Application of photoelectron diffraction theory to circular dichroism and spin-polarized photoelectron emission

Journal of Electron Spectroscopy and Related Phenomena 80 (1996) 137-142

Application of photoelectron diffraction theory to circular dichroism and spin-polarized photoelectron emission M.A. Van Hovea, A.P. Kaduwela~'b, H. Xiao~'b, W. Schattke c, and C.S. Fadleya'b Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA b Department of Physics, University of California - Davis, Davis, CA 95616, USA Institut ~ Theoretische Physik, Physikzentrum, Universitiit Kiel, D-24118 Kiel, Germany

We have developed theoretical methods for calculating the circular dichroism (CD), spin polarization (SP), magnetic circular dichroism (MCD), and magnetic linear dichroism (MLD) in core-level photoemission with circularly-polarized and linearly-polarized light. The formalism generalizes our previous computer codes for a fully-converged multiple-scattering treatment of photoelectron diffraction. The results of these new calculations are compared to experimental data from various groups for several illustrative cases: CD in photoemission from "non-chiral" surfaces [CO on Pd(lll), and Si(001)], SP photoemission from nonmagnetic and magnetic atoms and surfaces [Xe, W(110), and Fe(110)], and MCD from Fe(110). We discuss the conditions that give rise to circular dichroism in the absence of structural chirality or magnetism. We also emphasize the strong interplay between non-magnetic CD and magnetic CD, as well as the highly anisotropic behavior of SP emission and its importance in SP photoelectron diffraction studies of magnetic order.

1. INTRODUCTION The availability of high-intensity synchrotron radiation with polarization that is variable between circular and linear has led to a number of recent studies of circular and linear dichroism in core-level excitation. Such dichroism can be detected most simply via the x-ray absorption coefficient, leading for example to magnetic circular dichroism (MCD) or spin polarized extended x-ray absorption fine structure (SPEXAFS), or, in a more detailed view of the excitation, via the energy and angular distributions of the photoelectrons emitted from the core level, leading for example to circular dichroism in photoelectron angular distributions (CDAD) or spin polarized photoelectron diffraction (SPPD). This family of techniques thus provides versatile new probes of the short-range positional and magnetic order around a given type of absorbing atom. In this paper, we present theoretical calculations of the photoelectron emission process, 0368-2048/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved PII S0368- 2048 (96) 02941-6

in particular treating the excitation of a spin-orbitsplit core level near a surface with radiation of arbitrary polarization, and including all of the finalstate scattering and diffraction processes during photoelectron escape. Our results are compared to experimental data for both non-magnetic and magnetic systems, and their implications for both photoemission and x-ray absorption studies are discussed. Our theoretical methodology for calculating circular dichroism (CD) and spin-polarization (SP) in photoelectron emission starts with the separable Green's function method of Rehr and Albers [1], as implemented in a multiple-scattering cluster algorithm by Kaduwela, Friedman and Fadley [2]. This method was previously shown to be very successful with unpolarized and linearly polarized photoelectron excitation. Circular polarization is implemented simply by introducing the operators i + i9 (for light propagation along direction z), rather than the operators i or 9 as in the linearly

138 polarized case, thereby allowing m j --->m j + 1 transitions to occur. Magnetic effects are represented by the inclusion or exclusion of an exchange term in the atomic scattering. The codes allow any relative orientation of incident light, crystal axes, magnetization, emission and detected electron spin, with more details appearing elsewhere [3].

3. CD IN PHOTOEMISSION FROM "NONCHIRAL" Si(001)

(a) LCP

EXPERIMENT (b) RCP

[ll0] 2. CD IN PHOTOEMISSION FROM "NONCHIRAL" CO ON P d ( l l l )

As a first application of this methodology, we have performed CD calculations for an experiment involving CO molecules adsorbed on a P d ( l l l ) surface, as performed by Bansmann et al. [4]. The surface was illuminated with right- and left-circular polarized synchrotron radiation incident 50 ° from the surface normal. Core photoelectrons were emitted from the C ls level and detected along an arc that included the normal emission direction. Except at normal emission, one has chiral asymmetry due to the handedness of the light, even if the atomic locations are symmetrical, i.e. even if they show no handedness. As a result, one expects and finds in general a difference between the emission intensities due to right- vs. left-circularly polarized (LCP vs. RCP) light. The asymmetry ACD is defined as the ratio of the difference to the sum of the photoemission intensities with right- vs. leftcircular polarization. This angle-dependent asymmetry was measured at a series of electron kinetic energies in the range 22-97 eV, and large effects of up to 50-75% are found. Our calculations [5] fit the data well over the entire angle and energy ranges, and also agree well with earlier free-molecule calculations by McKoy and Stephens [6]. This indicates a relatively small dependence on the positioning of the CO molecules with respect to the underlying metal surface, due to the relatively large distance between molecule and metal. Nonetheless, the calculations predict enough sensitivity to these geometrical parameters to expect the possibility of determining the molecular adsorption geometry from careful and extensive experiments of this type, for example, by fitting curves calculated for various adsorption geometries to experiment.

(c) LCP

THEORY (d) RCP .2

.2 il lo]

(e) Unpolarized

[1 lO]

Figure 1. (a), fro): Photoelectron diffraction patterns for Si 2p emission from Si(O01) at 250 eV electron kinetic energy, observed by Daimon et al. [7]. The center of each pattern is normal emission, while the circular edges are about 45 ° fi'om normal emission. Patterns (a) and (b) were obtained with LCP and RCP, respectively. The crosses indicate rotated peak positions predicted by the forward scattering model of Daimon et al. (c), (d): The corresponding calculated patterns, including multiple scattering and full final-state interference between the s attd d channels. (e) The calculated result for unpolarized light, which can be obtained from the average of patterns (c) and (d).

139

CD in photoemission has also been measured for a clean non-magnetic single-crystal substrate by Daimon et al. [7]. The experiment involved 2s and 2p emission from Si(001) with electron kinetic energies from 150 to 450 eV, and yielded 2dimensional angular maps of emitted intensities at all azimuths over a polar angle range of about 0 to 45 ° from the surface normal, as exhibited in Figs. l(a) and (b). Even though the light incidence direction was normal to the surface and the surface structure is non-chiral (it has two mirror planes perpendicular to the surface), chirality was observed, in this case especially in the form of "azimuthal rotations" of the dominant peaks in the photoelectron diffraction pattern. Figs. l(a) and (b) in particular show such intensity peaks rotated counter-clockwise and clockwise, resp., for left- and right-circular polarized incident light. Unpolarized light would show unrotated, averaged positions for these peaks, as our calculation suggests in Fig. l(e). Our CD calculations for the same case, shown in Figs. l(c) and (d), reproduce the experimental observations well. The calculations in particular predict that peak rotations are generally expected with circular polarized light, including for nonchiral surfaces. To explain the origin of the observed peak rotation in simple terms, Daimon et al. [7] have proposed a useful approximate model based on forward focusing. The forward focusing phenomenon is the tendency for electrons to be scattered by atoms preferentially in the forward direction at energies above about 200 eV, as if each atom acted as a converging lens. In this model, the major peaks in Fig. 1 represent the directions from an emitter atom to nearby scattering (i.e. focusing) atoms. However, with circular polarized light, the electron wave hitting a scatterer has a non-zero magnetic quantum number m, as dictated by the dipole selection rule, and this has the effect of rotating the wavefronts by an angle on the order of 5-15 ° , counter-clockwise or clockwise depending on the light polarization. The forward focusing is then also rotated by a similar angle, as observed. To quantitatively predict the rotation angle of each peak, however, requires a full multiple scattering calculation to evaluate the correct strength of the different spherical wave components involved in any given scattering event.

4. SPIN-POLARIZED PHOTOEMISSION FROM ATOMIC Xe AND NON-MAGNETIC W(llO)

We have also calculated the spin polarization (SP) which occurs as a result of the spin-orbit splitting of core levels (the Fano effect) for two cases, and compared our results with experiment: 5p--~s+d photoemission by atomic Xe and 4f--~d+g photoemission from non-magnetic W(110). In the Xe case, Heckenkamp et al. [8] measured SP from the 5pl/2 level as a function of scattering angle at a very low kinetic electron energy of 1.1 eV. Our calculations reproduce the data very. closely, verifying in particular the theoretical approach used here, at least for this relatively simple case. For W(ll0), Starke et al. [9] considered the energy dependence of SP in photoemission from a non-magnetic solid with a fixed scattering geometry, in the much higher kinetic energy range 80-240 eV. The well-resolved spin-orbit-split W 4f7/2 and 4fsa photoemission lines are found to exhibit high polarizations of opposite signs along the light propagation axis: about -35% and +50%, respectively. The ratio of these polarizations, 1.4_+0.1, corresponds closely to the theoretically expected value for free W atoms [10]; Our calculations show that this ratio remains valid also for the solid-state case, even with the inclusion of single and multiple scattering from nearby atoms in the lattice [9]. Fig. 2(a) shows the measured energy dependence of the 4fs/2 SP, compared with calculations for the free atom (done both in a purely free-atom picture [10] and using our code with no scatterers present), and for a large surface-like cluster of atoms (in two azimuthal orientations, one the nominal experimental setting, and one 10° away from this). One finds good agreement, especially with the cluster turned some 10° from the nominal experimental geometry. Fig. 2(b) shows the calculated emission angle dependence of the W 4f5/2 polarization at 134 eV (one of the points in Fig. 2(b)) for a single W atom, while Fig. 2(c) gives the corresponding result for a cluster of 5 atoms (an emitter with 4 scatterers above it). These results further illustrate the strong effect that final-state single and multiple scattering by nearby atoms can have on the outgoing electron polarization.

140

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Figure 2. (a) Photon energy dependence of the spin polarization of the W 4fs/e photoemission peak as excited by circular-polarized light. The experimental data (solid circles) are compared to purely free-atom calculations (solid curve), free-atom calculations from a photoelectron diffraction program with zero-strength scattering (dashed curve), a multiple scattering calculation for a large cluster with the nominal experimental orientation (clash-dotted curve), and the same with the cluster rotated 10 ° azimuthally (doubledoO. (b) Three-dimensional representation of the magnitude of the W 4fx: polarization at 134 e V excitation energy as a function of electron emission direction for a free atom. (c) As (b), but for a 5-atom W cluster including multiple scattering.

5. MAGNETIC CIRCULAR DICHROISM AND SPIN-POLARIZATION IN PHOTOEMISSION FROM FERROMAGNETIC Fe(110) Finally, we present our calculations for both MCD and SP from Fe(ll0), comparing them with two different sets of experimental results available for this system [11,12].

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photoemission from Fe(l lO) with circularly polarized

light. (a) Results of Ebert et al. [ 1 3 I f or LCP light are sho•r as solid and dashed curves. Tire vertical bars represent the simulated intensities for each nb level. (b) Tire dashed lines are the broadened spectra of vertical

bars shown in panel (a). The sum of them for LCP light are shown as a dash-dot curve. The solid curve is for the total spectntm due to RCP light. A linear background as derived from the experiment was added to both spectra. The dotted line is the experimental spectrum of Baumgarten et al. [11] for linearly polarized light. (c) The simulated and experimental IWCD cut~,es.

In the first experiment, Baumgarten et al. [11] measured the photoelectron intensity from the Fe 2pt/2 and 2p3/2 levels of an Fe(ll0) surface using LCP light magnetized along its easy axis. The same measurement was then made with the magnetization direction reversed; the latter is equivalent to measuring the intensity from the first system with RCP light. A previous attempt to simulate these results theoretically has also been made by Ebert et al. [13].

141

Fig. 3 compares our calculated results with those due to Ebert et al. [13] for LCP light and also with experimental results of Baumgarten et al. [11]. Shown in Fig. 3(a) as dashed lines are the spectra for individual mj levels as calculated by Ebert et al. [ 13]; the solid line represents the total spectrum. The vertical bars represent our calculated intensities for each mj level, with these levels being split apart by an empirically-determined exchange splitting as used also by Ebert et al. [13], and intended to allow approximately for the separations of the different final-state multiplets. Our calculation was performed on a 5-atom Fe cluster at the full multiple-scattering level. The dashed curves of Fig. 3(b) show our mj levels of for LCP light, broadened appropriately to yield the experimental peak widths; the sum of these then produced the total spectrum for LCP light, shown as the dot-dash curve. Our total spectrum for the RCP light was also calculated in the same manner. The total spectrum obtained by Baumgarten et al. [11] is also shown in this panel for comparison. We have added a background to our total spectrum to permit a more direct comparison with experiment; this background was derived directly from the experimental data [11]. Finally, fig. 3(c) compares simulated and experimental MCD for this system; note that the experimental effects here are very small, at only a few %. The agreement between these two curves is excellent, especially in view of the fact that we used only a 5-atom cluster to mimic the Fe(110) surface. The second SP experiment on Fe(ll0) was performed using unpolarized AI K~ radiation (1486.7 eV) incident on a magnetized polycrystalline Fe film by Van Campen et al. [12]. In this experiment, the spin polarization of the photoelectrons was directly measured for both the Fe 2pin and 2p3/2 levels. Shown in fig. 4(a) are simulated and experimental spin-resolved spectra for the Fe 2p3/2 level. The A and V symbols represent the spin-up and spin-down experimental spectra with a linear background subtracted from the original experimental data. The calculations which are represented as the solid and dashed curves, were performed on a single Fe atom that is intended to represent a typical atom near a polycrystalline Fe surface, with photoelectron diffraction effects being expected to average out due to the polycrystalline character. The vertical bars

represent the calculated intensities for each mj level. Their separation is identical to that used by Ebert et al. [13] in explaining the prior MCD data. The solid and dashed lines are again the sum of the intensities of our broadened mj levels. The height of the calculated spectra for the spin-up electrons (solid line) has been adjusted to match the experiment. This yields a very satisfactory agreement between the experiment and the simulation for the spin-up intensity. For the spindown intensity we are able to predict the peak width, but the peak heights are not the same. This is at least partly due to the fact that we did not include multiplet-splittings in our simulation, as the higher multiplicity final states arising at lower kinetic energies are always stronger in intensity. Experiment: Van Campen et al. / - Spin Up/Down - Background Theory: E

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Binding Energy (eV) Figure 4. Spin-resolved photoelectron spectra fi'om polyccvstallme Fe 2p3/2 obtained by Van Campen et al. [12] and SP derived form them. Our simulated results are also shown. A linear background was subtracted front original experimental data for direct comparison with theol. The spin-up spectrum was shifted up for clarity.

142 Also shown in Fig. 4(b) are experimental and calculated spin polarizations. It is encouraging that the two curves have the same general shape. The only significant disagreement is that, largely due to our underestimation of the height of the spin-down peak, the calculated spin polarization is only about one-half of the experimental value in the region of maximum intensities (606-607 eV).

and N00014-94-1-0162), by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy (Contract No, DE-AC03-76SF00098), by the San Diego Supercomputer Center, and by the DOE National Energy Research Supercomputing Center. We thank Dr. Kai Starke for providing us with experimental data on W(ll0) prior to publication, and for many useful suggestions.

6. CONCLUSIONS The examples discussed in this paper illustrate the good agreement that can now be obtained between a multiple-scattering formalism of photoelectron diffraction, including circular dichroic and magnetic effects, and experiments performed on a wide variety of systems, from raregas free atoms to magnetic single-crystal surfaces. It should be clear that circular dichroism is a very general effect, which does not require a chiral structure in the classic sense, or the presence of magnetic order. It arises already when the scattering geometry relative to an atomic cluster or surface shows asymmetry, e.g. when the incident photon direction and/or the emitted electron direction break left/right symmetries (mirror planes) of the system. Another important observation is that magnetically induced dichroism, which is generally weak, rides on top of structural dichroism, which can be much stronger and is generally highly anisotropic. It is therefore imperative to choose the scattering geometry correctly and accurately in order to extract magnetic information from magnetic diehroism. Finally, excitation of spin-orbit-split levels in any atom with circularly-polarized light produces highly spin-polarized outgoing electrons, but with a polarization distribution that is highly anisotropic in space. This anisotropy should be useful in probing short-range magnetic order via SPEXAFS or SPPD, but it must also be allowed for in the theoretical interpretation of suclr experiments.

ACKNOWLEDGMENTS

This work was supported in part by the Office of Naval Research (Contract Nos. N00014-90-5-1457

REFERENCES

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