We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the K edge of Mn in the antiferromagnetic insulating manganite LaMnO3. We make use of the Keldysh-type Green-function formalism, in which the RIXS intensity is described by a product of an incident-photon-dependent factor and a density-density correlation function in the 3d states. We calculate the former factor using the 4p density of states given by an ab initio band structure calculation and the latter using a multi-orbital tight-binding model. The ground state of the model Hamiltonian is evaluated within the Hartree-Fock approximation. Correlation effects are treated within the random phase approximation (RPA). We obtain the RIXS intensity in a wide range of energy-loss 2-15 eV. The spectral shape is strongly modified by the RPA correlation, showing good agreement with the experiments. The incident-photon-energy dependence also agrees well with the experiments. The present mechanism that the RIXS spectra arise from band-to-band transitions to screen the core-hole potential is quite different from the orbiton picture previously proposed, enabling a comprehensive understanding of the RIXS spectra.
We express the cross section for indirect resonant inelastic X-ray scattering in terms of an intrinsic dynamic correlation function of the system that is studied with this technique. The cross section is a linear combination of the charge response function and the dynamic longitudinal spin density correlation function. This result is asymptotically exact for both strong and weak local core-hole potentials. We show that one can change the relative charge and spin contribution to the inelastic spectral weight by varying the incident photon energy.
Using a model Hamiltonian, we discuss how we could interpret data obtained from transition metal $K$-edge resonant inelastic x-ray scattering (RIXS) experiments. By analyzing the creation of valence excitations from the screening of the core hole and calculating corresponding RIXS spectra for metals and insulators, we find that the probability for excitations depends not only on the total energy but also on the asymmetric screening dynamics between electrons and holes.
We determine how the elementary excitations of iridium-oxide materials, which are dominated by a strong relativistic spin-orbit coupling, appear in Resonant Inelastic X-ray Scattering (RIXS). Whereas the RIXS spectral weight at the L2 x-ray edge vanishes, we find it to be strong at the L3-edge. Applying this to Sr2IrO4, we observe that RIXS, besides being sensitive to local doublet to quartet transitions, meticulously maps out the strongly dispersive delocalized excitations of the low-lying spin-orbit doublets.
We present a computational study of $L$-edge resonant inelastic x-ray scattering (RIXS) in correlated 3$d$ transition-metal oxides using an $ab$ $initio$ method based on local density approximation + dynamical mean-field theory (DMFT). The present method, building on Anderson impurity model with an optimized continuum bath within DMFT, is an extension of the cluster model to include unbound electron-hole pair excitations as well as material-specific charge-transfer excitations with less empirical parameters. We find a good agreement with available experimental data. The relationship between co…
X-ray absorption is the standard method to probe the unoccupied density of states at a given edge. Here we show that polarized Resonant Inelastic X-Ray Scattering in La2CuO4 at the Cu K-edge is extremely sensitive to the environment of the Cu atom and the fine structure in the Cu 4p density of states. Combined ab initio and many-body cluster calculations, used for the first time in such a context, show remarkable agreement with experiment. In particular we identify a non-local effect namely a transition to off-site Cu 3d states.
We study theoretically the collective orbital excitation named orbital wave in the orbital ordered manganites.The dispersion relation of the orbital wave is affected by the static spin structure through the coupling between spin and orbital degrees of freedom. As a probe to detect the dispersion relation, we propose two possible methods by utilizing resonant inelastic x-ray scattering. The transition probability of the orbital wave scattering is formulated, and the momentum and polarization dependences of the structure factor are calculated in several types of the orbital and spin structures. …
We use dynamical mean field theory to find an exact solution for inelastic light scattering in strongly correlated materials such as those near a quantum-critical metal-insulator transition. We evaluate the results for $\textbf{q}=0$ (Raman) scattering and find that resonant effects can be quite large, and yield a triple resonance, a significant enhancement of nonresonant scattering peaks, a joint resonance of both peaks when the incident photon frequency is on the order of $U$, and the appearance of an isosbestic point in all symmetry channels for an intermediate range of incident photon freq…
We show that high resolution Resonant Inelastic X-ray Scattering (RIXS) provides direct, element-specific and momentum-resolved information on the electron-phonon (e-p) coupling strength. Our theoretical analysis demonstrates that the e-p coupling can be extracted from RIXS spectra by determining the differential phonon scattering cross section. An alternative, very direct manner to extract the coupling is to use the one and two-phonon loss ratio, which is governed by the e-p coupling strength and the core-hole life-time. This allows measurement of the e-p coupling on an absolute energy scale.
We explore the general phenomenology of resonant inelastic scattering (RIXS) using CuB2O4, a network of CuO4 plaquettes electronically isolated by B+3 ions. Spectra show a small number of well-separated features, and we exploit the simple electronic structure to explore RIXS phenomenology by developing a calculation which allows for intermediate-state effects ignored in standard approaches. These effects are found to be non-negligible and good correspondence between our model and experiment leads to a simple picture of such phenomenology as the genesis of d-d excitations at the K edge and inte…
Resonant inelastic X-ray scattering (RIXS) spectra of model copper- and nickel-based transition metal oxides are measured over a wide range of energies near the M-edge (h$ν$=60-80eV) to better understand the properties of resonant scattering involving shallow core levels. Standard multiplet RIXS calculations are found to deviate significantly from the observed spectra. However, by incorporating the self consistently calculated decay lifetime for each intermediate resonance state within a given resonance edge, we obtain dramatically improved agreement between data and theory. Our results sugges…
We present a theory of the resonant inelastic x-ray scattering (RIXS) to study electronic excitations in orbital ordered manganites. The charge and orbital excitations of the Mn 3d electron are caused by the Coulomb interactions in the intermediate scattering state. The scattering cross section is formulated by the Liouville operator method where the local and itinerant natures of the excitations are taken into account on an equal footing. As a result, the cross section is expressed by the charge and orbital correlation functions associated with local corrections. The RIXS spectra are calculat…
We report the high resolution resonant inelastic EUV scattering study of quantum Heisenberg antiferromagnet KCoF3. By tuning the EUV photon energy to cobalt M23 edge, a complete set of low energy 3d spin-orbital excitations is revealed. These low-lying electronic excitations are modeled using an extended multiplet-based mean field calculation to identify the roles of lattice and magnetic degrees of freedom in modifying the RIXS spectral lineshape. We have demonstrated that the temperature dependence of RIXS features upon the antiferromagnetic ordering transition enables us to probe the energet…
In indirect resonant inelastic X-ray scattering (RIXS) an intermediate state is created with a core-hole that has a ultrashort lifetime. The core-hole potential therefore acts as a femtosecond pulse on the valence electrons. We show that this fact can be exploited to integrate out the intermediate states from the expressions for the scattering cross section. By this we obtain an effective scattering cross section that only contains the initial and final scattering states. We derive in detail the effective cross section which turns out to be a resonant scattering factor times a linear combinati…
Resonant inelastic x-ray scattering (RIXS) has become a powerful tool in the study of the electronic structure of condensed matter. Although the linewidths of many RIXS features are narrow, the experimental broadening can often hamper the identification of spectral features. Here, we show that the Maximum Entropy technique can successfully be applied in the deconvolution of RIXS spectra, improving the interpretation of the loss features without a severe increase in the noise ratio.
This paper provides a brief overview of applications of advanced X-ray spectroscopic techniques that take advantage of the resonant inelastic X-ray scattering (RIXS) in the hard and tender x-ray range and have recently become available for studying the electronic structure of actinides. We focus here on the high-energy-resolution X-ray absorption near edge structure (XANES) and core-to-core and core-to-valence RIXS spectroscopies at the U L and M edges of uranium compounds. The spectral features are analyzed using a number of theoretical methods, such as the density functional theory in the lo…
We develop a formalism to study the Resonant Inelastic X-ray Scattering (RIXS) response in metals based on the diagrammatic expansion for its cross section. The standard approach to the solution of the RIXS problem relies on two key approximations: short-range potentials and non-interacting conduction electrons. However, these approximations are inaccurate for charged particles in metals, where the long-range Coulomb interaction and dynamic screening effects are very important. In this work we study how to extract important information about collective excitations in the Coulomb plasma, plasmo…
We report resonant inelastic x-ray scattering (RIXS) excited by circularly polarized x-rays on Mn-Zn ferrite at the Mn L2,3-resonances. We demonstrate that crystal field excitations, as expected for localized systems, dominate the RIXS spectra and thus their dichroic asymmetry cannot be interpreted in terms of spin-resolved partial density of states, which has been the standard approach for RIXS dichroism. We observe large dichroic RIXS at the L2-resonance which we attribute to the absence of metallic core hole screening in the insulating Mn-ferrite. On the other hand, reduced L3-RIXS dichrois…
We discuss recent Cu K-edge resonant inelastic scattering (RIXS) results for CuB2O4, a model system consisting of electronically-isolated CuO4 plaquettes, which exhibits anomalies in the incident photon energy dependence that are not captured by electron-only models. We show that these anomalous features can be qualitatively described by extending the electron-only considerations to include the lattice degrees of freedom. Our findings have important general implications for the interpretation of K-edge RIXS results for electronically higher-dimensional transition metal oxides.
We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the Ni $K$ edge in an antiferromagnetic insulator NiO by applying the theory developed by the present authors. It is based on the Keldysh Green's function formalism, and treats the core-hole potential in the intermediate state within the Born approximation. We calculate the single-particle energy bands within the Hartree-Fock approximation on the basis of the multi-orbital tight-binding model. Using these energy bands together with the $4p$ density of states from an ab initio band structure calculation, we calculate the RIXS …
We present a detailed analysis of the incident-photon-energy and polarization dependences of the resonant inelastic x-ray scattering (RIXS) spectra at the Cu $K$ edge in La$_{2}$CuO$_{4}$. Our analysis is based on the formula developed by Nomura and Igarashi, which describes the spectra by a product of an incident-photon-dependent factor and a density-density correlation function for 3d states. We calculate the former factor using the $4p$ density of states from an ab initio band structure calculation and the latter using a multiorbital tight-binding model within the Hartree-Fock approximation…
We demonstrate the utility of point group representation theory for symmetry analysis in resonant inelastic x-ray scattering. From its polarization-dependence, we show that a 5 eV inelastic feature in Sr2CuO2Cl2 has pure B1g symmetry and assign it to a transition in the cell-perturbation calculations of Simon, et. al. [Phys. Rev. B., 54, R3780 (1996)]. We discuss how Raman selection rules are broken at nonzero momentum transfer and how this can also act as a probe of wave function symmetry.
We develop a formalism to study indirect resonant inelastic x-ray scattering (RIXS) in systems with itinerant electrons, accounting for the attraction between valence electrons and the positively-charged core hole exactly, and apply this formalism to the hole-doped cuprate superconductors. We focus on the relationship between RIXS lineshapes and band structure, including broken symmetries. We show that RIXS is capable of distinguishing between competing order parameters, establishing it as a useful probe of the pseudogap phase.
Ultrafast optical pulses are an increasingly important tool for controlling quantum materials and triggering novel photo-induced phase transitions. Understanding these dynamic phenomena requires a probe sensitive to spin, charge, and orbital degrees of freedom. Time-resolved resonant inelastic X-ray scattering (trRIXS) is an emerging spectroscopic method, which responds to this need by providing unprecedented access to the finite-momentum fluctuation spectrum of photoexcited solids. In this Perspective, we briefly review state-of-the-art trRIXS experiments on condensed matter systems, as well …
Resonant inelastic X-ray scattering (RIXS) is increasingly used to quantify vibronic interactions in materials. In the case of periodic systems, this is most often done through fitting experimental results to a parameterized, but exact analytical solution of a simple Holstein Hamiltonian that consists of a single electronic level coupled linearly to a single Einstein vibrational mode. Working within this standard framework, we consider the impact of minor generalizations of this model, namely, introducing a second Einstein oscillator, and allowing the curvature of the excited-state potential e…
We present calculations for resonant inelastic x-ray scattering (RIXS) in edge-shared copper oxide systems, such as CuGeO$_{3}$ and Li$_{2}$CuO$_{2}$, appropriate for hard x-ray scattering where the photoexcited electron lies above oxygen 2p and copper 3d orbital energies. We perform exact diagonalizations of the multi-band Hubbard and determine the energies, orbital character and resonance profiles of excitations which can be probed via RIXS. We find excellent agreement with recent results on Li$_{2}$CuO$_{2}$ and CuGeO$_{3}$ in the 2-7 eV photon energy loss range.
Recent improvements in instrumentation have established resonant inelastic x-ray scattering (RIXS) as a valuable new probe of the magnetic excitations in the cuprates. This article introduces RIXS, focusing on the Cu $L_3$ resonance, and reviews recent experiments using this technique. These are discussed in light of other experimental probes such as inelastic neutron scattering and Raman scattering. The success of these studies has motivated the development of several new RIXS spectrometers at synchrotrons around the world that promise, among other improvements, 5-10 times better energy resol…
We report the observation of multiple phonon satellite features in ultra thin superlattices of form $n$SrIrO$_3$/$m$SrTiO$_3$ using resonant inelastic x-ray scattering. As the values of $n$ and $m$ vary the energy loss spectra show a systematic evolution in the relative intensity of the phonon satellites. Using a closed-form solution for the cross section, we extract the variation in the electron-phonon coupling strength as a function of $n$ and $m$. Combined with the negligible carrier doping into the SrTiO$_3$ layers, these results indicate that tuning of the electron-phonon coupling can be …
We report a Cu K-edge resonant inelastic x-ray scattering (RIXS) study of momentum-dependent charge excitations in Nd$_{2-x}$Ce$_x$CuO$_4$ ($x$ = 0.075 and 0.18). The peak position and width of the excitations coincide excellently with those observed in Cu L$_3$-edge RIXS. It demonstrates that the same charge excitations are observed at the two edges.
Ru M$_3$-edge resonant inelastic x-ray scattering (RIXS) measurements of RuCl$_3$ with 27 meV resolution reveals a spin-orbit exciton without noticeable splitting. We extract values for the spin-orbit coupling constant ($λ=154\pm2$ meV) and trigonal distortion field energy ($\left|Δ\right|<65$ meV) which support the $j_{\rm eff}=1/2$ nature of RuCl$_3$. We demonstrate the feasibility of M-edge RIXS for $4d$ systems, which allows ultra high-resolution RIXS of $4d$ systems until instrumentation for L-edge RIXS improves.
The scattering cross section of the resonant inelastic light scattering is represented as a correlation function in the Keldysh-Schwinger functional integral formalism. The functional integral approach enables us to compute the cross section in the Feynman diagram perturbation theory where many-body effects can be fully incorporated. This approach is applied to the one G-phonon Raman scattering of graphene, and the result is shown to agree with the one previously obtained by the conventional Fermi golden rule formula. Also, this approach is generalized to the systems in non-equilibrium conditi…
Phonons, the quantum mechanical representation of lattice vibrations, and their coupling to the electronic degrees of freedom are important for understanding thermal and electric properties of materials. For the first time, phonons have been measured using resonant inelastic x-ray scattering (RIXS) across the Cu K-edge in cupric oxide (CuO). Analyzing these spectra using an ultra-short core-hole lifetime approximation and exact diagonalization techniques, we can explain the essential inelastic features. The relative spectral intensities are related to the electron-phonon coupling strengths.
I present a tractable theory for the Resonant Inelastic X-ray Scattering (RIXS) spectral function of magnons. The low-energy transition operator is written as a product of local spin operators times fundamental x-ray absorption spectra. This leads to simple selection rules for the magnetic cross section. The scattering cross section linear (quadratic) in spin operators is proportional to the magnetic circular (linear) dichroic absorption. RIXS is a novel tool to measure magnetic quasi particles (magnons) and the incoherent spectral weight, as well as multiple magnons up to very high energy los…
Orbital degrees of freedom play a major role in the physics of many strongly correlated transition metal compounds. However, they are still very difficult to access experimentally, in particular by neutron scattering. We propose here how to reveal orbital occupancies of the system ground state by magnetic resonant inelastic x-ray scattering (RIXS). This is possible because, unlike in neutron scattering, the intensity of the magnetic excitations in RIXS depends essentially on the symmetry of the orbitals where the spins are in.
We develop a framework to evaluate the time-dependent resonant inelastic X-ray scattering (RIXS) signal with the use of non-equilibrium dynamical mean field theory simulations. The approach is based on the solution of a time-dependent impurity model which explicitly incorporates the probe pulse. It avoids the need to compute four-point correlation functions, and can in principle be combined with different impurity solvers. This opens a path to study time-resolved RIXS processes in multi-orbital systems. The approach is exemplified with a study of the RIXS signal of a melting Mott antiferromagn…
Predictions are made for the momentum- and carrier-dependent degradation of the Mott gap upon doping in high-Tc cuprates as would be observed in Cu K-edge resonant inelastic x-ray scattering (RIXS). The two-dimensional Hubbard model with second- and third-nearest-neighbor hopping terms has been studied by numerical exact diagonalization. Special emphasis is placed on the particle-hole asymmetry of the Mott gap excitations. We argue that the Mott gap excitations observed by RIXS are significantly influenced by the interaction between charge carriers and antiferromagnetic correlations.
We report resonant inelastic x-ray measurements of insulating La$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$ taken with the incident energy tuned near the Cu K absorption edge. We show that the spectra are well described in a shakeup picture in 3rd order perturbation theory which exhibits both incoming and outgoing resonances, and demonstrate how to extract a spectral function from the raw data. We conclude by showing {\bf q}-dependent measurements of the charge transfer gap.
Effective symmetry-based transition operators for resonant inelastic X-ray scattering (RIXS) are derived that show how the scattering between different states depends on the polarization of the incoming and outgoing X-rays. In spherical symmetry, the effective operators can be rewritten in terms of spin operators, although the expressions depend on the nature of the ground state. For lower symmetries, the combined action of the crystal field and the spin-orbit interaction breaks up the spin space and spin operators are no longer appropiate operators. By taking iridium compounds as an example, …
Resonant inelastic x-ray scattering (RIXS) spectra at the Fe K-edge were measured for a single crystal of the iron oxypnictide superconductor PrFeAsO0.7 (Tc=42 K). They disclose a weak, broad feature centered around 4.5 eV energy loss, which is slightly resonantly enhanced when the incident energy is tuned in the vicinity of the 4p white line. We tentatively ascribe it to the charge-transfer excitation between As 4p and Fe 3d.
We study theoretically the resonant inelastic x-ray scattering in quasi-one-dimensional insulating copper oxides, where the incident photon energy is tuned to the Cu1s-4p absorption energy. Our attention is focused particularly on the strong momentum-transfer dependence of the spectral shape observed in recent experiments. We describe the antiferromagnetic ground state within the Hartree-Fock theory, and consider charge excitations from the ground state within the random phase approximation. By taking account of the electron correlation effects perturbatively, we obtain detailed momentum-trans…
The recent discovery that resonant inelastic x-ray scattering can probe single-magnon (SM) dispersions in transition metal (TM) oxides when the x-ray energy is tuned to the TM $L$-edge, has put this technique on a par with inelastic neutron scattering. It is generally presumed that selection rules forbid SM-scattering at oxygen (O) $K$-edges. However, based on a symmetry analysis and exact diagonalization study, we show that SM-scattering at O K-edges becomes allowed when (i) spin-orbit coupling is present in the TM d-shell and (ii) inversion symmetry at the O-site is broken. For cuprates the …
We report strongly momentum-dependent local charge screening dynamics in CE-type charge, orbital, and spin ordered La$_{0.5}$Sr$_{1.5}$MnO$_4$, based on Mn K-edge resonant inelastic x-ray scattering data. Through a comparison with theoretical calculations, we show that the observed momentum dependence reflects highly localized, nearest neighbor screening of the transient local charge perturbation in this compound with an exciton-like screening cloud, rather than delocalized screening. The size of the screening cloud is estmated to be about 0.4-0.5 interatomic distances.
Resonant inelastic x-ray scattering (RIXS) at the oxygen $K$-edge has recently accessed multi-spinon excitations in the one-dimensional antiferromagnet (1D-AFM) \sco, where four-spinon excitations are resolved separately from the two-spinon continuum. This technique, therefore, provides new opportunities to study fractionalized quasiparticle excitations in doped 1D-AFMs. To this end, we carried out exact diagonalization studies of the doped $t$-$J$ model and provided predictions for oxygen $K$-edge RIXS experiments on doped 1D-AFMs. We show that the RIXS spectra are rich, containing distinct t…
Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on both the symmetry of the orbitals that spins occupy, and on photon polarizations. We show in detail …
Recent experiments show that indirect resonant inelastic X-ray scattering (RIXS) is a new probe of spin dynamics. Here I derive the cross-section for magnetic RIXS and determine the momentum dependent four-spin correlation function that it measures. These results show that this technique offers information on spin dynamics that is complementary to e.g. neutron scattering. The RIXS spectrum of Heisenberg antiferromagnets is calculated. It turns out that only scattering processes that involve at least two magnons are allowed. Other selection rules imply that the scattering intensity vanishes for…
Element- and site-specific resonant inelastic x-ray scattering spectroscopy (RIXS) is employed to investigate electron correlation effects in {$\rm NaV_2O_5$}. In contrast to single photon techniques, RIXS at the vanadium $L_3$ edge is able to probe $d-d^*$ transitions between V d-bands. A sharp energy loss feature is observed at -1.56 eV, which is well reproduced by a model calculation including correlation effects. The calculation identifies the loss feature as excitation between the lower and upper Hubbard bands and permits an accurate determination of the Hubbard interaction term $U= 3.0 \…
We report a high-resolution resonant inelastic soft x-ray scattering study of the quantum magnetic spin-chain materials Li2CuO2 and CuGeO3. By tuning the incoming photon energy to the oxygen K-edge, a strong excitation around 3.5 eV energy loss is clearly resolved for both materials. Comparing the experimental data to many-body calculations, we identify this excitation as a Zhang-Rice singlet exciton on neighboring CuO4-plaquettes. We demonstrate that the strong temperature dependence of the inelastic scattering related to this high-energy exciton enables to probe short-range spin correlations…
We analyze resonant inelastic x-ray scattering (RIXS) at the Cu K edge in a typical orbital-ordered compound KCuF3 on the basis of a microscopic theory. Spectral shape and its dependence on polarization direction and momentum transfer of photons are explained consistently with experimental data within our microscopic calculation. According to our microscopic orbital-resolving analysis, high-energy spectral weights (above 5 eV) originate from charge-transfer excitations related to the Cu-dγorbitals, while the low-energy weights (below 2 eV) originate from the d-d orbital excitations among the f…
Using the three-orbital Hubbard model, we investigate the low-energy excitation spectra in the antiferromagnetic phase of Ca$_2$RuO$_4$. We calculate the dynamical susceptibilities in the low-energy region by the random phase approximation and find that the anisotropic dispersion of the transverse mode is in good agreement with the spectra recently reported by inelastic neutron scattering experiments. By the fast-collision approximation, we simulate the resonant inelastic x-ray scattering (RIXS) spectra of the Ru $L_3$ edge from the dynamical susceptibilities. We show that the dispersion of th…
We present a theoretical investigation of the origin of Raman-like and fluorescencelike (FL) features of resonant inelastic x-ray scattering (RIXS) spectra. Using a combination of local-density approximation + dynamical mean-field theory and a configuration interaction solver for Anderson impurity model, we calculate the $L$-edge RIXS and x-ray absorption spectra of high-valence transition-metal oxides LaCuO$_3$ and NaCuO$_2$. We analyze in detail the behavior of the FL feature and show how it is connected to the details of electronic and crystal structure. On the studied compounds we demonstr…
We provide a semiquantitative explanation of a recent experiment on the resonant inelastic x-ray scattering (RIXS) in insulating cuprate La2CuO4 (Y.J. Kim et al., Phys. Rev. Lett. 89, 177003 (2002).). We show theoretically that there are three characteristic peaks in RIXS spectra, two of which are attributed to the charge transfer excitation and are reasonably assigned to those observed experimentally. The lowest energy peak has a relatively large dispersion ($\sim 0.8$ eV) and is suppressed near the zone corner (π, π), in agreement with the experiment. We stress that electron correlation is a…
We calculate the resonant inelastic X-ray scattering (RIXS) response of the Kitaev honeycomb model, an exactly solvable quantum-spin-liquid model with fractionalized Majorana and flux excitations. We find that the fundamental RIXS channels, the spin-conserving (SC) and the non-spin-conserving (NSC) ones, do not interfere and give completely different responses. SC-RIXS picks up exclusively the Majorana sector with a pronounced momentum dispersion, whereas NSC-RIXS also creates immobile fluxes, thereby rendering the response only weakly momentum dependent, as in the spin structure factor measur…
We report the observation of temperature dependent electronic excitations in various manganites utilizing resonant inelastic x-ray scattering (RIXS) at the Mn K-edge. Excitations were observed between 1.5 and 16 eV with temperature dependence found as high as 10 eV. The change in spectral weight between 1.5 and 5 eV was found to be related to the magnetic order and independent of the conductivity. On the basis of LDA+U and Wannier function calculations, this dependence is associated with intersite d-d excitations. Finally, the connection between the RIXS cross-section and the loss function is …
We derive general expressions for resonant inelastic x-ray scattering (RIXS) operators for $t_{2g}$ orbital systems, which exhibit a rich array of unconventional magnetism arising from unquenched orbital moments. Within the fast collision approximation, which is valid especially for 4$d$ and 5$d$ transition metal compounds with short core-hole lifetimes, the RIXS operators are expressed in terms of total spin and orbital angular momenta of the constituent ions. We then map these operators onto pseudospins that represent spin-orbit entangled magnetic moments in systems with strong spin-orbit co…
We investigate magnetic excitations in the spin-ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ using high-resolution Cu $L_3$-edge Resonant Inelastic X-ray Scattering (RIXS). Our findings demonstrate that RIXS couples to collective spin excitations from a quantum spin-liquid ground state. In contrast to Inelastic Neutron Scattering (INS), the RIXS cross section changes only moderately over the entire Brillouin Zone (BZ), revealing a high sensitivity also at small momentum transfers. The two-triplon energy gap is found to be $100\pm 30$ meV. Our results are supported by calculations within an effec…
We develop a formalism for calculating resonant inelastic x-ray scattering (RIXS) spectra in systems of itinerant electrons with arbitrary band structures, accounting for the effect of the positively-charged core hole exactly. We apply this formalism to the cuprate superconductors and obtain quantitative agreement with experimental data over a wide range of dopings. We reproduce the dispersing peaks and non-trivial polarization dependence found in RIXS experiments on several materials. Thus we demonstrate that features previously attributed to collective magnetic modes can be explained by band…
We report a Cu K-edge resonant inelastic x-ray scattering (RIXS) study of orbital excitations in KCuF3 . By performing the polarization analysis of the scattered photons, we disclose that the excitation between the eg orbitals and the excitations from t2g to eg exhibit distinct polarization dependence. The polarization dependence of the respective excitations is interpreted based on a phenomenological consideration of the symmetry of the RIXS process that yields a necessary condition for observing the excitations. In addition, we show that the orbital excitations are dispersionless within our …
We present a study of the resonant inelastic scattering response of \ybin\ excited at the tender Yb $M_5$ X-ray edge. In the high-temperature, paramagnetic phase, we observe a multiplet structure which can be understood at an ionic level. Upon cooling through the valence transition at $T_v\sim$ 40$K$, we observe a strong renormalization of the low-energy spectra, indicating a sensitivity to the formation of an intermediate valence phase at low temperatures. Similar spectrum renormalization has been observed in the optical conductivity, which suggests that the low-energy electronic structure po…
Ruddlesden-Popper and reduced Ruddlesden-Popper nickelates are intriguing candidates for mimicking the properties of high-temperature superconducting cuprates. The degree of similarity between these nickelates and cuprates has been the subject of considerable debate. Resonant inelastic x-ray scattering (RIXS) has played an important role in exploring their electronic and magnetic excitations, but these efforts have been stymied by inconsistencies between different samples and the lack of publicly available data for detailed comparison. To address this issue, we present open RIXS data on La4Ni3…
We establish the spectral line shape of orbital excitations created by resonant inelastic X-ray scattering for the model Mott insulator CoO. Improved experimental energy resolution reveals that the line shapes are strikingly different from expectations in a first principles-based atomic multiplet model. Extended theoretical simulations are performed to identify the underlying physical origins, which include a pronounced thermal tail reminiscent of anti-Stokes scattering on the energy gain side of excitations, and an essential contribution from interatomic many-body dynamics on the energy loss …
