of the one observed on spin-resolved core level photoemission data of ferromag- here; however, there is much more structure beyond, also in netic solids are in place. In spin-resolved photoemission the isotropic spectrum. These structures are essentially due to spectroscopy of solids one usually finds that the background the localized nature of the d electrons in those model calcu- of secondary electrons is spin polarized. Since the secondary lations, which led to discrete satellites. Consequently, the electrons are generated by higher-kinetic-energy features in possibility of satellite-related features showing up in the di- the spectrum undergoing scattering processes, the spin polar- chroism cannot be completely excluded. ization in the background results from a spin dependence of Finally we show in Fig. 2 how the dichroism is affected these scattering processes or from spin polarization in the when the angle of electron emission is changed while the primary features. The spin polarization in the primary fea- angle between light polarization and electron emission re- tures is first of all due to what in photoelectron diffraction is mains constant. In an atomic picture, i.e., neglecting solid called the source function, i.e., with which polarization the state effects, the dichroism is determined solely by this photoelectrons emerge from the site from which they are angle, and a change of the dichroism can be caused, e.g., by being released. In a three-step model, this polarization may photoelectron diffraction. The result is quite surprising. Not be modified as the photoelectrons traverse to and through the only does one find for emission at 15° to the surface a sig- surface. The primary spin polarization may be affected by nificant reduction of the dichroism, but even a reversal of elastic as well as inelastic spin-dependent scattering. Spin- sign compared to normal emission. Intuitively, one might dependent inelastic scattering obviously will result in reduc- 53 MAGNETIC LINEAR DICHROISM IN SPIN-RESOLVED Fe 2p . . . 12 187 ing the elastic intensity of one spin channel more than the other, thereby affecting the spin polarization measured in the primary photoemission peak. Since in elastic scattering the energy is unchanged, the spin polarization can only be af- fected due to the angular dependence of the elastic scattering. If, e.g., the source function is angle dependent, i.e., aniso- tropic, and the elastic scattering is isotropic, then the ob- served spin polarization depends on the direction of observa- tion. The spin dependence of the mean free path can be inferred, e.g., from an experiment where one measures the spin polarization of an emission feature of a nonmagnetic material which is covered by a magnetic material. If such a feature acquires a spin polarization, one can conclude that this is due to a spin-dependent scattering cross section. Such experiments have been reported by Pappas et al.50 For low kinetic energies they find a spin-dependent mean free path, while at 50 eV the spin dependence disappears. In our ex- periments the kinetic energy of the photoelectrons is between 80 and 200 eV, where spin dependence of the mean free path is small. In our view the best empirical evidence for the influence of scattering on the spin polarization measured for a photo- emission feature derives from measuring the change in po- larization which is acquired by an electron beam - polar- ized or unpolarized - when it is scattered off a magnetic surface. If we consider elastic scattering from a single-crystal surface, this experiment is a spin-polarized LEED experi- ment. Such spin-polarized LEED experiments have been re- FIG. 3. Spin-resolved magnetic linear dichroism for Fe 2p3/2 ported by Waller and Gradmann for Fe 110 grown on photoemission (h 819 eV . W 110 , as is used also in this work, for 30­120 eV incident energy and 10°­45° incident angles.44 For energies around peak is much smaller relative to the peak than for 2p levels. 100 eV, it is found that the exchange asymmetry is in most This indicates that a portion of the step associated with the cases positive, between 2% and 5%. Therefore the ex- 2p spectrum is caused by effects other than inelastic scatter- change asymmetry is opposite to the minority polarization ing. Consequently, the ratio of the step height relative to the commonly observed in core spectra shown below. Spin-orbit primary intensity - in whichever way these are to be mea- asymmetries are found to be much smaller. In the context of sured - cannot be used as a measure for the inelastic spin- our experiment they can contribute only to the spin-orbit dependent scattering cross sections. Only the background on polarization. Hopster, Raue, and Clauberg51 performed an the low-BE side of the j 32 state is a background of pre- inelastic scattering experiment on an Fe-based metallic glass dominantly secondaries, since spectral features with higher between 45 and 180 eV incident energy. In that work, there energies - the L Auger lines and M photoemission lines - may be evidence for a small minority polarization in the are sufficiently far away. The intensity on the high-binding- elastic beam at low energy 45 eV ; however, the polariza- energy sides of the peaks must contain some other primary tion is negligible at 180 eV incident electron energy. This features, i.e., satellites, which are remnants of atomiclike indicates that a minority-spin polarization as observed here, multiplets. e.g., in Fig. 3, lower panel, is unlikely to be caused by spin- Figure 3 shows spin-resolved data for the Fe 2p3/2 level. dependent scattering. Furthermore, one may derive from an For each magnetization, the spectrum is split up into the elastic scattering experiment an estimate about what fraction majority and minority components. For the conditions of the of the intensity on the high-binding-energy side of a primary present experiment, the secondary background on the photoemission peak is due to secondary electrons. It is ap- low-BE side is unpolarized. For magnetization up, one finds parent from the data in the literature that only a small frac- on the high-BE side a majority polarization of about 10%; tion of the steplike intensity increase underlying the Fe 2p the individual line shapes are fairly similar to each other, and peaks is caused by secondaries. This can be further substan- the total polarization is small, as the intensities in the two tiated by comparing the relative step heights for different peaks are essentially identical. The main difference between core levels: If the step is exclusively caused by secondaries, the spin-resolved spectra is a shift in binding energy of 0.8 the number of secondaries relative to the intensity in the eV. For magnetization down, there is a pronounced line- primary peak should be the same for all photoemission shape difference between the minority- and majority-spin peaks, provided one chooses the photon energies such that spectra, and also an intensity difference overall polarization the primary peaks occur with similar kinetic energy. Inspect- about 17%). As argued above, a finite minority-spin po- ing, e.g., the Fe 3s spectrum measured with 250 eV larization, which is stronger for the magnetization-down photons,9 we see that here the step in the secondary back- case, is not caused by spin-dependent elastic or inelastic ground from the low- to the high-binding-energy side of the scattering. An important feature present in the data for both 12 188 F. U. HILLEBRECHT et al. 53 magnetizations is that the minority-spin component occurs with lower binding energy than the majority component. In- tuitively, one would expect a behavior in line with Hund's rule, i.e., a lower excitation energy when the spin of the remaining core shell is parallel to the spin of the d electrons. In that case the ejected photoelectron has its spin antiparallel to the majority-spin direction, as is found here experimen- tally for the low-BE side of the Fe 2p peaks. The spin- resolved spectra for the two magnetizations indicate that line shapes and overall spin polarization are affected by reversing the magnetization. These spectra are influenced by spin-orbit as well as by exchange interaction. Both interactions by themselves pro- duce a spin polarization in the spectrum. In electron scatter- ing it has been shown that it is possible to separate the po- larization effects by adding the polarized spectra in different ways.52 For core level photoemission excited by circularly polarized light an analogous procedure was suggested.30,42 If majority is added to majority, and minority to minority, then the effect of reversing the magnetization is canceled. Obser- vation of the dichroism requires reversing the magnetization; therefore this averaging removes the magnetic dichroism, and one is left with a spectrum representing the spin polar- ization induced by the exchange interaction between the core hole and the d electrons. This is shown in the upper panel of Fig. 4. As was noted above for the individual spin-resolved spectra, the minority emission occurs at lower binding en- ergy in both cases, and this is also seen in the summed spec- trum. Apart from the BE difference, the minority spectrum also has higher peak intensity and a narrower line shape than the majority component. A similar behavior has been ob- served for the Fe 3p spectrum if taken under conditions where no magnetic dichroism occurs.8,11 The differences in BE and width cause a sign change of the exchange-induced FIG. 4. Spin-resolved Fe 2p spin polarization from minority on the low-BE side of the 3/2 photoemission spectra, represent- ing exchange- top and spin-orbit-induced bottom spin polariza- peak to majority on the high-BE side. For circularly polar- tions. ized light, the difference between these two spectra has been termed the spin spectrum denoted by I01) in Ref. 30, and is similar to each other. Both spectra show a shoulder on the also shown in Fig. 4. high-BE side, which may be caused by residuals of atomic By adding the spectra for a fixed direction of spin in the multiplet structure. In the secondary background, the major- laboratory frame of reference, independent of magnetization, ity polarization is larger on the high-BE side of the peak than the exchange-induced polarization is removed, as majority on the low-BE side. The spectra for fixed spin direction in for one magnetization is added to minority for the other. the laboratory frame of reference, which reflect the spin- Consequently, if the spectra so obtained are different from orbit-induced polarization, are shown in Fig. 5 b . They ap- each other, then there is a spin polarization which is caused pear with the same peak height and binding energy. The by spin-orbit interaction. This is shown in the lower panel of binding energies should be the same, since we have averaged Fig. 4. The line shapes and intensities of the two different over magnetization. Nevertheless, there is an overall polar- spin channels are more similar to each other than in the ex- ization, since the base level of the up-spin peak is lower than change case. The most important difference to the exchange that of the down-spin peak. This polarization is opposite to polarization is that the sign of the spin-orbit polarization that found in the j 32 line. does not change through the spectrum. The spin-orbit- induced polarization is determined by coupling between spin DISCUSSION and orbital momenta. For a spin-orbit splitting of 13 eV, as For a qualitative description of the observed phenomena, for Fe 2p, the admixture of j 12 states to the j 32 final state we use an atomic model which is comprehensively covered is small, so that indeed the spin-orbit-induced polarization in separate publications.24,25 In this model the solid state ef- should not change its sign within one of the substate fects are taken into account only by introducing the energy spectra.30 splitting of the magnetic sublevels of the core hole state. This Figure 5 shows the equivalent sum spectra for the Fe energy splitting appears due to exchange interaction between 2p1/2 level. As for the j 32 level, exchange shifts the minor- the core and valence electrons, and is of the order of 1 eV for ity peak by 0.5 eV to lower binding energy compared to the the 2p and 3p levels of Fe.38­41 Therefore the hole state majority. The peak intensities as well as the line shapes are generated by photoemission will be characterized in the fol- 53 MAGNETIC LINEAR DICHROISM IN SPIN-RESOLVED Fe 2p . . . 12 189 standard parameters used to characterize the spin polariza- tion of photoelectrons ejected from unpolarized atoms,56 A1/2 1/2 2 A3/2 3/2 d2 2 s dd 1 2 2 d d . 4 2 sddcos d s ds d s and d and ds and dd are phase shifts and reduced dipole matrix elements for the p s and p d transitions, respectively.56 The expression 2 shows that the linear dichroism is an interference effect governed by the spin polarization param- eter , and is only finite if there is a finite cross section for both l 1 and l 1 final states. For the circular case, the dichroism is present in the incoherent cross section. Further- more, both the l 1 and the l 1 channels give mutually opposite contributions to the circular dichroism. This, and the contribution of an interference term, render a quantitative analysis much more difficult than in the linear case. Circular dichroism is small if dd ds . This is, in contrast, the con- dition under which the linear dichroism is maximum. In the linear case, disappearance of dichroism can be caused either by one of the matrix elements going through zero, or by the FIG. 5. Spin-resolved Fe 2p1/2 photoemission spectra, represent- phase shift difference going through a multiple of . In the ing exchange- top and spin-orbit-induced bottom spin polariza- particular case of the 2p subshell, both matrix elements ds tions. and dd do not have zeros,57 and dd ds . Consequently, lowing by the quantum numbers nl jm MCDAD does not have zeros, while MLDAD will have ze- j , where n is the prin- cipal quantum number, l is the orbital angular momentum ros at photon energies where the phase shift difference goes and j l 1 through a multiple of . So, in spite of the similarities be- 2 and m j are the total angular momentum and its projection on the direction of sample magnetization. The ef- tween the observed linear and circular dichroism curves dis- fects of spin-orbit interaction in the continuum are neglected, cussed above, these two cases have also essential differences, as they are expected to be smaller than other solid state per- which can be exploited by comparing their photon energy turbations neglected in our model. dependences. We first consider the spin-integrated magnetic dichroism The fact that the core hole state is split into sublevels with in the angular distribution. For linearly polarized light and a given projection of the total angular momentum mj is con- magnetization reversal perpendicular to the plane of inci- veniently described by state multipoles as described earlier.24 dence we obtain24,25 Using the numerical values of state multipoles from Table I of Ref. 24, the relation 2 between 3/2 and 1/2, and the fact that the cross section nl j for the j 32 state is two times IMLDAD nl j n larger than for j 1 j 2, one finds from 1 that the area under 2 10sin2 2 5 3/2, j 32 1 2 1/2, j 1 the MLDAD curve in the P 2 , 3/2 level should be four times larger than in the p with 1/2 level. This is approximately fulfilled in the experimental curve shown in Fig. 1 b . The fact that the dichroism starting from low binding energies is first positive 3 1/2 2 3/2 2 2 and then negative in the p3/2 level, and first negative and then d d . 2 2 sddsin d s / ds d positive in the p1/2 level, evidences that there is an opposite ordering of magnetic sublevels in these two levels, as was For circular light polarization and magnetization reversal in shown already by Ebert et al.38,39 Indeed, according to 1 the plane of incidence we obtain and 3 , both linear and circular dichroism are proportional to the first-state multipole n10 which for different magnetic sublevels has the same sign see Table I of Ref. 24 as the IMCDAD nl j n j 2 10cos 2 5 A3/2 12 3/2 , j 32 2 A1/2 1 projection mj . 2 1/2 , j 12 , 3 Next we consider spin-resolved spectra, applying the gen- eral equations from Refs. 24 and 25 to our particular situa- where is the angle between the light beam and the surface tion. One finds that for the spin-resolved spectra the third- normal, n n 10 are state multipoles53­55 characterizing polariza- state multipole 30 also gives a contribution, while for the tion of each magnetic sublevel, and A, , and are a set of non-spin-resolved spectra n20 is the highest-state multipole 12 190 F. U. HILLEBRECHT et al. 53 TABLE I. The ratios of intensities of different magnetic sublev- 14, and 34 for the magnetic sublevels mj 32, 12, 12, and els of np hole states in spin-resolved spectra to those in spin- 32 , respectively. Taking into account the experimental unresolved spectra for the geometry of experiment shown in Fig. 1 resolution and the intrinsic width of these levels, there is a and linearly polarized light. n is the direction of the sample mag- qualitative agreement between theory and experiment as far netization, e is the light polarization vector, and s is direction of as the sign change through the spectrum is concerned; how- spin. ever, the magnitudes of the positive and negative lobes and the line shapes are not in agreement. j 3/2 j 1/2 For the spectra with a fixed spin direction in the labora- mj 3/2 1/2 1/2 3/2 1/2 1/2 tory frame of reference one obtains analogously e n, s n 1 0 1 0 0 1 e n, s ( n) 0 1 0 1 1 0 I 3/2 n n 3/2 M ,s I3/2 M ,s e n, s n 0 1 0 0 1 0 2 00 12 20 1 e n, s ( n) 0 0 1 0 0 1 3 n 2 sin2 00 2 n 3/2sin2 , 6a for the p 20 3/2 subshell25 provided spin-orbit interaction in the continuum states is neglected.24 Therefore the spin-resolved spectra are a more stringent test for the theoretical model. I 3/2 n n 3/2 M ,s I3/2 M ,s 12 20 1 Turning to spin-resolved spectra one finds for the 2 00 minority-spin intensities of the j 32 final state24,25 summed 3 n over both magnetizations 2 sin2 00 2 n20 3/2sin2 , 6b 1 2 I 3/2 n n n 3/2 M ,s I3/2 M ,s where j is the spin polarization parameter defined above. 2 00 2 20 5 10 These spectra have a similar structure with nonzero contri- butions from all magnetic sublevels. The two spectra given 3 n 1 3 by 6a and 6b differ only by the sign of the term propor- 2 5 30 2 sin2 tional to 3/2. The experimental spectra shown in Fig. 4 b are also rather similar in shape, but differ in magnitude. Sub- 5a tracting 6b from 6a yields the spin-orbit spectrum Fig. and for the sum of majority-spin intensities 4 b , in which the relative sublevel intensities are 3, 1, 1, and 3 from mj 32, 12, 12, and 32, respectively, so that 1 2 overall the negative contribution should prevail over the I 3/2 n n n 3/2 M ,s I3/2 M ,s positive one, which is observed in the experiment see the 2 00 2 20 5 10 lower part of Fig. 4 b . Since the difference between these two curves is proportional to the parameter 3/2, it is in 3 n (1 3 principle possible to derive 3/2 from this experiment. 2 5 30 2 sin2 ). The analogous derivation25 for the np1/2 sublevel yields 5b 1/2 n n These expressions contain only the angular asymmetry pa- I1/2 M ,s I1/2 M ,s 1 22 00 10 rameter , but not the spin polarization parameter . This reflects the fact that in these spectra we have removed the 32 sin2 , 7a spin polarization due to spin-orbit interaction by summation. To construct model spectra, one has to evaluate this expres- sion for each m 1/2 n n j sublevel by inserting the state multipoles I1/2 M ,s I1/2 M ,s 00 10 1 from Table I of Ref. 24, convolute with the appropriate line 22 shape, and add the contributions of the different mj sublevels 3 shifted in energy by the exchange splitting. The contributions 2 sin2 . 7b of different mj sublevels are proportional to the expression in These expressions give the minority- 7a and majority- 7b the first bracket. Using Table I of Ref. 24 one finds that the spin spectra of the j 12 subshell. Inserting the state multi- minority component 5a is different from zero only for the poles from Table I of Ref. 24, one finds that only the mj 32 and 12 magnetic sublevels, while the majority com- mj 12 magnetic sublevel contributes to the minority-spin ponent 5b is different from zero for mj 12 and 32 sublev- channel, and only the mj 12 sublevel contributes to the els, independent of the angle . Table I shows the intensities majority-spin channel, while the intensities should be equal. in the spin-resolved spectra relative to those in the non-spin- Taking into account a difference in the backgrounds, one can resolved spectra obtained in this way. The different contrib- see that the corresponding experimental spectra shown in uting levels explain qualitatively the shift of one spectrum Fig. 5 a have just that behavior, that is, the peaks have the relative to the other observed in Fig. 4 a . The spin spectrum same shapes and intensities and are shifted in energy. This shown in Fig. 4 a should correspond to the difference of allows one to derive the positions of the j 12 magnetic sub- 5b and 5a , which is proportional to the factors 34, 14, levels with fairly high precision directly from the experimen- 53 MAGNETIC LINEAR DICHROISM IN SPIN-RESOLVED Fe 2p . . . 12 191 tal data shown in Fig. 5 a . We obtain from our data a split- Concerning the spin-orbit polarization, the experimental ting of 0.5 eV between the mj 12 and 12 sublevels of the spectra in Fig. 5 b have the same peak height; however, the j 12 final state. background under the two spectra is different, so that the For the sums with a fixed direction of spin in the labora- spin-up intensity is larger. Consequently, there is a finite tory frame one obtains polarization of about 10%. Again, this is governed by the spin polarization parameter 1/2, which is related to the ra- dial matrix elements and associated phase shifts for s- and I 1/2 n 1/2 M ,s I1/2 M ,s 1 22 00 d-like final states. Taking into account that 1/2 1/2 3/2 3/2, and using the state multipoles from 3 Table I of Ref. 24, one finds from Eqs. 6a , 6b , 8a , 8b 2 sin2 1/2sin2 , that the difference between the two curves in Fig. 4 b for the 8a j 32 level integrated over the peak width should have the same magnitude, but opposite sign compared to the differ- I 1/2 n ence between the corresponding curves of Fig. 5 b for the 1/2 M ,s I1/2 M ,s 1 22 00 j 12 level. We can summarize this as a sum rule by saying that the total emission out of the 2p subshell should be un- 32 sin2 1/2sin2 . polarized. Considering only the spin-orbit polarization in the 8b peak regions, the polarization in the 12 region is only about 13 of what it should be according to this sum rule, even Here, both magnetic sublevels give equal contributions to though it is opposite to that in the 32 peak. The spin-orbit each of these sums since they contain only the state multi- polarization on the high-BE side of the j 32 level and on the pole of zeroth order, so that the spectra should have a maxi- low-BE side j 12 is finite, showing a finite spin-orbit polar- mum in the middle between two magnetic sublevels. They ization also in the region between these two peaks. This ap- differ only by the sign of a term proportional to 1/2, which pears to be related to the finite magnetic dichroism in this will result in a difference in magnitudes of two peaks. In energy region. The finite integrated spin-orbit polarization agreement with these theoretical conclusions, the sums of may be related to the deviation of the observed branching experimental spectral with a fixed direction of spin in the ratio between the j 32 and 12 final states, R 2.3 0.1, from laboratory frame shown in Fig. 5 b are very similar, with the statistical value of 2. the maximum just in the middle between the maxima in Fig. The essential conclusion from the foregoing analysis is 5 a which correspond to the mj 12 and 12 magnetic sub- that the spin polarization can be classified with respect to levels. exchange or spin-orbit effects. The exchange polarization is Subtracting the spectra for fixed spin direction in the labo- of minority type at the low-energy threshold of the j 32 ratory frame of reference 6a and 6b and 8a and 8b level, changing sign to majority type somewhere in the spec- from each other, one is left with expressions proportional to trum. The spin-orbit-induced polarization has a certain sign . For a nonmagnetic system, e.g., for the case of photoion- for a given fine-structure component. The linear dichroism is ization of unpolarized atoms, this parameter describes the proportional to the same spin polarization parameter which spin polarization of photoelectrons ejected by linearly polar- governs the spin-orbit-related spin polarization in nonmag- ized light, which appears due to spin-orbit splitting of atomic netic systems. This illustrates the interplay between spin- levels.14,15 Therefore, what we have characterized in the dis- orbit and exchange interactions for the occurrence of mag- cussion above as spin-orbit-induced polarization is described netic dichroism. by the term proportional to the parameter , in analogy to For a more detailed comparison between experiment and the spin polarization induced by spin-orbit interaction for model, we restrict ourselves to the j 32 state since in the nonmagnetic systems like Cu.16 On the other hand, the ex- j 12 state there is a good qualitative agreement between pressions for the majority and minority spectra 5a and 5b theory and experiment. We start by considering the spin- and 7a and 7b do not contain the spin polarization param- integrated dichroic spectra which follow from the atomic eter . In the present model, for any value of , including model. As an approximation for the input parameters for the 0, the sum spectra for majority and minority would be particular situation of our experiment, we used the matrix unchanged. Consequently, the difference between the major- elements, phases, and atomic asymmetry parameter of ity and minority spectra shows the exchange spin polariza- Goldberg, Fadley, and Kono58 for Ni at 1000 eV photon tion. This justifies our characterization of the sum spectra energy. The spectral shape is not affected by the absolute obtained either in terms of majority/minority or with respect magnitudes of these parameters; furthermore, they do not to fixed spin direction as reflecting exchange- and spin-orbit- vary strongly with photon energy or between Fe and Ni. For induced spin polarization. One has to keep in mind, however, the splitting between the mj sublevels, we used 0.5 eV as that also the spectral shape of the spin-orbit polarization is derived from the j 12 spectrum. The relative sublevel inten- influenced by the magnetic ground state of the material in- sities obtained in this way are 2.86, 0.95, 1.08, and 3.23 for vestigated, since for a magnetic material the mj sublevels are magnetization up in order of decreasing mj ; for magnetiza- not degenerate, as they are, for example, in Cu. Hence the tion down the sequence of intensities is reversed. Each sub- natural way to discuss the spin-orbit polarization in a quan- level was represented by Doniach-Sunjic line shapes48 with titative manner is by considering its energy integral, relative 0.4, a Lorentzian width L 0.4 eV,59,60 and a Gaussian to the energy integral of the sum spectrum. The quantitative of 0.7 eV to account for the experimental resolution. Figure result may be influenced by photoelectron diffraction. 6 shows spin-integrated intensities for magnetization up and 12 192 F. U. HILLEBRECHT et al. 53 FIG. 6. Fe 2p3/2 spectrum derived from the atomic model using matrix elements and phases for Ni 2p at h 1000 eV from Gold- berg, Fadley, and Kono Ref. 58 . The lines are composed of four Doniach-Sunjic lines with intensities as given in the text; the asym- FIG. 7. Fit of the non-spin-resolved Fe 2p3/2 data after back- metry index is 0.4, the Lorentzian width is 0.4 eV, and the ground subtraction by four equidistant Doniach-Sunjic lines. The Gaussian broadening is 0.7 eV. Bottom panel shows linear mag- numbers in the panels give the energies and intensities of the indi- netic dichroism. vidual lines, chosen to give a sum close to 4. Dots show experimen- tal data, lines show the four individual lines and their sum. down obtained in this way, as well as their difference, i.e., We used the standard procedure, assuming that the back- the linear dichroism. The spectrum is dominated by the ground at a given energy in the spectrum is proportional to mj 32 and 32 states, leading to the two peaks in the spec- the signal integrated up to that energy. Figure 7 shows the trum, whose intensities are affected by reversing the magne- fits of experimental spectra with four Doniach-Sunjic lines48 tization. The total intensities in the dichroic spectra are with asymmetry index 0.4 and a Lorentzian lifetime equal, in agreement with experiment. However, the line broadening of 0.4 eV.59 To account for the experimental shapes are quite different from the experimental ones, the resolution, the spectra were convoluted with a 0.7 eV Gauss- latter apparently having a significantly reduced intensity for ian. We required the separation of the individual sublevels, the higher-binding-energy sublevels. If we maintain that the which is caused by the exchange interaction, to be constant spectra are composed of four lines for the j 32 final states, within the j 32 multiplet, and equal to 0.5 eV, since this is then the experimentally observed line shape can only be ex- the exchange splitting found in the j 12 spectrum. Figure 7 plained if the individual lines have intensities quite different shows the individual lines, as well as the combined spectra from those in atomic model. The cause for this deviation is full lines , compared to the experimental results dots . The not known at present. main features of the peaks can be well described by this A comparison of the spin-resolved model spectra with procedure. There is some disagreement in the energy region experiment would lead to a similar disparity as for the spin- at BE's higher than 710 eV; however, in this region the integrated dichroic spectra. However, even though the model effect of possibly inadequate background subtraction, is not able to describe the spin-integrated dichroic spectra, it Lorentzian lifetime broadening, or many-body excitations might yield an adequate description of the spin dependen- may be significant. cies. As the present theoretical model does not give the cor- For obtaining the spin-resolved spectra, we multiply the rect intensities of the individual sublevels, we determine contribution of each magnetic sublevel in Fig. 7 by the ap- these intensities empirically from a fit to the spin-unresolved propriate factor given in Table I. The fact that only 0 and 1 experimental data by four evenly spaced mj sublevels. For occur in Table I reflects the theoretical result that the contri- that purpose experimental spectra free from secondary ef- butions of the individual sublevels should be fully polarized. fects are desirable. Even though we argued above that the The spectra obtained by this procedure are shown in Fig. 8. background is not entirely due to secondary electrons, we For comparison with experiment, we subtracted backgrounds treated the experimental spectra as though this were the case. in the same way as above. The general trend of the peak 53 MAGNETIC LINEAR DICHROISM IN SPIN-RESOLVED Fe 2p . . . 12 193 asymmetry, it is clear49 that photoelectron diffraction strongly influences the experimental result. This is impres- sively demonstrated by the reversal of sign of the dichroism observed with sample rotation, where the unchanged angle between light polarization and electron emission should yield the same dichroism Fig. 2 . The lower degrees of spin po- larization which are obtained from experiment may be partly due to scattering processes, although it appears that the in- fluence of spin-dependent scattering should be small. The 0.4­0.5 eV exchange splitting between the mj sublevels which we derive from the 2p1/2 spectrum is significantly larger than the 0.27 eV calculated by Ebert,38 but about a factor of 2 smaller than the value derived by Tamura et al.41 for the 3p level. A different splitting would have a slight effect on the spin-resolved spectra derived from an analysis as shown in Figs. 7 and 8; however, no qualitative change is expected. An aspect which is possibly relevant to our investigation is the suggestion of Tamura et al.41 that, apart from spin polarizations generated exclusively by exchange or by spin- orbit interactions, there may be an interference between these two. If a geometry is chosen where these exchange and spin- orbit polarizations are normal to the direction of electron emission and orthogonal to each other, the interference gen- erates a spin polarization in the third, longitudinal direction. In that situation there may still be a magnetic dichroism, since magnetization reversal reverses the exchange-induced polarization, and due to the interference with the fixed spin- orbit polarization a dichroism may occur. As yet there is no FIG. 8. Comparison of the spin-resolved Fe 2p3/2 data to spectra experimental evidence for this effect, and it is not clear how derived from the fit shown in Fig. 7. Filled triangles show majority- spin spectrum, empty triangles minority-spin spectrum. Lines give it may affect the magnetic dichroism and spin polarization in result of model spin polarizations combined with fit to measured the experiment discussed here. spectra shown in Fig. 7; full and dashed correspond to majority and minority spin, respectively. The numbers in the three columns give SUMMARY energies and spin-up and spin-down intensities for each of the in- dividual lines. Only two of the mj sublevels contribute to each of We have investigated the magnetic linear dichroism in the four spectra. angle-resolved Fe 2p photoemission in transverse geometry, which is an uneven function of the magnetization, so that it heights differing more strongly for magnetization down than appears on magnetization reversal. The dichroism is compa- up is correctly reproduced by the model. Also, the low-BE rable in size to circular dichroism, despite the fact that it is sides of the lines are generally steeper than the high-BE an interference effect. Spin-resolved data have been obtained sides, which is due to the input intensities obtained as in Fig. and analyzed with respect to spin-orbit- and exchange- 7. While these details are in agreement with experiment, the induced effects. The distinction between these two mecha- spin polarization derived in this way is always significantly nisms refers to the spin polarization being governed either by larger and shows more structure than observed in experi- the spin-orbit interaction in the 2p level, making it indepen- ment, despite the use of the empirical sublevel intensities. dent of temperature, or by the exchange interaction. Spin- The experimental majority spectrum for magnetization down orbit-induced spin polarization does not depend on the clearly has a lower threshold than in the model spectrum. sample being magnetically ordered. Using an atomic model, While the atomic model describes the general trends in it was possible to interpret the main trends of the observed agreement with experiment, it appears that for the line spectra, and to connect them with the parameters used to shapes not only of the spin-integrated spectra, but also of the characterize the spin polarization of atomic photoelectrons. spin-resolved ones, some ingredient is missing in the de- According to the atomic model, both linear dichroism and scription. the spin-orbit-induced spin polarization are proportional to Within the atomic model the decrease of intensities of the spin polarization parameter and go to zero if goes to magnetic sublevels with negative mj can be connected with zero. Even though the observed line shapes were not in the dependence of the initial-state wave function of mj , but agreement with experiment, this result is general. The this effect hardly can account for the large differences which exchange-induced polarization, which depends on the split- are apparent in Figs. 6 and 7. Another possibility is the in- ting of the mj levels, is not affected by the spin polarization fluence of the term structure of the final state due to nonzero parameter . The exchange-induced spin polarization in pure total angular momentum of the valence shell, which was also form can be measured either in a geometry in which there is neglected in the atomic model. With regard to MLDAD no magnetic dichroism, or by averaging over both magneti- 12 194 F. U. HILLEBRECHT et al. 53 zations. From the analysis of the spin-resolved data for the a number of theoretical analyses,24,33,35,36 as well as by the p12 state we determined the splitting between the mj sublev- analysis given here. For the Fe 2p level, there are to date no els to 0.5 0.1 eV. experimental results on circular dichroism similar to the re- The rich structure observed in the spin-resolved spectra is sults shown here for linearly polarized light which allow a at present not fully understood. The spin-orbit polarization detailed comparison. As the high quality of the present data apparently deviates from the sum rule that its integral should shows, the study of magnetic dichroism using linearly polar- vanish. The finite spin-orbit polarization between the two ized light is a viable alternative to the use of circular dichro- main photoemission peaks appears to be related to the non- ism. The high flux and nearly 100% polarization provided at vanishing magnetic circular as well as linear dichroism in state-of-the-art synchrotron beamlines, combined with effi- this region. The influence of photoelectron diffraction28,49 on cient spin analysis, allows one to achieve high energy reso- magnetic dichroism, for which evidence was found here, as lution in spin-resolved studies on the 2p levels of the 3d well as on spin polarization has to be incorporated in an transition metals. analysis of magnetic dichroism. In our initial experiments on magnetic linear dichroism21 ACKNOWLEDGMENTS on the Fe 3p level we studied also circular dichroism on the same samples under identical conditions.42 It was noticed It is a pleasure to thank T. Mo¨ller and F. Federmann of that the asymmetry showed the same spectral dependence in HASYLAB for help in running the fabulous BW3 beamline. both cases;42 there was, however, a difference in the size of Funding by the Bundesministerium fu¨r Forschung and Tech- the linear and circular dichroisms. The observed linear di- nologie BMFT under Grant No. 05 5PF DAB 3 as well as chroism was larger than the circular one; however, taking the by the Deutsche Forschungsgemeinschaft DFG within finite degree of circular polarization into account, the asym- Project SFB 166/G7 is gratefully acknowledged. N.A.C. metry in circular dichroism was about 32 times that of linear would like to express his gratitude to the Alexander von dichroism. The close similarity of the dichroisms was an Humboldt-Stiftung for financial support and to Bielefeld empirical indication suggesting that the underlying physics is University for the hospitality extended to him during his stay the same in both cases.42 This view has been substantiated by there. *Permanent address: State Academy of Aerospace Instrumentation, ings No. 313 Materials Research Society, Pittsburgh, 1993 , p. 190000 St. Petersburg, Russia. 589. 1 C. S. Fadley, D. A. Shirley, A J. Freeman, P. S. Bagus, and J. V. 14 N. A. Cherepkov, Sov. Phys. 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