Resonant inelastic scattering at intermediate X-ray energies

Journal of Electron Spectroscopy and Related Phenomena 110–111 (2000) 179–187 www.elsevier.nl / locate / elspec

Resonant inelastic scattering at intermediate X-ray energies C.F. Hague a

a,b ,

*, J.-M. Mariot a , L. Journel a , J.-J. Gallet a , A. Rogalev c , G. Krill b , J.-P. Kappler b,d

` et Rayonnement ( UMR 7614), Universite´ P. et M. Curie, 11 rue P. et M. Curie, Laboratoire de Chimie Physique-Matiere F-75231 Paris Cedex 05, France b ˆ . 209 D, B.P. 34, F-91898 Orsay Cedex, France LURE, Centre Universitaire Paris Sud, Bat c ESRF, BP 220, F-38043 Grenoble Cedex, France d IPCMS, 23 rue du Loess, F-67037 Strasbourg, France

Abstract We describe resonant inelastic X-ray scattering (RIXS) experiments and magnetic circular dichroism (MCD) in X-ray fluorescence performed in the 3–5 keV range. The examples chosen are X-ray fluorescence MCD of FeRh and RIXS experiments performed at the L3 edge of Ce. FeRh is antiferromagnetic at room temperature but has a transition to the ferromagnetic state above 400 K. The Rh MCD signal is confronted to an augmented spherical wave calculation. The experiment confirms the predicted spin polarization of the Rh 4d valence states. The RIXS measurements on Ce compounds and intermetallics address the problem of mixed valency especially in systems where degeneracy with the Fermi level remains small. Examples are taken from the 2p → (4f 5d)11 followed by 3d → 2p RIXS for a highly ionic compound CeF 3 and for almost g-like CeCuSi.  2000 Elsevier Science B.V. All rights reserved. Keywords: Inelastic X-ray scattering; Magnetic circular dichroism; Mixed valency

1. Introduction The rapid development of experiments using inelastic X-ray scattering (IXS) and resonant inelastic X-ray scattering (RIXS), in recent years, is the result of progress made with synchrotron radiation sources over a remarkably large portion of the X-ray spectrum. IXS uses mainly hard X-rays (.10 keV), while RIXS has been concerned mostly with soft X-rays (,1 keV). In IXS the actual energy of the incident photons used depends essentially on technical considerations. Owing to the fact that the energy losses of interest are very small, the scattered and *Corresponding author. Tel.: 133-14-427-6615; fax: 133-14427-6226. E-mail address: [email protected] (C.F. Hague).

incident photon energies are almost the same. The energy of the incident photons is irrelevant provided the bandpass is extremely narrow (¯1 meV has been achieved [1]). The incident photon energy is selected for maximum flux, given a particular undulator beamline and the necessary optimization of the monochromator and analyzer both as concerns resolving power and efficiency. Currently the best example of such a set-up is that described by Masciovecchio et al. [2,3] at ESRF. RIXS experiments have been concerned mainly with the electronic structure of the lighter elements (up to the 3d transition metals) in both inorganic and organic solids and gases [4]. This paper describes work performed in the intermediate energy range which can be defined as covering the ¯1–5 keV energy range. It includes, for instance, the 4f → 3d

0368-2048 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 00 )00197-3

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and 3d → 2p radiative transitions of the rare earths and 4d → 2p transitions for the 4d transition elements. Of course synchrotron radiation may also be used for non-resonant X-ray fluorescence, but it is generally only justified where polarized X-rays are needed, as in the magnetic circular dichroism (MCD) experiments to be described here, or if a small spot size is required [5]. In this paper we will briefly cover the use of broad bandpass excitations applied to MCD in X-ray fluorescence involving the valence states of 4d–3d magnetic materials. We then concentrate on the use of RIXS to study correlation effects in Ce compounds and intermetallics. First we will discuss the technical aspects which arise when dealing with the analysis of X-rays in the intermediate energy range.

2. Experimental In recent years, the challenge has been to design monochromators with very high resolving powers for use with high flux (photons / s / 0.1% BW) and especially high brilliance (photons / s / 0.1% BW/ mm 2 / mrad 2 ) undulator beamlines but the experience gained is not directly transposable to X-ray spectrometers for analyzing the energy distribution of secondary X-rays because they are emitted isotropically from a target. Refocusing the X-ray emission is generally not a practical proposition, instead emphasis must be placed on obtaining the largest possible spectrometer acceptance angle. It means that a compromise has to be found between resolution DE and acceptance angle. An efficient way of doing this in the intermediate X-ray energy range is to use a spherically or cylindrically bent crystal spectrometer. In the portable UHV-compatible design we have adopted [6] we use a cylindrical bending device which allows the use of a wide range of crystals. DE 5 (a 2 / 2)R cos u, where 2a is the acceptance angle in the plane of the Rowland circle as determined by the aperture of the analyzing crystal and u is the Bragg angle. The solid angle is optimized if a point source of secondary X-rays is situated on the Rowland circle. The classic way to record simultaneously a broad spectral range is to move the X-ray source to a position inside the Rowland circle so as

to create a virtual extended source on the Rowland circle and to place a position sensitive detector (PSD) on the Rowland circle. Then the effective acceptance angle is reduced, in one dimension, to the width of the diffraction pattern. It introduces extra broadening effects in the other. The choice of detector is clearly important. The efficiency of resistive anode multichannel plate PSD’s [7], though good in the soft X-ray region, drops to below 1% for photon energies above ¯3 keV. Gas-filled proportional counters have a very high efficiency over a wide range of energies, but nonlinearity at high count rates is a limitation. In a bent crystal design described by Brennan et al. [8], the detector is a gas-filled PSD of the backgammon type. If position sensitivity is not required, a normal proportional counter or a solid-state photodiode [9] may also be used with close on 100% efficiency at intermediate photon energies because the radiation is weakly absorbed by the dead layer but sufficiently absorbed by the active layer. They are more difficult to use with low count rates. Avalanche PIN diodes can deal with low count rates but their size (a few mm 2 ) restricts their use to spherically bent crystal spectrometers. All the data presented here were taken with a gas-filled proportional counter. The next factor to influence the choice of a spectrometer is the beamline. Beamline ID12 at ESRF can serve as a reference as it is particularly well adapted to the intermediate energy region. Two branches between them cover approximately 0.5–6.5 keV (2–6.5 keV on ID12A and 0.5–1.5 keV on ID12B). ID12A uses a two crystal [Si(111)] Kohzu monochromator and ID12B a Dragon-like grating monochromator. Concentrating on the important features for RIXS, both beamlines are fitted with mirrors up-stream from the monochromators to absorb most of the heat load and eliminate higher order radiation. Both are fitted with refocusing optics down-stream from the monochromator. In the case of the Dragon beamline, focusing is performed by a spherical concave mirror. ID12A uses mechanically bent mirrors to produce focusing. In either case a line focus of ¯20 mm can be achieved (the beam size is ¯1000320 mm 2 ). To take full advantage of this feature we place the spectrometer perpendicular to the beamline such that the Rowland circle intercepts the beam at the focal

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point. The target is then placed at the focal point and the secondary photons are observed in the horizontal scattering plane. The geometrical limit to resolving power is mainly defined by the size of the source and the energy dispersion. The energy dispersion of a bent crystal spectrometer as a function of Bragg angle is given by DE /E 5 Du cot u. To make DE /E compatible with the size of the source, the Bragg angle should lie in the 608 to 808 range. Then Du is of the order of 30 mrad if one wishes to scan the spectra in 100-meV steps at 5 keV. This is mechanically easy to achieve. A suitable range of crystal lattice spacings is available [10] to meet these requirements. Fig. 1 shows the width of elastically scattered radiation at 4.8 keV using a focal ¯ crystal bent to spot of ¯60 mm and a quartz (2023) a radius of ¯0.5 m. It indicates that a combined resolving power of ¯4500 can be obtained quite readily. For reasons to be explained in the next section, the broad-band excitation for the MCD experiments were performed by placing the sample up-stream

Fig. 1. Elastic peak measured at 4846 eV indicating the overall resolving power of the RIXS experiments described here. The peak is fitted with a Gaussian lineshape with full-width at half maximum of 1.1 eV. A small defect can be seen towards the high energy side of the peak. This is probably due to a less than optimum intersection of the X-ray source with the Rowland circle.

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from the monochromator. This meant that focusing was not available and the size of the source was a 100 mm vertically as determined by the entrance slit fitted to the beamline. In that case the resolving power was estimated to be ¯2500 at 3 keV.

3. X-ray fluorescence MCD in a 4d element Investigating the spin polarization in magnetic materials via X-ray fluorescence is dependent on the availability of circularly polarized synchrotron radiation. In fact, the main criterion for obtaining clear dichroic signals is a very high degree of circular polarization (CP) in the primary beam. Grazingincidence grating monochromators, as used in the energy region of the L2,3 -edges of Fe, Co and Ni, have a very high CP transfer. However, studies at the L2,3 edges of 4d transition metals require the use of a crystal monochromator. In practice, Si(111) doublecrystal monochromators are used to study the Rh and Pd L-edges. The Bragg angle then approaches the Brewster angle so the CP transfer rate is a few percent. By placing the sample directly in the unmonochromatized undulator beam the full circular polarization of Helios II (¯92% CP) [11] was retained in the experiments described in this section. We had shown earlier that magnetic circular dichroism in X-ray fluorescence could be observed with the use of non-monochromatic photons [12]. This is because the excitation of a core electron to the continuum favors the formation of an up or down spin hole according to the handedness of the circular polarization even without involving the empty spin polarized states as in a RIXS experiment [13]. Furthermore, we have demonstrated [14,15] that there are advantages to using the relatively narrow bandpass of an undulator peak such as Helios II on beamline ID12A. By suitably tuning the gap of the undulator, the Lb2,15 (4d → 2p3 / 2 ) fluorescence of Rh was excited 70 eV above the L3 threshold with a bandpass of ¯133 eV (see Fig. 2). The excitation energy is insufficient to excite the L2 and L1 corehole configurations and mainly continuum states are involved. We thus avoid interference from the L2 2 L3 M4,5 and L1 –L3 M4,5 Coster–Kronig transitions. Note that normal non-radiative Auger transitions still

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Fig. 2. Rh Lb2,15 X-ray fluorescence excited with the undulator peak energy tuned to 3500 eV (upper curve) and to 3100 eV (lower curve). The insert shows the energy distribution of the undulator peak.

need to be considered before any quantitative estimates of the dichroism may be performed [16,17]. Here we present FeRh (50 at.% Fe and Rh) as an interesting example of the type of information which may be obtained. At room temperature FeRh is antiferromagnetic (AF) with local moments on Fe of 3 m B . At higher temperatures the CsCl structure is unchanged but it becomes ferromagnetic (FM) and is accompanied by enhanced thermal expansion. The transition temperature is T tr ¯ 400 K as can be seen from our magnetization measurements performed with a vibrating sample magnetometer (Fig. 3). The Curie temperature T C is ¯700 K. Recently Moruzzi and Marcus [18] have performed an augmented spherical wave (ASW) band structure calculation from which they deduce the total energy with the system constrained to have a particular magnetic moment. It allows them to conclude that the AF and FM solutions coexist over a wide range of volume. Their ASW calculation also provides them with the spin-resolved local densities of states (DOS) for the Fe and Rh sites in both the AF and FM states. In the former, the up and down Rh DOS are identical but in the FM state the Rh bands split to give a local moment of 1 m B in good agreement with the conclusions which can be drawn from magnetization measurements under saturation conditions.

Fig. 3. Magnetic moment as a function of temperature for the FeRh sample under study for MCD in X-ray fluorescence. The sample is AF up to ¯400 K then becomes FM. The Curie temperature is situated at ¯700 K.

Our purpose here was to follow the transition from the magnetic to nonmagnetic state as the sample temperature was increased across T C . The Rh 4d → 2p3 / 2 X-ray fluorescence MCD presented in Fig. 4 was obtained by taking the difference between two Rh Lb2,15 emission bands measured for two magnetization directions parallel and antiparallel to the spin of the incoming photons. The applied magnetic field was reversed at each energy step thus avoiding the uncertainties of a normalization procedure. The experimental spectra taken at a measured sample temperature of ¯300 K show a marked dichroic signal. The sum and difference of the spectra for the two magnetization directions are shown along with the ASW DOS in Fig. 4. The vertical line indicates the Fermi energy (EF ). In the experiment the position of EF is estimated from the binding energy of the 2p3 / 2 core level. Measurements performed at ¯450 K (not shown) revealed no dichroic signal indicating that the sample had in fact gone through T C . This is a very useful illustration of temperature effects which need to be taken into consideration when unfiltered radiation from an undulator peak is used to excite spectra. The heat transferred from the incident beam (its attenuation

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Fig. 4. (a) MCD in X-ray fluorescence for Rh in FeRh in the FM state. Also shown is the sum of the Rh Lb2,15 emission bands for each direction of magnetization; (b) spin polarization calculated for Rh sites in FeRh (deduced from an ASW calculation [18]); (c) spin resolved local DOS of Rh in FeRh in the FM state according to Ref. [18].

length is ¯0.6 mm under these excitation conditions) has a critical impact on the temperature locally. The interpretation we can give to the shape of the dichroic signal is suggested by the calculation and indeed the calculated DOS are qualitatively confirmed by our experiment (note that transition matrix elements are not included). Close to EF the DOS for up-spins is strong due to hybridization with the Fe up-spin states. Approximately 3 eV below EF , there is an increased contribution from down-spins compared to up-spins, which explains that we observe a negative signal in this region. The measured MCD is small (here ¯1.5%). Several reasons may be invoked. One is that the decay does not reflect the statistical weight expected from the core level spin polarization rates. This is mainly due to other relaxation processes before radiative decay. It should be born in mind also that the applied magnetic field is relatively small. From Fig. 3 it will be seen that a field of 1.3 kOe results in a magnetic moment of 0.5 m B per formula unit compared to 1.6 m B at saturation. The spectra were recorded under roughly equivalent conditions. Another limitation to MCD in

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X-ray fluorescence is the overall resolution of the experiment. It is evident that there is no significant structure in the Rh Lb2,15 emission band so we would not expect to detect any of the fine structure predicted in calculated spin polarization. Even so it is apparent that the general shape of the spin polarization may be determined. This information is not readily available by other techniques in an alloy. We have not performed X-ray fluorescence MCD at the Fe L2,3 edges, but the calculation indicates that the spin polarization of the Fe 3d DOS in the ferromagnetic state is closely similar to that for elemental Fe. We therefore conclude from the good agreement between experiment and theory concerning spin polarization at the Rh sites that the magnetization reflects hybridization between the 3d and 4d states. Certainly these MCD experiments remain difficult to interpret because, as already mentioned, competing relaxation processes have to be taken into account. However, just as X-ray emission spectroscopy is a tool for measuring the partial local densities of states in complex materials, MCD in X-ray fluorescence can be valuable in helping to understand the hybridization and exchange coupling mechanisms which determine the local spin polarization.

4. Correlation effects in Ce RIXS experiments which monitor the energy-resolved decay of an absorption process (or the X-ray Raman process if the excitation is below threshold) were originally motivated by the possibility of eliminating core-lifetime broadening [19–21]. Such experiments use very well monochromatized photons to excite the core electron and a narrow energy bandpass for the analyzer. However, Carra et al. [22] have demonstrated that such a procedure leads to an incomplete picture of the spectral densities of states. A correct picture can only be reconstructed from energy scans of the scattered photons as a function of incident photon energy across the absorption edge. Krisch et al. [23] were the first to perform such an experiment with a rare earth and to fully analyze the 2p 6 4f 7 → 2p 5 4f 5 → 2p 6 3d 9 4f 8 process in Gd. Note

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that it involves a quadrupole transition to the intermediate state. We have studied the 2p3d RIXS in a number of Ce compounds and intermetallics. A particularly good illustration of the results which may be obtained is provided by the Ce L3 RIXS spectra of CeF 3 , a highly ionic compound in which Ce has the 4f 1 5d 0 configuration in the ground state. The RIXS data (taken from Ref. [24]) are shown in Fig. 5 on an energy transfer scale, along with with the Ce L3 X-ray absorption spectrum (XAS). The configuration of Ce following the excitation of the 2p3 / 2 core 5 2 0 electron (intermediate state) will be either 2p 4f 5d or 2p 5 4f 1 5d 1 . The former configuration may result from a quadrupole transition only, while the latter

Fig. 5. Ce L3 XAS spectrum for CeF 3 (top panel); 2p → (4f 5d)11 followed by 3d → 2p RIXS process plotted on an energy transfer scale (excitation energy–scattered energy).

corresponds to a normal dipole transition. 4f 2 5d 0 is well screened by the two 4f electrons and so must be more tightly bound. The peak at 878 eV corresponds to a highly localized 2p 6 3d 9 4f 2 final state. The localization is confirmed by the fact that the peak remains at constant energy transfer; it is an X-ray Raman transition. It reaches peak intensity for a primary photon energy of 5719.2 eV. It will be noted that the energy loss is comparable to the Ce 3d binding energy given by X-ray photoelectron spec9 2 troscopy (XPS) for Ce compounds in a 3d 4f final state [25]. A structure ¯3.5 eV above this feature is 9 2 interpreted as corresponding to a 3d 4f configuration with antiparallel spins [26]. As the excitation energy is increased, the intensity of the dipole contribution situated at 887 eV rises rapidly as we approach the maximum of the absorption white line. For excitations above the white line the main decay channel is normal X-ray fluorescence. This shows as a dispersion of the X-ray emission (curves c–g), i.e., the scattered X-ray energy is unchanged whatever the energy of the incident photons. More surprising is the observation of a strong Raman peak which persists at an energy transfer of ¯888 eV even for excitations above the L3 threshold. It means that there is strong coupling between the core-hole and the excited electron and may be viewed as an excitonic effect (see Ref. [27]). The small offset to higher energies compared to excitation below threshold reflects the width of the 5d band in this compound. Small shifts also observed for excitations just below the white line maximum are simply the consequence of convolution between the incident photon peak and the excitation spectrum. Ce intermetallics are of special interest because they fall into the category of mixed valent systems with varyingly strong correlation effects. For instance Ce metal itself within the same f.c.c. structure has a low temperature paramagnetic phase and a higher temperature magnetic phase corresponding to different localizations of the 4f states. The 4f states are spatially localized with a smaller radial extent than the 5s, 5p wave functions but with an energy comparable to the valence states. Over the years several theoretical models have been developed to explain these properties. The consensus is that in the g (higher temperature) phase the f electrons are localized, whereas in a-Ce the f electrons play some

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part in cohesion. The theoretical description of Ce based on band structure calculations has progressed lately as a result of self-interaction corrections to density functional theory [28–31]. Even so, comparison with high energy spectra is hampered by the presence of large Coulomb interaction between the core hole and an f electron. RIXS experiments involving quadrupole transitions to localized f states may be treated within an atomic model so are well understood [32–35] whereas dipole transitions to less localized hybridized 5d states are more difficult to deal with in such a context. This in itself justifies developing RIXS experiments further. Excitation spectra are best interpreted on the basis of an Anderson impurity model approach. The ground state is described as:

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uCG l 5 c 0G u f 0 v n11 l 1 c 1G u f 1 v n l 1 c 2G u f 2 v n21 l where c 0G , etc., are coefficients. Note that the total electron count must be unchanged and that n50 in the case of CeF 3 . An excitation spectrum will similarly contain a mixture of terms which will depend on their interaction in the final state. In Figs. 6 and 7 we present the Ce L3 XAS spectrum and RIXS data for CeCuSi. Fig. 6 shows a contour plot of the 3d 3 / 2 →2p3 / 2 and 3d 5 / 2 →2p3 / 2 radiative decay. The abscissa is the energy scale of the scattered photons and spectra are stacked in increasing incident photon energies, the values of which are indicated on the XAS curve. Parts of the RIXS spectra can be seen to disperse; others are at constant scattered energy. On this scale dispersion is

Fig. 6. Contour plot of 3d → 2p X-ray emission as a function of excitation energy in the vicinity of the Ce L3 edge in CeCuSi. Spectra are stacked in increasing excitation energies indicated on the XAS spectrum (top panel).

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measured in the total X-ray fluorescence curve but the shape of the 3d →2p radiative decay which contributes to the absorption spectrum is significantly different. This intermetallic compound is g-like, i.e., in the ground state c 1G 4 c 0G and n53. In u-like compounds extra structure is observed in the absorption spectrum and the RIXS data are also quite different [24]. Full RIXS data-sets such as these used to fix parameters entering model calculations should lead to a better understanding of the interaction between 4f and conduction states. We anticipate that these experiments will be particularly helpful where the interaction is small.

5. Conclusion

Fig. 7. Ce 2p3d RIXS in CeCuSi (the excitation energies are indicated in Fig. 6).

indicative of Raman emission, whereas constant energy indicates normal X-ray fluorescence. The RIXS data is also shown on an energy transfer scale in Fig. 7. There is a marked structure at 879 eV which we attribute to the 4f 2 configuration. The 4f 1 v n11 related peak lies at 885 eV. Spectra are similar to those for CeF 3 except that, as the fluorescence peak shifts away from 885 eV, only a low intensity shoulder is apparent at constant energy indicating a weak X-ray Raman effect above threshold. Even so from the contour plot it is seen that this Raman part of the spectrum extends to at least 12 eV above the white line. It illustrates in part the point made by Carra et al. For instance points e and i have similar intensities on the absorption curve

RIXS and MCD X-ray fluorescence experiments are unquestionably difficult to interpret quantitatively, though powerful theoretical models are being developed [32,33,36]. Here the challenge is to correctly model not only localized electron states which can be dealt with on the same footing as in atomic calculations but also to include as correctly as possible the correlation and relaxation effects. Nevertheless it is becoming more and more apparent that these X-ray fluorescence techniques provide information not easily available from other spectroscopies. Resonant X-ray fluorescence, in particular, makes it possible to spotlight specific excitations such as f n1l , f n , f n21 configurations in rare earths or to probe low energy excitations (see for instance Refs. [37,38]). When dealing with bulk materials or multicomponent materials these techniques are element selective and have low sensitivity to surface contamination. The advantages of using only photons for both the excitation and analysis in the study of magnetic materials and insulators is also clear. They are all well known advantages compared to photoemission techniques. As instrumentation improves, the overall resolving power of the experiments are also improving. RIXS is far from attaining the resolving power of state-of-the-art photoemission though IXS under ideal conditions does. Already, as we demonstrate here, resolution is not very different from standard XPS.

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Acknowledgements We are grateful for stimulating discussions with Jose´ Goulon and for the keen interest he has shown in this work. We would like to thank G. Schmerber ´ for sample preparation and A. Derory for performing the magnetization measurements. CFH acknowledges financial support from the ´ Departement des Sciences Chimiques du CNRS.

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