We demonstrate that the temperature dependence of structural as well as magnetic fluctuations can be probed by the use of the Magnetic Extended X-ray Absorption Fine Structure (MEXAFS) spectroscopy. We compare those to the dynamic disorder as probed by the EXAFS. Here we present temperature-dependent MEXAFS investigations carried out at the L-edges of a thin Fe film and a Gd single crystal. By comparing the experimental results to ab initio calculations the single-scattering contributions are separated from multiple-scattering contributions. It is found that the multiple-scattering contributions are enhanced for the MEXAFS compared to the normal EXAFS

Arvanitis, D.

Baberschke, K.

Freeland, J.

Idzerda, Y.

Lograsso, Thomas

Poulopoulos, P.

Rogalev, A.

Schlagel, Deborah

Wende, H.

Wilhelm, F.

We demonstrate that the temperature dependence of structural as well as magnetic fluctuations can be probed by the use of the Magnetic Extended X-ray Absorption Fine Structure (MEXAFS) spectroscopy. We compare those to the dynamic disorder as probed by the EXAFS. Here we present temperature-dependent MEXAFS investigations carried out at the L-edges of a thin Fe film and a Gd single crystal. By comparing the experimental results to ab initio calculations the single-scattering contributions are separated from multiple-scattering contributions. It is found that the multiple-scattering contributions are enhanced for the MEXAFS compared to the normal EXAFS.Copyright 2000 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
The following article appeared in AIP Conference Proceedings 514 (2000): 140–147 and may be found at http://dx.doi.org/10.1063/1.1303841.</p

Digital Repository @ Iowa State University (ISU)

On the Temperature Dependence ofMultiple- and Single-ScatteringContributions in Magnetic EXAFSH. Wende1, F. Wilhelm1, P. Poulopoulos1, K. Baberschke1,J.W. Freeland2*, Y.U. Idzerda2, A. Rogalev3, D.L. Schlagel4,T.A. Lograsso4, and D. Arvanitis51Institut fur Experimentalphysik, Freie Universitat Berlin,Arnimallee 14, D-14195 Berlin-Dahlem, Germany2Naval Research Laboratory, Washington, D.C. 20375, USA,3ESRF, B.P. 220, 38043 Grenoble, France,4Ames Laboratory, Iowa State University, Ames, IA 50011, USA5 Department of Physics, Uppsala University, Box 530, 75121 Uppsala, SwedenAbstract. We demonstrate that the temperature dependence of structural as wellas magnetic uctuations can be probed by the use of the Magnetic Extended X-rayAbsorption Fine Structure (MEXAFS) spectroscopy. We compare those to the dynamicdisorder as probed by the EXAFS. Here we present temperature-dependent MEXAFSinvestigations carried out at the L-edges of a thin Fe lm and a Gd single crystal.By comparing the experimental results to ab initio calculations the single-scatteringcontributions are separated from multiple-scattering contributions. It is found thatthe multiple-scattering contributions are enhanced for the MEXAFS compared to thenormal EXAFS.INTRODUCTIONToday, the Extended X-ray Absorption Fine Structure (EXAFS) spectroscopyis a standard tool to in order to investigate local structure and dynamics. Theimportance of its spin-dependent counterpart { the so-called Magnetic EXAFS(MEXAFS) { has been recognized after the rst wiggles in the extended energyrange have been detected in 1989 [1]. Now, adequate literature exists on the the-oretical description of the MEXAFS phenomena [2{4]. In the present work wedemonstrate that a basic understanding of the spin-dependent electron scatteringcan be achieved by comparing ab initio calculations carried out using the FEFF7code [2] with experimental data. We nd an enhancement of the multiple-scatteringcontributions for the magnetic EXAFS compared to the normal EXAFS. The sep-aration of the multiple- from the single-scattering paths can be easily carried outby 'turning o' the contributions of the multiple-scattering paths in the calcula-tions. The use of this computational tool assisted us to develop a better insightinto the spin-dependent electron scattering. Although temperature-dependent EX-AFS measurements have been shown to provide essential information on the localdynamics, it is surprising that only few MEXAFS measurements have been carriedout as a function of temperature [5{9]. Here we present temperature dependentMEXAFS measurements at the L3;2-edges of a polycrystalline Fe lm and at theL3-edge of a Gd single crystal. After the separation of the multiple- from single-scattering paths, the temperature dependence of those contributions can be studiedindividually.EXPERIMENTAL DETAILSThe Gd single crystal was investigated at the ID12A beamline of the ESRF.The crystal had the shape of a plate and was magnetized normal to the surface(hard axis). The measurements were carried out at normal x-ray incidence usinguorescence yield. The MEXAFS measurements of the polycrystalline Fe lm havebeen carried out at the NRL facility located at the U4B beamline of the NSLS.The lm was magnetized in-plane (easy axis). The data were taken at 45Æ x-rayincidence in transmission geometry. The comparison of the normal EXAFS of thepolycrystalline lm to data recorded for an epitaxially grown Fe lm on a Cu(100)substrate revealed that the polycrystalline lm is well ordered on a local scale [8].We have shown earlier that the overlap of the L3- with the L2-edge does not hinderthe MEXAFS analysis [5{9]. The data for the Gd and the Fe samples were taken inan applied magnetic eld high enough for magnetic saturation as was determinedby means of element-specic hysteresis loops.RESULTS AND DISCUSSIONWe start with a qualitative discussion of the temperature dependence of theMEXAFS and EXAFS oscillations at the Gd L3-edge. The experimental dataare presented in Fig. 1 for two temperatures (10K and 250K). The upper panelshows the EXAFS wiggles which exhibit a clear temperature-dependent damping.Using a correlated Debye-model we determine a Debye-temperature of D=155K.This justies the strong reduction of the EXAFS wiggles at 250K > D since oneexpects an exponential attenuation via the EXAFS Debye-Waller factor e 22k2.Here, 2 is the mean square relative displacement. The exponential damping is seenclearer when the intensity decrease at low k-values is compared to the damping athigher k-values. At k=4.5A 1 the EXAFS signal at 250K is reduced to 69% of the10K value whereas at k=10.0A 1 the signal decreases to 16%. A similar dampingof exponential form is found for the MEXAFS. This indicates that the thermalvibrations inuence the magnetic EXAFS signal as well. Furthermore, there is atleast an additional damping for the MEXAFS as the temperature increases due tothe reduction of the magnetization.We have observed such eect for Gd, Fe and Co [5{9]. This indicates that sucheects are general in nature and are not linked to the specic electronic structure ofthe material. In order to discuss the dierent aspects of the temperature-dependent4 6 8 10 12-0.015-0.010-0.0050.0000.0050.0100.015MEXAFSk χ M(k) [Å-1]k [Å-1]-0.15-0.10-0.050.000.050.100.150.20EXAFS 10K 250Kk χ(k) [Å-1]FIGURE 1. Temperature dependent Gd EXAFS k(k) and MEXAFS kM (k) taken at the L3edge.damping of the EXAFS and the MEXAFS in more detail, we now turn to a quanti-tative discussion for the EXAFS and MEXAFS of a polycrystalline Fe lm. Beforeinvestigating the temperature dependence, it is useful analyze the Fourier trans-formed EXAFS and MEXAFS data at the lowest temperature. For a better under-standing of the contributing scattering paths theoretical calculations were carriedout using the ab initio FEFF7 code [2]. The results are presented in Fig. 2 where theFourier transform of (a) the EXAFS and (b) the MEXAFS oscillations are shown.In both cases the dotted lines represent the results using single-scattering pathsonly. The calculations including single- and multiple-scattering contributions aregiven as solid lines. These calculations combining multiple- and single-scatteringare in good agreement with the experimental data as can be seen in comparisonto the inset of Fig. 3 and in Refs. [7,8]. The main peak of the EXAFS as wellas the MEXAFS is determined by the nearest (1-2-1) and the next nearest (1-3-1)neighbor single-scattering paths. Comparing the calculation for the second andthe third peak in the Fourier transform of the EXAFS and the MEXAFS a clearenhancement of the multiple-scattering contributions can be determined for themagnetic case. The triangular scattering path 1-2-3-1 contributes about 20% tothe intensity of the second peak for the normal EXAFS whereas a contributionof about 40% is found for the MEXAFS. The enhanced multiple-scattering is alsofound for the third peak. Here numerous multiple-scattering paths are identied.The strongest contribution is due to the focusing path 1-2-6-2-1. For the thirdpeak of the MEXAFS Fourier transform the multiple-scattering paths dominatethe single-scattering ones, as about 65% of the peak intensity are due to multiple-scattering. A contribution of 50% only is found for the normal EXAFS. The en-hancement of the multiple-scattering paths for the MEXAFS can be described ina phenomenological picture as discussed in Ref. [10]. The eect of the exchangeinteraction is introduced into the scattering process by means of a spin-dependentscattering amplitude FM . This is scaled by the spin-polarization hzi and is addedto the Coulomb scattering amplitude F0. Therefore, the backscattering amplitudebecomes F = F0hziFM for right and left circularly polarized light, respectively.The backscattering amplitude for a multiple-scattering path of n scattering eventscan then be approximated to:(F0 + hzi  FM)n  F n01 + n  hzi FMF0: (1)Thus, the multiple-scattering contributions can be enhanced for the MEXAFS bythe factor n compared to the normal EXAFS.Since the individual contributions to the Fourier transform peaks have been iden-tied by means of the ab initio calculations, we now turn to the analysis of theexperimental results. The temperature-dependent Fourier transforms of the exper-imental EXAFS and MEXAFS oscillations for the polycrystalline Fe lm are pre-sented in the inset of Fig. 3. A clear temperature-dependent damping can be seenfor both cases. It was shown earlier that the lattice vibrations which determine thedamping of the EXAFS are well described by a Debye-Temperature of D=520K [7]analyzing the rst EXAFS peak. An even stronger temperature-dependent damp-ing is found for the rst MEXAFS peak. We try now to correlate this damping tothe magnetic part of the disorder. We show in Fig. 3 the reduced spontaneous mag-netization as a function of the reduced temperature together with the intensity ofthe near edge Magnetic Circular X-ray Dichroism (MCXD) signal and (a) the rst,(b) second and (c) third EXAFS and MEXAFS Fourier transform intensities. For0 2 4 60.0000.0050.0100.0150.0200.025|FT[ k χ L3  (k)]| (arb. units)(b)   MEXAFS|FT[ k χ M,L3(k)]| (arb. units)1-5-11-4-11-3-11-2-1 Theory MS+SS Theory SSR (Å)1-2-5-11-2-4-11-2-3-1 1-2-6-2-1  1-3-4-10.0000.1000.2000.3000.400(a)   EXAFS Theory MS+SS Theory SSFIGURE 2. Ab initio calculation of Fourier transforms jFT [kL3(k)]j and jFT [kM;L3(k)]j of(a) the EXAFS (b) and MEXAFS oscillations for Fe bcc structure at 70K using the FEFF7 code.The single-scattering contributions (dotted lines) are separated from the combined multiple- andsingle-scattering contributions (solid lines). The peaks are assigned to the dierent scatteringpaths which are labeled according to the inset.a relative comparison, the MCXD as well as the EXAFS and MEXAFS intensitiesare scaled to match the literature at the lowest temperature. The MCXD signalfollows the temperature dependence of the magnetization as shown in Fig. 3(a).This is not the case for the rst EXAFS and MEXAFS peak of the Fourier trans-form. First we discuss why the EXAFS peak exhibits a much stronger temperaturedependence. The temperature dependence of the normal EXAFS is determinedby the Debye-temperature of D=520K. Therefore a much stronger damping is0.00.10.20.30.40.50.60.70.80.91.0(b) Literature EXAFS 2. peak MEXAFS 2. peak σs/ σ s(0)0.0 0.1 0.2 0.3 0.4 0.50.00.10.20.30.40.50.60.70.80.91.0(c) Literature EXAFS 3. peak MEXAFS 3. peak σs/ σ s(0)T/Tc0.00.10.20.30.40.50.60.70.80.91.0(a)|FT[k χM,L3(k)]| |FT[k χL3(k)]| 70K200K300K400K0 . 00 . 10 . 20 . 30 2 4 60 . 0 0 00 . 0 0 50 . 0 1 00 . 0 1 50 . 0 2 0R  ( Å ) Literature MCXD  EXAFS 1. peak MEXAFS 1. peak σs/ σ s(0)FIGURE 3. Temperature dependence of the EXAFS and MEXAFS Fourier transform intensi-ties for the polycrystalline Fe lm. The reduced spontaneous magnetization is given as a functionof the reduced temperature (taken from the literature [11]). The Fourier transform intensities arescaled to match the literature values at the lowest temperature. The inset shows the temperaturedependence of the Fourier transforms for the experimental EXAFS (top) and MEXAFS (bottom)oscillations.found at T=400K (which corresponds to a reduced temperature of T=TC=0.38)in comparison to the reduction of the MCXD signal which is determined by theCurie-temperature of TC=1050K. This is due to the fact that up to a reduced tem-perature of T=TC  0:3 the attenuation of the MCXD signal is described by a1 T32 law. This shows a much smaller temperature-dependent decrease than theexponential damping which describes the normal EXAFS. A surprising result istherefore the even stronger temperature dependence of the rst MEXAFS Fourierpeak in comparison to the EXAFS signal (Fig. 3(a)). At a temperature of 400K(T=TC=0.38) the MCXD signal is reduced to only 97% of the T=0K value whereasthe EXAFS signal is reduced to 74%. This shows that a simple multiplication ofthose values leading to 72% does not describe the observed damping of the MEX-AFS of 61% with respect to the T=0K value (Fig. 3). This indicates that there isa larger magnetic disorder on a local scale (probed with the MEXAFS) comparedto the long-range spin uctuations (probed with MCXD) leading to the decreaseof the magnetization. This dierence in the \probing length" of the MCXD andthe MEXAFS technique is due to the fact, that the mean free path of the scat-tered photoelectron is a function of the kinetic energy of the electron and diersfor both cases. In the near-edge energy range (MCXD) the mean free path tendsto diverge and therefore a long-range order is probed. In contrast, the MEXAFSprobes the magnetism on a nearest neighbor length scale due to its more local-ized scattering origin and the fact that the mean free path exhibits a minimum ofabout 7A at k=3.0A 1 and increases to about 30A at k=13.0A 1. Up to now wediscussed the rst peak of the Fourier transform which includes single-scatteringcontributions only. The second and third Fourier transform peaks contain strongmultiple-scattering contributions for the MEXAFS case as can be seen in Fig. 2.This can be the origin of the observed anomaly in the damping of the MEXAFSsignals around T=TC=0.18, where a slower intensity decrease is observed (see Fig.3 (b) and (c)). It is known that multiple-scattering contributions exhibit a strongertemperature-dependent damping. Therefore the damping of the multiple scatter-ing paths will be seen mostly at lower temperatures, whereas the damping of thesingle-scattering paths will become eective at higher temperatures. Indeed forthe second as well as the third peaks the same trend of a stronger temperature-dependent damping of the MEXAFS in comparison to the EXAFS is found in Fig.3 (b) and (c) around T=TC=0.4. These observations allow us to set boundaries tothe temperature range in which each of those two mechanisms is mostly responsiblefor the damping.CONCLUSIONWe have presented two temperature-dependent magnetic EXAFS studies. Forthe Gd single crystal as well as for the polycrystalline Fe a clear temperature-dependent damping for the normal EXAFS and the magnetic EXAFS were deter-mined. The quantitative analysis for the polycrystalline Fe lm shows that thermalvibrations also inuence the MEXAFS signal. The comparison of the damping ofthe normal EXAFS with the MEXAFS demonstrates that there must be a higherlocal magnetic disorder compared to the long-range order probed with MCXD. Abinitio calculations carried out with and without multiple-scattering contributionsclearly indicate an enhancement of multiple-scattering paths for the magnetic EX-AFS. This separation enabled us to discuss the temperature dependence of theindividual multiple- and single-scattering paths.ACKNOWLEDGMENTSThis work is supported by BMBF (05 SC8KEA-3), DFG (Sfb 290) and ESRF(experiment HE-536). We want to thank J.J. Rehr and A.L. Ankudinov for helpfuldiscussions and providing the most recent FEFF versions to us.REFERENCES*Permanent address: Adv. Photon Source, Argonne, IL 60439, USA1. Schutz, G., Frahm, R., Mautner, P., Wienke, R., Wagner, W., Wilhelm, W., andKienle, P., Phys. Rev. Lett. 62, 2620 (1989).2. Ankudinov, A.L., and Rehr, J.J., Phys. Rev. B 56, R1712 (1997).3. Brouder, Ch., Alouani, M., Bennemann, K.H., Phys. Rev. B 54, 7334 (1996).4. Ebert, H., Popescu, V., Ahlers, D., Schutz, G., Lemke, L., Wende, H., Srivastava,P., and Baberschke, K., Europhys. Lett. 42, 295 (1998).5. Lemke, L., Wende, H., Srivastava, P., Chauvistre, R., Haack, N., Baberschke, K.,Hunter-Dunn, J., Arvanitis, D., Martensson, N., Ankudinov, A., and Rehr, J.J., J.Phys.: Condens. Matter 10, 1917 (1998).6. Srivastava, P., Lemke, L., Wende, H., Chauvistre, R., Haack, N., Baberschke, K.,Hunter-Dunn, J., Arvanitis, D., Martensson, N., Ankudinov, A., Rehr, J.J., J. Appl.Phys. 83, 7025 (1998)7. Wende, H., Freeland, J.W., Chakarian, V.,Idzerda, Y.U., Lemke, L., and Baberschke,K., J. Appl. Phys. 83, 7028 (1998).8. Wende, H., Srivastava, P., Arvanitis, D., Wilhelm, F., Lemke, L., Ankudinov, A.,Rehr, J.J., Freeland, J.W., Idzerda, Y.U., and Baberschke, K., J. Synchrotron Rad.6, 696 (1999).9. Wende, H., Ph.D. thesis, Freie Universitat Berlin, Extended X-ray Absorption FineStructure Spectroscopy of Surfaces and Thin Films: Local Structure, Dynamic andMagnetic Properties, Berlin: Verlag Dr. Koster (1999), ISBN 3-89574-341-010. Schutz, G., and Ahlers, D., in Lecture Notes in Physics: Spin-Orbit-Inuenced Spec-troscopies of Magnetic Solids, edited by H. Ebert and G. Schutz, Berlin: Springer(1996), p. 22911. Stearns, M.B., in Magnetic Properties of Metals, edited by Wijn H.P.J., Landolt-Bornstein, Vol. III/19a, Berlin: Springer (1986), p. 37

On the temperature dependence of multiple- and single-scattering contributions in magnetic EXAFS

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On the temperature dependence of multiple- and single-scattering contributions in magnetic EXAFS

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