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.
Spin-orbit Mott insulators composed of $t_{2g}^4$ transition metal ions may host excitonic magnetism due to the condensation of spin-orbital $J=1$ triplons. Prior experiments suggest that the $4d$ antiferromagnet Ca$_{2}$RuO$_{4}$ embodies this notion, but a $J = 0$ nonmagnetic state as a basis of the excitonic picture remains to be confirmed. We use Ru $L_3$-edge resonant inelastic x-ray scattering to reveal archetypal $J$ multiplets with a $J=0$ ground state in the cubic compound K$_{2}$RuCl$_{6}$, which are well described within the $LS$-coupling scheme. This result highlights the critical …
We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of $α$-RuCl$_3$, a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identify most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered r…
$α$-RuCl$_{3}$ is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of $α$-RuCl$_{3}$ by a resonant inelastic x-ray scattering study at the Ru $L_{3}$ absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilize…
What is the correct low-energy spin Hamiltonian description of $α$-RuCl$_3$? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat usin…
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $α$-RuCl3 using inelastic X-ray scattering with meV resolut…
Intermediate Field Spin(on) Dynamics in $α$-RuCl$_3$
Oak Ridge National Laboratory（橡树岭国家实验室）；Purdue University（普渡大学）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Single crystal inelastic neutron scattering data contain rich information about the structure and dynamics of a material. Yet the challenge of matching sophisticated theoretical models with large data volumes is compounded by computational complexity and the ill-posed nature of the inverse scattering problem. Here we utilize a novel machine-learning-assisted framework featuring multiple neural network architectures to address this via high-dimensional modeling and numerical methods. A comprehensive data set of diffraction and inelastic neutron scattering measured on the Kitaev material $α-$RuC…
An external magnetic field can induce a transition in $α$-RuCl$_3$ from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here we present new field dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin liquid phase at an upper field limit $B_u$. The neutron scattering shows three distinct regimes of magnetic response. In the low field ordered state the response shows magnon peaks; the intermediate field regime shows only continuum scattering…
We use an exact numerical diagonalization method to calculate the dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet $α$-RuCl$_3$. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor (NN) spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the $Γ$ point in the DSFs increases with…
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.
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.
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.
The layered honeycomb magnet alpha-RuCl3 has been proposed as a candidate to realize a Kitaev spin model with strongly frustrated, bond-dependent, anisotropic interactions between spin-orbit entangled jeff=1/2 Ru4+ magnetic moments. Here we report a detailed study of the three-dimensional crystal structure using x-ray diffraction on untwinned crystals combined with structural relaxation calculations. We consider several models for the stacking of honeycomb layers and find evidence for a crystal structure with a monoclinic unit cell corresponding to a stacking of layers with a unidirectional in…
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, …
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…
$α$-RuCl$_3$ has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on $α$-RuCl$_3$ single crystals to explore the scattering continuum around the $Γ$ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that while the spin-wave excitations around the M point vanish above the transition tempe…
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.
Kitaev interactions underlying a quantum spin liquid have been long sought, but experimental data from which their strengths can be determined directly is still lacking. Here, by carrying out inelastic neutron scattering measurements on high-quality single crystals of $α$-RuCl$_3$, we observe spin-wave spectra with a gap of $\sim$2 meV around the M point of the two-dimensional Brillouin zone. We derive an effective-spin model in the strong-coupling limit based on energy bands obtained from first-principle calculations, and find that the anisotropic Kitaev interaction $K$ term and the isotropic…
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 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 …
Collective excitations contain rich information about photoinduced transient states in correlated systems. In a Mott insulator, charge degrees of freedom are frozen, but can be activated by photodoping. The energy-momentum distribution of the charge excitation spectrum reflects the propagation of charge degrees of freedom, and provides information about the interplay among various intertwined instabilities on the time scale set by the pump. To reveal charge excitations out of equilibrium, we simulate time-resolved x-ray absorption and resonant inelastic x-ray scattering using a Hubbard model. …
The low energy excitations in Na2IrO3 have been investigated using resonant inelastic x-ray scattering (RIXS). A magnetic excitation branch can be resolved, whose dispersion reaches a maximum energy of about 35 meV at the Γ-point. The momentum dependence of the excitation energy is much larger along the Γ-X direction compared to that along the Γ-Y direction. The observed dispersion relation is consistent with a recent theoretical prediction based on Heisenberg-Kitaev model. At high temperatures, we find large contributions from lattice vibrational modes to our RIXS spectra, suggesting that a s…
We report empirical comparisons of Cu K-edge indirect resonant inelastic x-ray scattering (RIXS) spectra, taken at the Brillouin zone center, with optical dielectric loss functions measured in a number of copper oxides. The RIXS data are obtained for Bi$_2$CuO$_4$, CuGeO$_3$, Sr$_2$Cu$_3$O$_4$Cl$_2$, La$_2$CuO$_4$, and Sr$_2$CuO$_2$Cl$_2$, and analyzed by considering both incident and scattered photon resonances. An incident-energy-independent response function is then extracted. The dielectric loss functions, measured with spectroscopic ellipsometry, agree well with this RIXS response, especi…
We report on the most complete investigation to date of the 4f-electron properties at the gamma-alpha transition in elemental Ce by resonant inelastic x-ray scattering (RIXS). The Ce 2p3d-RIXS spectra were measured directly in the bulk material as a function of pressure through the transition. The spectra were simulated within the Anderson impurity model. The occupation number nf was derived from the calculations in both gamma- and alpha-phases in the ground state along with the f doubleoccupancy. We find that the electronic structure changes result mainly from band formation of 4f electrons w…
We report a resonant inelastic x-ray scattering study of the dispersion relations of charge transfer excitations in insulating La$_2$CuO$_4$. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of $\sim 2.2$ eV at the zone center, and a dispersion of $\sim 1$ eV. The spectral weight of this mode becomes dramatically smaller around ($π$, $π$). The second peak shows a smaller dispersion ($\sim 0.5$ eV) with a zone-center energy of $\sim 3.9$ eV. We argue that these are both highly dispersive exciton modes damped by the pr…
More than 50 years ago the electron-hole attraction was proposed to drive narrow gap semiconductors or semimetals to a new phase, the excitonic insulator. The experimental proof of its existence in bulk materials remains elusive. In strongly correlated insulators, the proximity of the excitonic insulator phase is reflected by the presence of dispersive electron-hole excitations with a small gap above a singlet ground state. Recently, such an excitation spectrum was proposed to be realized in perovskite oxide LaCoO$_3$. In this Letter we use Co $L_3$-edge resonant inelastic X-ray scattering to …
We analyze theoretically the resonant inelastic x-ray scattering (RIXS) at the Ni K edge in the stripe-ordered state of La_{2-x}Sr_xNiO_4 at x=1/3. In the calculation of RIXS spectra, the stripe-ordered ground state is described within the Hartree-Fock approximation by using a realistic tight-binding model for Ni3dγand O2p_{x, y} orbitals, and the electron correlations in the electronic excitation processes are taken into account within the random-phase approximation. The calculated RIXS spectrum shows a tail toward the low-energy region when the momentum transfer of photons equals the stripe …
