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A RIXS cookbook: Five recipes for successful RIXS applications
Journal of Electron Spectroscopy and Related Phenomena 188 (2013) 10–16
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Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
A RIXS cookbook: Five recipes for successful RIXS applications J.-P. Rueff a,b,∗ , A. Shukla c a
Synchrotron SOLEIL, L‘Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette Cedex, France Laboratoire de Chimie Physique – Matière et Rayonnement, CNRS-UMR 7614, UPMC, 75005 Paris, France c Université Pierre et Marie Curie, IMPMC, CNRS UMR7590, 4 Place Jussieu, 75005 Paris, France b
a r t i c l e
i n f o
Article history: Available online 23 May 2013 Keywords: Synchrotron RIXS High-pressure Excitations Valence Correlated materials
a b s t r a c t In this “cookbook”, we present some recipes of pertinent Resonant Inelastic X-ray Scattering (RIXS) experiments with a focus on hard X-ray range. As a starter, we discuss the new possibilities of investigation of materials introduced by this method. Our 5 recipes focus on spectroscopic innovations or new physical insights, and the dessert looks very briefly at perspectives for the years to come. © 2013 Published by Elsevier B.V.
1. Introduction Resonant Inelastic X-ray Scattering (RIXS) is becoming a routine technique of investigation of the electronic or magnetic properties of materials. RIXS combines the advantages of resonant X-ray spectroscopy, chemical and orbital selectivity with a unique sensitivity to fundamental excitations of solids and the possibility to measure these at non-zero momentum transfer. As an all photon technique, RIXS is a bulk sensitive probe, offering new possibilities of investigation of materials. RIXS is specially well suited for constrained sample environments such as in a high pressure (HP) cell [1,2] or in a reaction cell for catalysis [3]. Finally the RIXS sharpening effect allows enhanced resolving power with respect to standard techniques (e.g. X-ray absorption) below usual core-hole lifetime broadening. Yet, RIXS is often reputed for its considerable complexity, somewhat precluding its widespread use in the scientific community. In this ‘cookbook’, we provide simple “recipes” using RIXS as the main ingredient with the aim to emphasize some of its most useful aspects for material science by providing examples of recent measurements in the hard X-ray range. The soft X-ray range (see for example Refs. [4–8]) merits a review of its own and is treated in other contributions in this volume. Both RIXS in the hard and soft X-ray regions are complementary. From the technical point of view, the instrumentation, challenges and solutions are completely different. They can however be used to investigate the same
∗ Corresponding author at: Synchrotron SOLEIL, L’Orme des Merisiers, SaintAubin, BP 48, 91192 Gif-sur-Yvette Cedex, France. Tel.: +33 169359670. E-mail addresses: [email protected] (J.-P. Rueff), [email protected] (A. Shukla). 0368-2048/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.elspec.2013.04.014
materials to gain added insights on different physical phenomena such as crystal field excitations, charge transfer excitations, magnetic excitations and the dispersion characteristics of all these. 2. Revolutionize absorption spectroscopy 2.1. Improve resolution beyond natural lifetime broadening A much-acclaimed RIXS feature is its ability to overcome core-hole lifetime broadening effects that cripple standard XAS spectroscopy. In essence, the RIXS sharpening effect is related to the specifics of its cross section [9,10]. The cross section is defined by the Kramers–Heisenberg formula that depicts the absorption of a photon from the ground state |g> to the intermediates states |n> under the action of the transition operator T1 , followed by the secondary emission (transition operator T2 ) toward the final states |f > Lifetime broadening effects are accounted for by Lorenztian functions of width n and f for the intermediate and final states respectively, centered at 1 and 1 − 2 :
2
f |T2 |nn|T1 |g d2 ˛ dω1 dω2 Eg − En + hω1 − in /2 f n
×
f /2 2
(Eg − Ef + hω1 − hω2 ) + f2 /4
The general aspect of the RIXS cross section is shown in Fig. 1 in the usual incident 1 (horizontal) vs. transfer energy 1 − 2 (vertical) axis. Localized features appear at constant final state energy (vertical axis) and resonate at well-defined incident energy
J.-P. Rueff, A. Shukla / Journal of Electron Spectroscopy and Related Phenomena 188 (2013) 10–16
Fig. 1. RIXS intensity map as a function of incident (1 ) and transfer (1 − 2 ) energies (adapted from Ref. [1]).
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Fig. 2. Ce L3 edge in Ce oxides in TFY and PFY modes illustrating the sharpening effect of RIXS (from Ref [6]).
2.2. K-edge MCD with RIXS below the edge while dispersive features above the edge belong to the fluorescence like decay process. Notice that Raman features are elongated along the incident energy axis as a direct consequence of the different lifetime broadening in the intermediate and final states. A standard absorption spectrum can be retrieved form the RIXS map by projecting it onto the incident energy axis. A cut along the main diagonal at fixed emitted energy, yields the so-called partial fluorescence yield absorption spectra (PFY-XAS) (or high-energy resolution fluorescence-detected X-ray absorption spectroscopy (HERFD-XAS) [11]) that mimics XAS without lifetime broadening effects. Indeed, the total PFY-XAS broadening reads:
PFY
1 n2
+
1
−1
f2
As a general rule, the lifetime broadening effect is stronger in the intermediate state with respect to the final state because of the deeper core hole involved, hence n > > f , and PFY ∼ f . With respect to standard X-ray absorption spectroscopy, RIXS therefore provides improved intrinsic resolution. This sharpening effect is illustrated in CeO2 [12]. The standard XAS spectrum at the Ce L3 edge (total fluorescence yield, TFY, measurement) is compared to the same spectrum measured by RIXS in the PFY mode. The broadening contribution is effectively reduced when passing from TFY to PFY mode, with the benefit of a much steeper edge rise, and sharper pre-edge. The latter are crucial spectral feature as they provide a direct access in the hard X-ray range to the 3d electrons at the K-edge of transition metal or 4f/5f electrons at the L3 edge of lanthanides and actinides via quadrupolar transitions. This unique capacity of RIXS to disclose clean pre-edge features offers new possibility of investigation of the electronic properties of materials as discussed below. As already pointed out in Ref. [10], the PFY spectra are not necessarily a high-resolution version of standard XAS. Extra features may appear because of interference effects between the absorption and emission paths in the RIXS process.
An exciting extension of the method was recently proposed with the aim to extract magnetic information out of the pre-edge feature [13–15]. Similarly to X-ray magnetic circular dichroism (XMCD), the measurements are carried out with circular polarized light. By inversing the helicity of the incident photons, it is possible to retrieve a dichroic signal in the pre-edge region of comparable intensity with that obtained at the L2,3 edge while the high photon energy allow in situ, bulk sensitive measurements. As shown in magnetite (Fig. 3), the signal exhibits clear signatures of the 3d magnetism; hence sum rules could be applied. One obvious application would be the investigation of 3d or 4f magnetism under high pressure (Fig. 2). 2.3. Absorption spectroscopy of dilute elements in a matrix A standard absorption spectroscopy procedure involves the detection of fluorescence with a solid state detector with low energy resolution to measure the absorption edge. This measurement, though easy and efficient from the count-rate point of view, can be problematic in the case of samples where the signal of interest is due to dilute impurities embedded in a matrix which itself has a strong ‘parasite’ fluorescence signal in the measured energy range. In this case the much higher energy resolution available from a standard RIXS crystal analyzer spectrometer provides an improved signal to noise ratio of the signal of interest by filtering the unwanted ‘parasite’ signal. This is particularly useful in the case of samples of geochemical interest and such a measurement can be implemented on a standard absorption synchrotron beamline. In the example that we cite the beamline is CRG-FAME (French absorption spectroscopy beamline in material and environmental sciences) at the European Synchrotron Radiation Facility and the signal of interest corresponds to Cu impurities in goethite (␣-FeOOH) [16]. The Cu/(Cu + Fe) mole fraction of the sample is 0.015, and above the Cu K-edge the integrated number of photons from the Cu K␣ fluorescence line is about two orders of magnitude lower than the total number of background photons from the Fe K␣ lines and the Compton scattering peak which account for the parasite signal. Absorption spectra are recorded on the one hand by
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Fig. 3. (a) Fe K-edge in magnetite; (b and c) RIXS-derived dichroic signals acquired at the maximum of K␣1 fluorescence line (dots) or using the integrated intensity [thick (green) line] (from Ref. [7]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
measuring the intensity of the Cu K␣ lines with a standard 13element Ge SSD combined with a chromium filter to attenuate the parasite signal and on the other hand by measuring a fraction of the intensity of the Cu K␣ PFY with the crystal analyzer spectrometer. Fig. 4 shows the Cu K pre-edge thus measured and the improved single-to-noise obtained through the RIXS measurement. 3. Perform ultrafast time resolved spectroscopy (at no extra cost) Fast time resolved spectroscopy is of wide relevance in various fields such as femtochemistry, catalysis, photochemistry, etc. Of particular interest for these is the charge transfer dynamics [17]. A direct and appealing approach to fast dynamics is the pump-probe measurements where relaxation time of the order of 10 fs can be accessed. Though such ultra-fast measurements through IXS are impossible, an alternate and very attractive option for looking at fast dynamical processes is based on the so-called core hole “clock”, where the time scale is given by the core-hole decay. Depending on the energy detuning from the resonance , it is possible to control the effective time scale of the probe according to [18]: −1 =
˝2 + 2
with the core-hole lifetime.
This approach differs fundamentally from pump-probe measurements: (i) the experiments are carried out in the energy domain instead of time domain, (ii) the shortness of the core-hole lifetime gives access to characteristic times «10 fs, barely accessible to pump-probe methods (iii) the technique possesses the element and orbital selectivity of the underlying core spectroscopy. Of importance here is the relaxation process of the excited core electron in the intermediate state: In the case where the system is not isolated, the excited electron may decay before the core hole. We consider that exponential decay laws can describe the different transition rates involved. The relationship between the non-resonant IXES and resonant intensity of the relaxed state IR then reads as: IXES r = IR + IXES c + r where c is the core-hole lifetime broadening (transition rate) and r is the electron relaxation rate. Thus, the evolution of the intensity ratio as function of the incident energy provides fruitful information on the dynamics of the relaxation process (charge transfer) or the details of the tunneling process. Best examples of core-hole clock experiments have been obtained by Resonant Auger Electron Spectroscopy so far, but recent studies have demonstrated the advantage of RIXS [19,20] for this type of experiments. Because RIXS is an all photon technique, fast dynamics in fluid, buried layers, catalytic processes or systems under pressure could be investigated.
4. Determine the spin state of materials
Fig. 4. Comparison of Cu K pre-edge absorption spectra for ␣-FeO(OH) (goethite) containing copper (2000 ppm). Measurements were made in the fluorescence mode using a RIXS crystal spectrometer (from Ref. [8]).
In 3d elements, off-resonant X-ray emission spectroscopy (XES) can be efficiently used as a probe of the metal spin state when performed around the metal K-edge. Among the different decay channels that follows the creation of a 1s core-hole, the K␣ (2p → 1s) and K (3p → 1s) lines are of special interest as they involve a p-symmetry core-hole in the XES final state. Final state interactions between the 2p or 3p core-hole and the spin-polarized 3d band yield the sensitivity to the spin magnetic moment. A closer look at the K emission line shows a splitting of the emission line into several multiplet states determined by both Coulomb and exchange interactions. This produces several satellite features near the main line. As the 3d moment changes, so will the energy splitting and intensity of these satellite features. Thus, XES is a local, bulk probe of the spin state. It is insensitive to long range magnetic order and does not require an applied magnetic field.
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Fig. 5. (a) K␣ and K emission lines in Fe II complex through the low-spin (LS) – high-spin transition (HS) (b) corresponding RIXS intensity maps and close-up on the pre-edge region (upper panels) (from Ref. [12]).
4.1. Spin transition in cross-over complexes “Spin Crossover” compounds are the ideal test bench for spin state transitions. These transition metal complexes are coordination compounds with medium ligand field strength and an electronic configuration ranging between 3d4 and 3d7 . In these systems, the spin state of the molecules can be switched back and forth between low-spin and high-spin states by triggering a redistribution of the 3d electrons among the t2g and eg orbitals either through temperature or pressure change, irradiation with light, or application of a high magnetic field. As spin states can be easily controlled, spin crossover complexes are foreseen for data storage applications and display devices. The symmetry of the metal site, and ground state spin configuration can be tuned by chemical engineering. In a recent study, several of these spin crossovers complexes with Fe3+ , Fe2+ and Co2+ were investigated by RIXS [21]. Fig. 5 summarizes the results obtained for a Fe2+ complex during the low spin (S = 0) to high spin (S = 2) temperature- induced transition. We observed clear signature of the spin transition in the different emission lines (panel a), in the 1s2p-RIXS map and Fe K pre-edge region (panel b).
probably AF fluctuations and the simultaneous existence of these with superconductivity (SC) in the HP hcp phase of Fe brings up the interesting possibility of SC pairing mediated by spin fluctuations. 5. Accurately extract valence in 4f electron systems The 4f valence determines the interaction of f-electrons with the conduction band and hence hybridization effects along with the tendency toward delocalization. Under pressure for instance, valence is expected to rise as f-electrons progressively lose their localized character. The quantitative view of how this happens is of prime importance for the general understanding of f-electron behavior especially in heavy fermion compounds that show intriguing properties such as large effective electron mass or non Fermi liquid behavior around a quantum critical point (QCP). RIXS happens to be a prominent method of investigation of f-electron mixed-valent states owing to its improved resolving power providing higher accuracy when assessing the valence state, and its bulk sensitivity, necessary to explore the complete heavy
4.2. Remnant magnetism in the high pressure hcp phase of iron The high pressure magnetism of Fe is a key to the understanding of electronic, magnetic, and structural properties of 3d electrons. Experimentally it is well established that the HP ␣ (bcc) to (hcp) transition is simultaneously accompanied by a magnetic transition from ferromagnetic to purportedly nonmagnetic states. Theoretically, both the ambient pressure bcc ferromagnetic ground state and the structural and magnetic transitions are predicted as well as AF in the hcp phase. In our experiment we search for magnetism in the HP regime using high-energy XES (measured at ESRF ID16 beam line) [22]. In Fig. 6, we show the variation of the integrated difference (see inset) between the measured K line at a given pressure and a nonmagnetic reference which is taken to be the highest pressure bulk Fe data. Since this is a relative measurement, the ambient pressure value is normalized to unity and the variation of this signal with pressure is used to follow the magnetic transition. The striking conclusion is that bulk Fe remains clearly magnetic for pressures greater than 20 GPa, after the magnetic collapse accompanying the structural transition, which is at different pressures for bulk Fe and Fe nanoparticles. The origin of this magnetism is
Fig. 6. Integrated absolute difference (hatched area shown in the inset) between the Fe K fluorescence measured at a given pressure with respect to a reference for bulk Fe and 10 nm Fe nanoparticles. This signal, used to follow the magnetic transition with pressure indicates remnant magnetism in the high pressure hcp phase (from Ref. [13]).
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Fig. 7. RIXS spectra in CeCu2 Si2 under pressure and low temperature across the valence transition. (Left) PFY-XAS spectra at the Ce L3 edge (from Ref. [16]); (right) RXES, Ce L␣1 line measured in the pre-edge region, at 5718 eV. The f2 , f1 , f0 labels refer to the f-state components of the Ce mixed-valent ground state.
fermion phase diagram. A mixed-valent state can be formally written as a degenerated superposition, in the ground state, of different f-states: |g = cn |fn + cn+1 |fn+1 + cn+2 |fn+2 , with cn the weights of the fcomponents. Core-hole spectroscopy is an efficient mean to access mixedvalent behavior: Core-hole screening on the different f-states lifts the mixed-valent degeneracy; second its short lifetime allows the mixed valent state to be monitored on a fs time scale, comparable to that of mixed valence fluctuations. Most of the results have been obtained so far by X-ray photoemission or X-ray Absorption Spectroscopy (XAS). But the electron detection involved in photoemission precludes high-pressure studies and access to the QCP region, while the lack of sensitivity of XAS may hamper the description of f-electron delocalization process. As discussed earlier, RIXS does not suffer from these limitations. The so-called 2p3d RIXS process is of particular interest for mixed valent materials. The incident energy is set at the L2,3 absorption edge and L␣1 (3d → 2p) line serves for the resonant emission. Both radiative channels (absorption and emission) are necessary to obtain the whole picture of the f-state configuration, but valence can be extracted from the spectral analysis of either absorption or emission. The 2p3d-RIXS method was amply utilized in rare earth and actinides [1,23].
5.1. Valence fluctuation and superconductivity in CeCu2 Si2 A recent example where RIXS is necessary is CeCu2 Si2 , an antiferromagnetic heavy fermion at low temperature and superconductor under pressure with a Tc ∼ 1 K. Interestingly, the superconducting phase extends away from the magnetic phase and QCP showing a resurgence of Tc at high pressure. Unlike the lowpressure superconducting phase (SC I), the high-pressure phase (SC II) is not related to magnetic fluctuations but could be due to a new type of electron pairing triggered by critical valence fluctuations (CVF) [24]. RIXS was used to extract the variation of the Ce valence under both high pressure and low temperature conditions in close proximity of the superconducting SC-II phase [25]. The main results are illustrated in Fig. 7. Both PFY-XAS and RXES spectra show clear sign of mixed valency as well-defined spectral features as indicated. Upon pressure increase, we notice a reduction of the f1 feature while f0 is enhanced; f2 shows little change. A rapid and efficient way to extract the valence is by data fitting. This applies for both PFY-XAS and RXES data but, because of its
simpler lineshape, RXES is undoubtedly a better candidate for the data treatment. A more advanced approach implies simulation of the spectra, as carried out for CeCu2 Si2 within the Anderson Impurity Model (AIM). The valence is found to decrease continuously through the SC-II phase with a clear change of slope at the pressure where Tc reaches a maximum. This result gives strong support to the CVF model.
6. Investigate dispersive behavior of excitations in correlated systems Electronic excitations in materials with strong electronic correlations provide information about the energy and dispersion of empty electronic levels. This information, often unique, is complementary to that about occupied levels provided by spectroscopies such as photoemission. Combining both, a reasonable idea about the electronic structure of these materials can be formed. RIXS has been used in the last few years with this aim [1,26 and references therein]. In this method the incident energy is chosen in the region of an absorption edge. This choice also determines the intermediate state of the scattering process which involves a core hole generated by the incident photon. Electronic decay follows filling the core hole. However the system may nevertheless find itself in an excited final state, resulting in inelastic features. Since the photon can exchange sizeable momentum with excitations in the system, their dispersion can be measured. The method is bulk sensitive, with an enhanced cross section due to the core-hole. The core-hole is however absent from the final state, so that information relevant to the physics of the materials in question is directly obtained. This technique has been used to study the dispersion of electronic excitations so as to determine their nature and to confront them with theoretical predictions of electronic structure and dynamics. Here we cite an example of the utility of this method and the information obtained from it in a study of RIXS [27] at the Cu–K absorption edge in La2 CuO4 and at the Ni–K absorption edge in La2 NiO4 . The cuprates and nickelates are almost completely iso-structural but with remarkably different physical properties. No superconductivity has been reported in the nickelates and metallic behavior arises at very high doping. Ni ions are embedded in O octahedra with a nominally 3d8 electronic configuration. It is known that Ni ions are high spin (HS), with both eg orbitals 3dz2−r2 and 3dx2−y2 occupied by one electron and a total spin S = 1 per Ni ion as opposed to S = 1/2 in the cuprates.
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Fig. 8. RIXS measurements at different Brillouin Zone points at (a) the Cu–K edge in La2 CuO4 . Dispersion of the charge transfer exciton obtained from RIXS measurements for (b) La2 CuO4 and (c) La2 NiO4 (from Ref. [18]).
6.1. Exciton dispersion in cuprates and nickelates The measurements were carried out at SPring-8 on BL12XU. Spherically bent 2 m radius Si analyzers were used to reach a total resolution of 300 meV [28]. In Fig. 8a which shows RIXS scans with the momentum transfer parallel to the a/b axis in samples of La2 CuO4 at an energy loss of 2.2 eV, a peak is seen (arrow) near the center of the BZ, which we assign to the fundamental charge transfer exciton. As the momentum transfer increases from the zone center to the zone edge, the peak disperses to higher energy loss and its intensity simultaneously vanishes, Fig. 8b. The exciton disperses quadratically (dashed line) by about 0.5 eV. In the nickelate, a similar analysis allows us to identify an excitonic peak at about 3.6 eV which loses intensity in going from zone center to edge. However no dispersion is seen (Fig. 8c) indicating complete localization of the charge transfer exciton in La2 NiO4 . The physical insight that can be had from this information is the following. In La2 CuO4 , the CuO2 unit cell in the plane contains one hole on the Cu site. Consider a plaquette consisting of a central Cu atom and four surrounding O atoms. With the transfer of an electron from the O 2p orbitals on the plaquette, a neighboring Cu site assumes the Cu 3d10 configuration. The O 2p hole and the transferred electron can then form a bound exciton. The dynamics of this exciton in the CuO2 plane also depends on the interaction of the O 2p hole and the 3d9 hole on the central Cu of the plaquette. These two holes can interact to form a singlet state or a triplet state. An important consequence of singlet formation on the plaquette is that the exciton which consists of two spinless Cu sites moves through the CuO2 plane without upsetting the AF S = 1/2 background [29]. In the nickelate charge transfer can also potentially result in the formation of a bound exciton and to a spin zero Ni site for a singlet coupling between the spins of the Ni 3d9 (S = 1/2) hole and the (S = 1/2) O 2p hole. But, in contrast to the cuprate, the central Ni site with a 3d8 configuration is high spin (S = 1) [30]. The
direct consequence of this difference is the observed change in exciton dynamics: the single spin zero site in the S = 1 NiO2 AF lattice can only hop by disrupting the AF order [31] and thus should have reduced mobility with respect to the twin spin zero Cu sites in the S = 1/2 CuO2 AF lattice. The very recent example of unraveling magnetic interactions from Irridates further shows that RIXS is becoming a routine technique for mapping magnetic excitations in hard X-ray regime [32]. The extension of the RIXS technique for probing collective magnetic excitations and their dynamics initiated by soft RIXS now provides an alternative to Inelastic Neutron Scattering (INS). 7. Conclusion and perspectives The recipes for the application of RIXS that we have provided in this short cookbook should convince the reader that this method is now fairly widely applicable for a variety of problems of interest in the physics and chemistry of materials and the study of their electronic and magnetic properties. Further developments in this field hinge on the advances that will be made in the instrumental and theoretical domains. Several synchrotron beamlines among which the GALAXIES beamline at SOLEIL synchrotron are in the process of equipping themselves with updated spectrometers which will improve count-rates by one or two orders of magnitude with the use of multiple crystal analyzers and large solid-angle spectrometers. Another, more straightforward development is the integration of simple RIXS spectrometers on existing absorption beamlines. New instruments permitting ultra high resolution (below 100 meV) are currently being developed at third generation synchrotron facilities. This will allow the measurements of low energy excitations (charge, magnetic, orbital) and presumable help to unravel the physics of highly correlated electron systems. On the theoretical front, several developments have been made so as to help interpret RIXS spectra and link measured
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features to predictions from various electronic structure calculations. Both these developments should permit the extended use of this powerful method in the coming future and provide newer and ‘tastier’ recipes. References [1] J.-P. Rueff, A. Shukla, Rev. Mod. Phys. 82 (2010) 847. [2] A. Shukla, J.-P. Rueff, J. Badro, G. Vanko, A.F.M. Mattila, F. de Groot, F. Sette, Phys. Rev. B 67 (081101(R)) (2003). [3] P. Glatzel, et al., J. Am. Chem. Soc. 132 (2010) 2555. [4] J. Schlappa, et al., Phys. Rev. Lett. 103 (2009) 047401. [5] M. Guarise, et al., Phys. Rev. Lett. 105 (2010) 157006. [6] L. Braicovich, et al., Phys. Rev. Lett. 104 (2010) 077002. [7] L.J.P. Ament, et al., Rev. Mod. Phys. 83 (2011) 705. [8] M. Le Tacon, et al., Nature Phys. 7 (2011) 725. [9] K. Hämäläinen, D.P. Siddons, J.B. Hastings, L.E. Berman, Phys. Rev. Lett. 67 (1991) 2850. [10] P. Carra, M. Fabrizio, B.T. Thole, Phys. Rev. Lett. 74 (1995) 3700. [11] P. Glatzel, U. Bergmann, Coord. Chem. Rev. 249 (65) (2005). [12] K.O. Kvashnina, Sergei M. Butorin, J. Pieter Glatzel, J. Anal. At. Spectrom. 26 (2011) 1265. [13] W.A. Caliebe, C.-C. Kao, L.E. Berman, J.B. Hastings, M.H. Krisch, F. Sette, K. Hamalainen, J. Appl. Phys. 79 (1996) 6509. [14] M.H. Krisch, F. Sette, U. Bergmann, C. Masciovecchio, R. Verbeni, J. Goulon, W. Caliebe, C.-C. Kao, Phys. Rev. B 54 (1996) R12673.
[15] M. Sikora, A. Juhin, T.-C. Weng, P. Sainctavit, C. Detlefs, F. de Groot, P. Glatzel, Phys. Rev. Lett. 105 (2010) 037202. [16] J.-L. Hazemann, et al., J. Synchrotron. Radiat. 16 (2009) 283. [17] P.A. Brühwiler, O. Karis, N. Martensson, Rev. Mod. Phys. 74 (2002) 703. [18] F. Gel’mukhanov, H. Agren, Phys. Rep. 312 (1999) 87. [19] T. Marchenko, L. Journel, T. Marin, R. Guillemin, S. Carniato, et al., J. Chem. Phys. 134 (2011) 144308. [20] M. Simon, L. Journel, R. Guillemin, W.C. Stolte, I. Minkov, F. Gel’mukhanov, P. Sałek, H. Ågren, S. Carniato, R. Taieb, A.C. Hudson, D.W. Lindle, Phys. Rev. A 73 (2006) 020706. [21] G. Vanko, T. Neisius, G. Molnar, F. Renz, S. Karpati, A. Shukla, F.M.F. de Groot, J. Phys. Chem. B 110 (2006) 11647. [22] A. Monza, A. Meffre, F. Baudelet, J.P. Rueff, M. d’Astuto, P. Munsch, S. Huotari, S. Lachaize, B. Chaudret, A. Shukla, Phys. Rev. Lett. 106 (2011) 247201. [23] C. Dallera, M. Grioni, A. Shukla, G. Vanko, J.L. Sarrao, J.-P. Rueff, D.L. Cox, Phys. Rev. Lett. 88 (2002) 196403. [24] Y. Onishi, K. Miyake, J. Phys. Soc. Jap. 69 (2000) 3955. [25] J.-P. Rueff, S. Raymond, M. Taguchi, M. Sikora, J.-P. Itié, F. Baudelet, D. Braithwaite, G. Knebel, D. Jaccard, Phys. Rev. Lett. 106 (2011) 186405. [26] L.J.P. Ament, M. van Veenendaal, T.P. Devereaux, J.P. Hill, J. van den Brink, Rev. Mod. Phys. 83 (2011) 705. [27] E. Collart, A. Shukla, J.-P. Rueff, P. Leininger, H. Ishii, I. Jarrige, Y.Q. Cai, S.-W. Cheong, G. Dhalenne, Phys. Rev. Lett. 96 (2006) 157004. [28] E. Collart, et al., J. Synchrotron. Radiat. 12 (2005) 473. [29] F.C. Zhang, K.K. Ng, Phys. Rev. B 58 (1998) 13520. [30] V.I. Anisimov, et al., Phys. Rev. B 59 (1999) 7901. [31] J. Zaanen, P.B. Littlewood, Phys. Rev. B 50 (1994) 7222. [32] J. Kim, et al., Phys. Rev. Lett. 108 (2012) 177003.
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A RIXS cookbook: Five recipes for successful RIXS applications J.-P. Rueff a,b,∗ , A. Shukla c a
Synchrotron SOLEIL, L‘Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette Cedex, France Laboratoire de Chimie Physique – Matière et Rayonnement, CNRS-UMR 7614, UPMC, 75005 Paris, France c Université Pierre et Marie Curie, IMPMC, CNRS UMR7590, 4 Place Jussieu, 75005 Paris, France b
a r t i c l e
i n f o
Article history: Available online 23 May 2013 Keywords: Synchrotron RIXS High-pressure Excitations Valence Correlated materials
a b s t r a c t In this “cookbook”, we present some recipes of pertinent Resonant Inelastic X-ray Scattering (RIXS) experiments with a focus on hard X-ray range. As a starter, we discuss the new possibilities of investigation of materials introduced by this method. Our 5 recipes focus on spectroscopic innovations or new physical insights, and the dessert looks very briefly at perspectives for the years to come. © 2013 Published by Elsevier B.V.
1. Introduction Resonant Inelastic X-ray Scattering (RIXS) is becoming a routine technique of investigation of the electronic or magnetic properties of materials. RIXS combines the advantages of resonant X-ray spectroscopy, chemical and orbital selectivity with a unique sensitivity to fundamental excitations of solids and the possibility to measure these at non-zero momentum transfer. As an all photon technique, RIXS is a bulk sensitive probe, offering new possibilities of investigation of materials. RIXS is specially well suited for constrained sample environments such as in a high pressure (HP) cell [1,2] or in a reaction cell for catalysis [3]. Finally the RIXS sharpening effect allows enhanced resolving power with respect to standard techniques (e.g. X-ray absorption) below usual core-hole lifetime broadening. Yet, RIXS is often reputed for its considerable complexity, somewhat precluding its widespread use in the scientific community. In this ‘cookbook’, we provide simple “recipes” using RIXS as the main ingredient with the aim to emphasize some of its most useful aspects for material science by providing examples of recent measurements in the hard X-ray range. The soft X-ray range (see for example Refs. [4–8]) merits a review of its own and is treated in other contributions in this volume. Both RIXS in the hard and soft X-ray regions are complementary. From the technical point of view, the instrumentation, challenges and solutions are completely different. They can however be used to investigate the same
∗ Corresponding author at: Synchrotron SOLEIL, L’Orme des Merisiers, SaintAubin, BP 48, 91192 Gif-sur-Yvette Cedex, France. Tel.: +33 169359670. E-mail addresses: [email protected] (J.-P. Rueff), [email protected] (A. Shukla). 0368-2048/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.elspec.2013.04.014
materials to gain added insights on different physical phenomena such as crystal field excitations, charge transfer excitations, magnetic excitations and the dispersion characteristics of all these. 2. Revolutionize absorption spectroscopy 2.1. Improve resolution beyond natural lifetime broadening A much-acclaimed RIXS feature is its ability to overcome core-hole lifetime broadening effects that cripple standard XAS spectroscopy. In essence, the RIXS sharpening effect is related to the specifics of its cross section [9,10]. The cross section is defined by the Kramers–Heisenberg formula that depicts the absorption of a photon from the ground state |g> to the intermediates states |n> under the action of the transition operator T1 , followed by the secondary emission (transition operator T2 ) toward the final states |f > Lifetime broadening effects are accounted for by Lorenztian functions of width n and f for the intermediate and final states respectively, centered at 1 and 1 − 2 :
2
f |T2 |nn|T1 |g d2 ˛ dω1 dω2 Eg − En + hω1 − in /2 f n
×
f /2 2
(Eg − Ef + hω1 − hω2 ) + f2 /4
The general aspect of the RIXS cross section is shown in Fig. 1 in the usual incident 1 (horizontal) vs. transfer energy 1 − 2 (vertical) axis. Localized features appear at constant final state energy (vertical axis) and resonate at well-defined incident energy
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Fig. 1. RIXS intensity map as a function of incident (1 ) and transfer (1 − 2 ) energies (adapted from Ref. [1]).
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Fig. 2. Ce L3 edge in Ce oxides in TFY and PFY modes illustrating the sharpening effect of RIXS (from Ref [6]).
2.2. K-edge MCD with RIXS below the edge while dispersive features above the edge belong to the fluorescence like decay process. Notice that Raman features are elongated along the incident energy axis as a direct consequence of the different lifetime broadening in the intermediate and final states. A standard absorption spectrum can be retrieved form the RIXS map by projecting it onto the incident energy axis. A cut along the main diagonal at fixed emitted energy, yields the so-called partial fluorescence yield absorption spectra (PFY-XAS) (or high-energy resolution fluorescence-detected X-ray absorption spectroscopy (HERFD-XAS) [11]) that mimics XAS without lifetime broadening effects. Indeed, the total PFY-XAS broadening reads:
PFY
1 n2
+
1
−1
f2
As a general rule, the lifetime broadening effect is stronger in the intermediate state with respect to the final state because of the deeper core hole involved, hence n > > f , and PFY ∼ f . With respect to standard X-ray absorption spectroscopy, RIXS therefore provides improved intrinsic resolution. This sharpening effect is illustrated in CeO2 [12]. The standard XAS spectrum at the Ce L3 edge (total fluorescence yield, TFY, measurement) is compared to the same spectrum measured by RIXS in the PFY mode. The broadening contribution is effectively reduced when passing from TFY to PFY mode, with the benefit of a much steeper edge rise, and sharper pre-edge. The latter are crucial spectral feature as they provide a direct access in the hard X-ray range to the 3d electrons at the K-edge of transition metal or 4f/5f electrons at the L3 edge of lanthanides and actinides via quadrupolar transitions. This unique capacity of RIXS to disclose clean pre-edge features offers new possibility of investigation of the electronic properties of materials as discussed below. As already pointed out in Ref. [10], the PFY spectra are not necessarily a high-resolution version of standard XAS. Extra features may appear because of interference effects between the absorption and emission paths in the RIXS process.
An exciting extension of the method was recently proposed with the aim to extract magnetic information out of the pre-edge feature [13–15]. Similarly to X-ray magnetic circular dichroism (XMCD), the measurements are carried out with circular polarized light. By inversing the helicity of the incident photons, it is possible to retrieve a dichroic signal in the pre-edge region of comparable intensity with that obtained at the L2,3 edge while the high photon energy allow in situ, bulk sensitive measurements. As shown in magnetite (Fig. 3), the signal exhibits clear signatures of the 3d magnetism; hence sum rules could be applied. One obvious application would be the investigation of 3d or 4f magnetism under high pressure (Fig. 2). 2.3. Absorption spectroscopy of dilute elements in a matrix A standard absorption spectroscopy procedure involves the detection of fluorescence with a solid state detector with low energy resolution to measure the absorption edge. This measurement, though easy and efficient from the count-rate point of view, can be problematic in the case of samples where the signal of interest is due to dilute impurities embedded in a matrix which itself has a strong ‘parasite’ fluorescence signal in the measured energy range. In this case the much higher energy resolution available from a standard RIXS crystal analyzer spectrometer provides an improved signal to noise ratio of the signal of interest by filtering the unwanted ‘parasite’ signal. This is particularly useful in the case of samples of geochemical interest and such a measurement can be implemented on a standard absorption synchrotron beamline. In the example that we cite the beamline is CRG-FAME (French absorption spectroscopy beamline in material and environmental sciences) at the European Synchrotron Radiation Facility and the signal of interest corresponds to Cu impurities in goethite (␣-FeOOH) [16]. The Cu/(Cu + Fe) mole fraction of the sample is 0.015, and above the Cu K-edge the integrated number of photons from the Cu K␣ fluorescence line is about two orders of magnitude lower than the total number of background photons from the Fe K␣ lines and the Compton scattering peak which account for the parasite signal. Absorption spectra are recorded on the one hand by
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Fig. 3. (a) Fe K-edge in magnetite; (b and c) RIXS-derived dichroic signals acquired at the maximum of K␣1 fluorescence line (dots) or using the integrated intensity [thick (green) line] (from Ref. [7]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
measuring the intensity of the Cu K␣ lines with a standard 13element Ge SSD combined with a chromium filter to attenuate the parasite signal and on the other hand by measuring a fraction of the intensity of the Cu K␣ PFY with the crystal analyzer spectrometer. Fig. 4 shows the Cu K pre-edge thus measured and the improved single-to-noise obtained through the RIXS measurement. 3. Perform ultrafast time resolved spectroscopy (at no extra cost) Fast time resolved spectroscopy is of wide relevance in various fields such as femtochemistry, catalysis, photochemistry, etc. Of particular interest for these is the charge transfer dynamics [17]. A direct and appealing approach to fast dynamics is the pump-probe measurements where relaxation time of the order of 10 fs can be accessed. Though such ultra-fast measurements through IXS are impossible, an alternate and very attractive option for looking at fast dynamical processes is based on the so-called core hole “clock”, where the time scale is given by the core-hole decay. Depending on the energy detuning from the resonance , it is possible to control the effective time scale of the probe according to [18]: −1 =
˝2 + 2
with the core-hole lifetime.
This approach differs fundamentally from pump-probe measurements: (i) the experiments are carried out in the energy domain instead of time domain, (ii) the shortness of the core-hole lifetime gives access to characteristic times «10 fs, barely accessible to pump-probe methods (iii) the technique possesses the element and orbital selectivity of the underlying core spectroscopy. Of importance here is the relaxation process of the excited core electron in the intermediate state: In the case where the system is not isolated, the excited electron may decay before the core hole. We consider that exponential decay laws can describe the different transition rates involved. The relationship between the non-resonant IXES and resonant intensity of the relaxed state IR then reads as: IXES r = IR + IXES c + r where c is the core-hole lifetime broadening (transition rate) and r is the electron relaxation rate. Thus, the evolution of the intensity ratio as function of the incident energy provides fruitful information on the dynamics of the relaxation process (charge transfer) or the details of the tunneling process. Best examples of core-hole clock experiments have been obtained by Resonant Auger Electron Spectroscopy so far, but recent studies have demonstrated the advantage of RIXS [19,20] for this type of experiments. Because RIXS is an all photon technique, fast dynamics in fluid, buried layers, catalytic processes or systems under pressure could be investigated.
4. Determine the spin state of materials
Fig. 4. Comparison of Cu K pre-edge absorption spectra for ␣-FeO(OH) (goethite) containing copper (2000 ppm). Measurements were made in the fluorescence mode using a RIXS crystal spectrometer (from Ref. [8]).
In 3d elements, off-resonant X-ray emission spectroscopy (XES) can be efficiently used as a probe of the metal spin state when performed around the metal K-edge. Among the different decay channels that follows the creation of a 1s core-hole, the K␣ (2p → 1s) and K (3p → 1s) lines are of special interest as they involve a p-symmetry core-hole in the XES final state. Final state interactions between the 2p or 3p core-hole and the spin-polarized 3d band yield the sensitivity to the spin magnetic moment. A closer look at the K emission line shows a splitting of the emission line into several multiplet states determined by both Coulomb and exchange interactions. This produces several satellite features near the main line. As the 3d moment changes, so will the energy splitting and intensity of these satellite features. Thus, XES is a local, bulk probe of the spin state. It is insensitive to long range magnetic order and does not require an applied magnetic field.
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Fig. 5. (a) K␣ and K emission lines in Fe II complex through the low-spin (LS) – high-spin transition (HS) (b) corresponding RIXS intensity maps and close-up on the pre-edge region (upper panels) (from Ref. [12]).
4.1. Spin transition in cross-over complexes “Spin Crossover” compounds are the ideal test bench for spin state transitions. These transition metal complexes are coordination compounds with medium ligand field strength and an electronic configuration ranging between 3d4 and 3d7 . In these systems, the spin state of the molecules can be switched back and forth between low-spin and high-spin states by triggering a redistribution of the 3d electrons among the t2g and eg orbitals either through temperature or pressure change, irradiation with light, or application of a high magnetic field. As spin states can be easily controlled, spin crossover complexes are foreseen for data storage applications and display devices. The symmetry of the metal site, and ground state spin configuration can be tuned by chemical engineering. In a recent study, several of these spin crossovers complexes with Fe3+ , Fe2+ and Co2+ were investigated by RIXS [21]. Fig. 5 summarizes the results obtained for a Fe2+ complex during the low spin (S = 0) to high spin (S = 2) temperature- induced transition. We observed clear signature of the spin transition in the different emission lines (panel a), in the 1s2p-RIXS map and Fe K pre-edge region (panel b).
probably AF fluctuations and the simultaneous existence of these with superconductivity (SC) in the HP hcp phase of Fe brings up the interesting possibility of SC pairing mediated by spin fluctuations. 5. Accurately extract valence in 4f electron systems The 4f valence determines the interaction of f-electrons with the conduction band and hence hybridization effects along with the tendency toward delocalization. Under pressure for instance, valence is expected to rise as f-electrons progressively lose their localized character. The quantitative view of how this happens is of prime importance for the general understanding of f-electron behavior especially in heavy fermion compounds that show intriguing properties such as large effective electron mass or non Fermi liquid behavior around a quantum critical point (QCP). RIXS happens to be a prominent method of investigation of f-electron mixed-valent states owing to its improved resolving power providing higher accuracy when assessing the valence state, and its bulk sensitivity, necessary to explore the complete heavy
4.2. Remnant magnetism in the high pressure hcp phase of iron The high pressure magnetism of Fe is a key to the understanding of electronic, magnetic, and structural properties of 3d electrons. Experimentally it is well established that the HP ␣ (bcc) to (hcp) transition is simultaneously accompanied by a magnetic transition from ferromagnetic to purportedly nonmagnetic states. Theoretically, both the ambient pressure bcc ferromagnetic ground state and the structural and magnetic transitions are predicted as well as AF in the hcp phase. In our experiment we search for magnetism in the HP regime using high-energy XES (measured at ESRF ID16 beam line) [22]. In Fig. 6, we show the variation of the integrated difference (see inset) between the measured K line at a given pressure and a nonmagnetic reference which is taken to be the highest pressure bulk Fe data. Since this is a relative measurement, the ambient pressure value is normalized to unity and the variation of this signal with pressure is used to follow the magnetic transition. The striking conclusion is that bulk Fe remains clearly magnetic for pressures greater than 20 GPa, after the magnetic collapse accompanying the structural transition, which is at different pressures for bulk Fe and Fe nanoparticles. The origin of this magnetism is
Fig. 6. Integrated absolute difference (hatched area shown in the inset) between the Fe K fluorescence measured at a given pressure with respect to a reference for bulk Fe and 10 nm Fe nanoparticles. This signal, used to follow the magnetic transition with pressure indicates remnant magnetism in the high pressure hcp phase (from Ref. [13]).
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Fig. 7. RIXS spectra in CeCu2 Si2 under pressure and low temperature across the valence transition. (Left) PFY-XAS spectra at the Ce L3 edge (from Ref. [16]); (right) RXES, Ce L␣1 line measured in the pre-edge region, at 5718 eV. The f2 , f1 , f0 labels refer to the f-state components of the Ce mixed-valent ground state.
fermion phase diagram. A mixed-valent state can be formally written as a degenerated superposition, in the ground state, of different f-states: |g = cn |fn + cn+1 |fn+1 + cn+2 |fn+2 , with cn the weights of the fcomponents. Core-hole spectroscopy is an efficient mean to access mixedvalent behavior: Core-hole screening on the different f-states lifts the mixed-valent degeneracy; second its short lifetime allows the mixed valent state to be monitored on a fs time scale, comparable to that of mixed valence fluctuations. Most of the results have been obtained so far by X-ray photoemission or X-ray Absorption Spectroscopy (XAS). But the electron detection involved in photoemission precludes high-pressure studies and access to the QCP region, while the lack of sensitivity of XAS may hamper the description of f-electron delocalization process. As discussed earlier, RIXS does not suffer from these limitations. The so-called 2p3d RIXS process is of particular interest for mixed valent materials. The incident energy is set at the L2,3 absorption edge and L␣1 (3d → 2p) line serves for the resonant emission. Both radiative channels (absorption and emission) are necessary to obtain the whole picture of the f-state configuration, but valence can be extracted from the spectral analysis of either absorption or emission. The 2p3d-RIXS method was amply utilized in rare earth and actinides [1,23].
5.1. Valence fluctuation and superconductivity in CeCu2 Si2 A recent example where RIXS is necessary is CeCu2 Si2 , an antiferromagnetic heavy fermion at low temperature and superconductor under pressure with a Tc ∼ 1 K. Interestingly, the superconducting phase extends away from the magnetic phase and QCP showing a resurgence of Tc at high pressure. Unlike the lowpressure superconducting phase (SC I), the high-pressure phase (SC II) is not related to magnetic fluctuations but could be due to a new type of electron pairing triggered by critical valence fluctuations (CVF) [24]. RIXS was used to extract the variation of the Ce valence under both high pressure and low temperature conditions in close proximity of the superconducting SC-II phase [25]. The main results are illustrated in Fig. 7. Both PFY-XAS and RXES spectra show clear sign of mixed valency as well-defined spectral features as indicated. Upon pressure increase, we notice a reduction of the f1 feature while f0 is enhanced; f2 shows little change. A rapid and efficient way to extract the valence is by data fitting. This applies for both PFY-XAS and RXES data but, because of its
simpler lineshape, RXES is undoubtedly a better candidate for the data treatment. A more advanced approach implies simulation of the spectra, as carried out for CeCu2 Si2 within the Anderson Impurity Model (AIM). The valence is found to decrease continuously through the SC-II phase with a clear change of slope at the pressure where Tc reaches a maximum. This result gives strong support to the CVF model.
6. Investigate dispersive behavior of excitations in correlated systems Electronic excitations in materials with strong electronic correlations provide information about the energy and dispersion of empty electronic levels. This information, often unique, is complementary to that about occupied levels provided by spectroscopies such as photoemission. Combining both, a reasonable idea about the electronic structure of these materials can be formed. RIXS has been used in the last few years with this aim [1,26 and references therein]. In this method the incident energy is chosen in the region of an absorption edge. This choice also determines the intermediate state of the scattering process which involves a core hole generated by the incident photon. Electronic decay follows filling the core hole. However the system may nevertheless find itself in an excited final state, resulting in inelastic features. Since the photon can exchange sizeable momentum with excitations in the system, their dispersion can be measured. The method is bulk sensitive, with an enhanced cross section due to the core-hole. The core-hole is however absent from the final state, so that information relevant to the physics of the materials in question is directly obtained. This technique has been used to study the dispersion of electronic excitations so as to determine their nature and to confront them with theoretical predictions of electronic structure and dynamics. Here we cite an example of the utility of this method and the information obtained from it in a study of RIXS [27] at the Cu–K absorption edge in La2 CuO4 and at the Ni–K absorption edge in La2 NiO4 . The cuprates and nickelates are almost completely iso-structural but with remarkably different physical properties. No superconductivity has been reported in the nickelates and metallic behavior arises at very high doping. Ni ions are embedded in O octahedra with a nominally 3d8 electronic configuration. It is known that Ni ions are high spin (HS), with both eg orbitals 3dz2−r2 and 3dx2−y2 occupied by one electron and a total spin S = 1 per Ni ion as opposed to S = 1/2 in the cuprates.
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Fig. 8. RIXS measurements at different Brillouin Zone points at (a) the Cu–K edge in La2 CuO4 . Dispersion of the charge transfer exciton obtained from RIXS measurements for (b) La2 CuO4 and (c) La2 NiO4 (from Ref. [18]).
6.1. Exciton dispersion in cuprates and nickelates The measurements were carried out at SPring-8 on BL12XU. Spherically bent 2 m radius Si analyzers were used to reach a total resolution of 300 meV [28]. In Fig. 8a which shows RIXS scans with the momentum transfer parallel to the a/b axis in samples of La2 CuO4 at an energy loss of 2.2 eV, a peak is seen (arrow) near the center of the BZ, which we assign to the fundamental charge transfer exciton. As the momentum transfer increases from the zone center to the zone edge, the peak disperses to higher energy loss and its intensity simultaneously vanishes, Fig. 8b. The exciton disperses quadratically (dashed line) by about 0.5 eV. In the nickelate, a similar analysis allows us to identify an excitonic peak at about 3.6 eV which loses intensity in going from zone center to edge. However no dispersion is seen (Fig. 8c) indicating complete localization of the charge transfer exciton in La2 NiO4 . The physical insight that can be had from this information is the following. In La2 CuO4 , the CuO2 unit cell in the plane contains one hole on the Cu site. Consider a plaquette consisting of a central Cu atom and four surrounding O atoms. With the transfer of an electron from the O 2p orbitals on the plaquette, a neighboring Cu site assumes the Cu 3d10 configuration. The O 2p hole and the transferred electron can then form a bound exciton. The dynamics of this exciton in the CuO2 plane also depends on the interaction of the O 2p hole and the 3d9 hole on the central Cu of the plaquette. These two holes can interact to form a singlet state or a triplet state. An important consequence of singlet formation on the plaquette is that the exciton which consists of two spinless Cu sites moves through the CuO2 plane without upsetting the AF S = 1/2 background [29]. In the nickelate charge transfer can also potentially result in the formation of a bound exciton and to a spin zero Ni site for a singlet coupling between the spins of the Ni 3d9 (S = 1/2) hole and the (S = 1/2) O 2p hole. But, in contrast to the cuprate, the central Ni site with a 3d8 configuration is high spin (S = 1) [30]. The
direct consequence of this difference is the observed change in exciton dynamics: the single spin zero site in the S = 1 NiO2 AF lattice can only hop by disrupting the AF order [31] and thus should have reduced mobility with respect to the twin spin zero Cu sites in the S = 1/2 CuO2 AF lattice. The very recent example of unraveling magnetic interactions from Irridates further shows that RIXS is becoming a routine technique for mapping magnetic excitations in hard X-ray regime [32]. The extension of the RIXS technique for probing collective magnetic excitations and their dynamics initiated by soft RIXS now provides an alternative to Inelastic Neutron Scattering (INS). 7. Conclusion and perspectives The recipes for the application of RIXS that we have provided in this short cookbook should convince the reader that this method is now fairly widely applicable for a variety of problems of interest in the physics and chemistry of materials and the study of their electronic and magnetic properties. Further developments in this field hinge on the advances that will be made in the instrumental and theoretical domains. Several synchrotron beamlines among which the GALAXIES beamline at SOLEIL synchrotron are in the process of equipping themselves with updated spectrometers which will improve count-rates by one or two orders of magnitude with the use of multiple crystal analyzers and large solid-angle spectrometers. Another, more straightforward development is the integration of simple RIXS spectrometers on existing absorption beamlines. New instruments permitting ultra high resolution (below 100 meV) are currently being developed at third generation synchrotron facilities. This will allow the measurements of low energy excitations (charge, magnetic, orbital) and presumable help to unravel the physics of highly correlated electron systems. On the theoretical front, several developments have been made so as to help interpret RIXS spectra and link measured
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features to predictions from various electronic structure calculations. Both these developments should permit the extended use of this powerful method in the coming future and provide newer and ‘tastier’ recipes. References [1] J.-P. Rueff, A. Shukla, Rev. Mod. Phys. 82 (2010) 847. [2] A. Shukla, J.-P. Rueff, J. Badro, G. Vanko, A.F.M. Mattila, F. de Groot, F. Sette, Phys. Rev. B 67 (081101(R)) (2003). [3] P. Glatzel, et al., J. Am. Chem. Soc. 132 (2010) 2555. [4] J. Schlappa, et al., Phys. Rev. Lett. 103 (2009) 047401. [5] M. Guarise, et al., Phys. Rev. Lett. 105 (2010) 157006. [6] L. Braicovich, et al., Phys. Rev. Lett. 104 (2010) 077002. [7] L.J.P. Ament, et al., Rev. Mod. Phys. 83 (2011) 705. [8] M. Le Tacon, et al., Nature Phys. 7 (2011) 725. [9] K. Hämäläinen, D.P. Siddons, J.B. Hastings, L.E. Berman, Phys. Rev. Lett. 67 (1991) 2850. [10] P. Carra, M. Fabrizio, B.T. Thole, Phys. Rev. Lett. 74 (1995) 3700. [11] P. Glatzel, U. Bergmann, Coord. Chem. Rev. 249 (65) (2005). [12] K.O. Kvashnina, Sergei M. Butorin, J. Pieter Glatzel, J. Anal. At. Spectrom. 26 (2011) 1265. [13] W.A. Caliebe, C.-C. Kao, L.E. Berman, J.B. Hastings, M.H. Krisch, F. Sette, K. Hamalainen, J. Appl. Phys. 79 (1996) 6509. [14] M.H. Krisch, F. Sette, U. Bergmann, C. Masciovecchio, R. Verbeni, J. Goulon, W. Caliebe, C.-C. Kao, Phys. Rev. B 54 (1996) R12673.
[15] M. Sikora, A. Juhin, T.-C. Weng, P. Sainctavit, C. Detlefs, F. de Groot, P. Glatzel, Phys. Rev. Lett. 105 (2010) 037202. [16] J.-L. Hazemann, et al., J. Synchrotron. Radiat. 16 (2009) 283. [17] P.A. Brühwiler, O. Karis, N. Martensson, Rev. Mod. Phys. 74 (2002) 703. [18] F. Gel’mukhanov, H. Agren, Phys. Rep. 312 (1999) 87. [19] T. Marchenko, L. Journel, T. Marin, R. Guillemin, S. Carniato, et al., J. Chem. Phys. 134 (2011) 144308. [20] M. Simon, L. Journel, R. Guillemin, W.C. Stolte, I. Minkov, F. Gel’mukhanov, P. Sałek, H. Ågren, S. Carniato, R. Taieb, A.C. Hudson, D.W. Lindle, Phys. Rev. A 73 (2006) 020706. [21] G. Vanko, T. Neisius, G. Molnar, F. Renz, S. Karpati, A. Shukla, F.M.F. de Groot, J. Phys. Chem. B 110 (2006) 11647. [22] A. Monza, A. Meffre, F. Baudelet, J.P. Rueff, M. d’Astuto, P. Munsch, S. Huotari, S. Lachaize, B. Chaudret, A. Shukla, Phys. Rev. Lett. 106 (2011) 247201. [23] C. Dallera, M. Grioni, A. Shukla, G. Vanko, J.L. Sarrao, J.-P. Rueff, D.L. Cox, Phys. Rev. Lett. 88 (2002) 196403. [24] Y. Onishi, K. Miyake, J. Phys. Soc. Jap. 69 (2000) 3955. [25] J.-P. Rueff, S. Raymond, M. Taguchi, M. Sikora, J.-P. Itié, F. Baudelet, D. Braithwaite, G. Knebel, D. Jaccard, Phys. Rev. Lett. 106 (2011) 186405. [26] L.J.P. Ament, M. van Veenendaal, T.P. Devereaux, J.P. Hill, J. van den Brink, Rev. Mod. Phys. 83 (2011) 705. [27] E. Collart, A. Shukla, J.-P. Rueff, P. Leininger, H. Ishii, I. Jarrige, Y.Q. Cai, S.-W. Cheong, G. Dhalenne, Phys. Rev. Lett. 96 (2006) 157004. [28] E. Collart, et al., J. Synchrotron. Radiat. 12 (2005) 473. [29] F.C. Zhang, K.K. Ng, Phys. Rev. B 58 (1998) 13520. [30] V.I. Anisimov, et al., Phys. Rev. B 59 (1999) 7901. [31] J. Zaanen, P.B. Littlewood, Phys. Rev. B 50 (1994) 7222. [32] J. Kim, et al., Phys. Rev. Lett. 108 (2012) 177003.