Determining the Short-Range Spin Correlations in Cuprate Chain Materials with Resonant Inelastic X-ray Scattering
Claude Monney, Valentina Bisogni, Ke Jin Zhou, Roberto Kraus, Vladimir N. Strocov, Gunter Behr, Jiri Malek, Roman Kuzian, Stefan-Ludwig Drechsler, Steve Johnsto… 展开作者
Claude Monney, Valentina Bisogni, Ke Jin Zhou, Roberto Kraus, Vladimir N. Strocov, Gunter Behr, Jiri Malek, Roman Kuzian, Stefan-Ludwig Drechsler, Steve Johnston, Alexandre Revcolevschi, Bernd Buchner, Henrik M. Ronnow, Jeroen van den Brink, Jochen Geck, Thorsten Schmitt
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 on the 1 meV scale with outstanding sensitivity.
The inelastic neutron scattering spectrum in cuprate superconductors is discussed on the basis of the itinerant-localized duality model for strongly correlated electrons. In Appendix the consistency with recent rigorous theoretical result on ARPES is discussed.
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.
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 investigate electronic excitations in La2-x(Br,Sr)xCuO4 using resonant inelastic x-ray scattering (RIXS) at the oxygen K edge. RIXS spectra of the hole-doped cuprates show clear momentum dependence below 1 eV. The spectral weight exhibits positive dispersion and shifts to higher energy with increasing hole concentration. Theoretical calculation of the dynamical charge structure factor on oxygen orbitals in a three-band Hubbard model is consistent with the experimental observation of the momentum and doping dependence, and therefore the dispersive mode is ascribed to intraband charge excitat…
We examine the effect of core-hole lifetime on the spectral weight of resonant inelastic x-ray scattering (RIXS) in hole-doped cuprates. We calculate the spectral weight by using exact diagonalization technique for a 4x4 doped Hubbard lattice and find that spin-flip channel detecting single-magnon excitation is less sensitive to the core-hole lifetime while in non-spin-flip channel the spectral weight is strongly dependent on the lifetime. In the latter, charge and two-magnon excitations predominately contribute to RIXS for short and long core-hole lifetimes, respectively. For a realistic valu…
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…
Tunneling and inelastic neutron scattering (INS) measurements in cuprates are discussed. There is a clear discrepancy among energy-gap values for different 90 K cuprates, inferred from tunneling measurements. By using the phase diagram of hole-doped cuprates we interpret tunneling measurements in 90 K cuprates and INS data in YBCO.
We present a computation of Cu K-edge resonant inelastic x-ray scattering (RIXS) spectra for electron-doped cuprates which includes coupling to bosonic fluctuations. Comparison with experiment over a wide range of energy and momentum transfers allows us to identify the signatures of three key normal-state energy scales: the pseudogap, charge transfer gap, and Mott gap. The calculations involve a three band Hubbard Hamiltonian based on Cu $d_{x^2-y^2}$ and O $p_x$, $p_y$ orbitals, with a self-energy correction which arises due to spin and charge fluctuations. Our theory reproduces characteristi…
The magnetic excitation spectra in the vicinity of the resonant peak, as observed by inelastic neutron scattering in cuprates, are studied within the memory-function approach. It is shown that at intermediate doping the superconducting gap induces a double dispersion of the peak, with an anisotropy rotated between the downward and upward branch. Similar behavior, but with a spin-wave dispersion at higher energies, is obtained for the low-doping case assuming a large pairing pseudogap.
We theoretically analyze the intensity of the resonant inelastic X-ray scattering (RIXS) based on Ansatz that the electron is fractionalized into two components. By fitting the angle resolved photoemission spectroscopy (ARPES) data of a cuprate high-$T_{\rm c}$ superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ and the accompanied machine learning results obtained before by Yamaji {\it et al.} (arXiv:1903.08060), we determine the paprameters of the two-component fermion model which describes the electron fractionalization. The RIXS spectra are predicted by using this description. We find that the in…
We theoretically investigate the incident-photon energy omega_i dependence of resonant inelastic x-ray scattering (RIXS) tuned for the Cu L edge in cuprate superconductors by using the exact diagonalization technique for a single-band Hubbard model. Depending on the value of core-hole Coulomb interaction in the intermediate state, RIXS for non-spin-flip channel shows either a omega_i-dependent fluorescencelike or omega_i-independent Raman-like behavior for hole doping. An analysis of x-ray absorption suggests that the core-hole Coulomb interaction is larger than on-site Coulomb interaction in …
We study the magnetic excitation spectra of L-edge resonant inelastic x-ray scattering (RIXS) from the spin singlet ground state in one-dimensional undoped cuprates. Analyzing the transition amplitudes of the magnetic excitations in the second-order dipole allowed process, we find that the magnetic excitations are brought about not only on the core-hole site but also on the neighboring sites. The RIXS spectra are expressed by the one-spin correlation function in the scattering channel with changing polarization, and the two-spin correlation function in the scattering channel without changing p…
We show that Resonant Inelastic X-ray scattering (RIXS) is sensitive to three-magnon excitations in cuprates. Even if it requires three electrons to simultaneously flip their spin, the RIXS tri-magnon scattering amplitude is not small. At the Cu $L$-edge its intensity is generally larger than the bi-magnon one and at low transferred momentum even larger than the single-magnon intensity. At the copper $M$-edge the situation is yet more extreme: in this case three-magnon scattering is dominating over all other magnetic channels.
We study the dynamical, momentum dependent two- and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t-J$ system the four-spin response vanishes at $π$, whereas the two-spin correlator is peaked around $π/2$, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping…
Inelastic Neutron Scattering (INS) data in LSCO, YBCO and Bi2212 are discussed. In the literature, the INS spectra remain far from being comprehensively understood. We show that local (Q-integrated) susceptibility data and the energy dependence of the spin susceptibility at antiferromagnetic vector, Q = (p,p), can be interpreted by using the phase diagram for hole-doped cuprates. We analyze also the origin of the resonant peak which relates to the order parameter for long-range phase coherence in hole-doped cuprates. Thus, we present an interpretation of neutron data in LSCO, YBCO and Bi2212 p…
The tunneling path between the CuO2-layers in cuprate superconductors and a scanning tunneling microscope tip passes through a barrier made from other oxide layers. This opens up the possibility that inelastic processes in the barrier contribute to the tunneling spectra. Such processes cause one or possibly more peaks in the second derivative current-voltage spectra displaced by phonon energies from the density of states singularity associated with superconductivity. Calculations of inelastic processes generated by apical O-phonons show good qualitative agreement with recent experiments report…
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 study the magnetic excitation spectra of resonant inelastic x-ray scattering (RIXS) at the $L$-edge from undoped cuprates beyond the fast collision approximation. We analyse the effect of the symmetry breaking ground state on the RIXS process of the Heisenberg model by using a projection procedure. We derive the expressions of the scattering amplitude in both one-magnon and two-magnon excitation channels. Each of them consists of the isotropic and anisotropic contributions. The latter is a new finding and attributed to the long range order of the ground state. The presence of anisotropic te…
The resonant inelastic x-ray scattering spectrum in insulating cuprates is examined by using the exact diagonalization technique on small clusters in the two-dimensional Hubbard model with second and third neighbor hopping terms. When the incident photon energy is tuned near the Cu K absorption edges, we find that the features of the unoccupied upper Hubbard band can be extracted from the spectrum through an anisotropic momentum dependence. They provide an opportunity for the understanding of the different behavior of hole- and electron-doped superconductors.
There are two commonly discussed points of view in theoretical description of cuprate superconductors, (i) Cuprates can be described by the modified t-J model. (ii) Overdoped cuprates are close to the regime of normal Fermi liquid (NFL). We argue that recent resonant inelastic X-ray scattering data challenge both points. While the modified t-J model describes well the strongly underdoped regime, it fails to describe high energy magnetic excitations when approaching optimal doping. This probably indicates failure of the Zhang-Rice singlet picture. In the overdoped regime the momentum-integrated…
We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the Cu and Ni K edges in La2CuO4 and La2NiO4, respectively. We make use of the Keldysh-Green-function formalism, in which the RIXS intensity is described by a product of incident-photon-dependent factor and density-density correlation function in the 3d states. The former factor is calculated using the $4p$ density of states given by an ab initio band structure calculation and the latter using the wavefunctions given by a Hartree-Fock calculation of a multi-orbital tight-binding model. The initial state is described within th…
We investigate resonant inelastic X-ray scattering (RIXS) at the O $K$-edge in insulating cuprates by means of three methods: cluster perturbation theory (CPT), Hartree--Fock approximation (HFA) and exact diagonalization (ED) method. We consider the three-band Hubbard model and show the overall momentum-dependence of the Zhang--Rice singlet (ZRS) excitation and charge-transfer excitation by the CPT combining with the perturbation scheme. A comparison of the RIXS spectra calculated using CPT and HFA reveals different momentum-dependencies through the changes in the properties of the upper Hubba…
We report particle-hole pair excitations in a cuprate insulator in the intermediate regimes of momentum-transfers using high energy inelastic x-ray scattering. The excitation spectra show dispersive features near the Mott edge which shed light on the momentum structure of the upper Hubbard band in cuprates. We briefly discuss the potential use of such a technique to study the momentum dependence of unoccupied bands and q-dependent charge fluctuations in complex insulators.
Resonant inelastic x-ray scattering (RIXS) tuned for the Cu L edge is a possible tool to detect charge excitations in cuprate superconductors. We theoretically investigate the possibility for observing a collective charge excitation by the RIXS. The RIXS process via the intermediate state inevitably makes the spectral weight of charge excitation stronger in electron doping than in hole doping. Electron-hole asymmetry also appears in the dynamical charge structure factor, showing a new enhanced small-momentum low-energy mode in electron doping. These facts indicate a possibility of detecting th…
High Tc superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic X-ray scattering (RIXS) to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors [La2-xSrxCuO4 (LSCO) and Bi2Sr1.6La0.4CuO6+d (Bi2201)], crucially completing t…
We present a three-band Hubbard Hamiltonian and the associated Cu K-edge RIXS spectra for electron and hole doped cuprates over a wide range of energy and momentum transfers. By comparing computed spectra for the unfilled case with the corresponding results for 15% electron or hole doping at two different values of the effective Hubbard parameter U, generic signatures of the collapse of the magnetic gap and the characteristic momentum dependencies and evolution of the spectra with doping are identified. Available RIXS data support the gap collapse scenario for electron doped cuprates, but the …
The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-…
The ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ is of interest both as a quasi-one-dimensional analog of the superconducting cuprates and as a superconductor in its own right when Sr is substituted by Ca. In order to model resonant inelastic x-ray scattering (RIXS) spectra for this compound, we investigate the simpler SrCu$_{2}$O$_{3}$ system in which the crystal structure contains very similar ladder planes. We approximate the LDA dispersion of SrCu$_{2}$O$_{3}$ by a Cu only two-band tight-binding model. Strong correlation effects are incorporated by assuming an anti-ferromagnetic ground state…
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 used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor YBa2Cu3O6+x over a wide range of doping levels (0.1 < x < 1). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all x. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rath…
We report a Cu K-edge resonant inelastic x-ray scattering (RIXS) study of high-Tc cuprates. Momentum-resolved charge excitations in the CuO2 plane are examined from parent Mott insulators to carrier-doped superconductors. The Mott gap excitation in undoped insulators is found to commonly show a larger dispersion along the [pi,pi] direction than the [pi,0] direction. On the other hand, the resonance condition displays material dependence. Upon hole doping, the dispersion of the Mott gap excitation becomes weaker and an intraband excitation appears as a continuum intensity below the gap at the s…
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 spin dynamics of high temperature superconductors measured by inelastic neutron scattering is reviewed. The spin susceptibility evolves a lot with increasing doping from the undoped insulating state to the overdoped metallic state. In the superconducting state, a strong magnetic resonance peak occurs in the spin excitation spectrum whose energy is proportional to the superconducting temperature. In underdoped and optimally doped regimes, normal state antiferromagnetic fluctuations are observed, proving the existence of strong electronic correlations in cuprates. They are characterized by a…
Assuming the exchange of antiferromagnetic spin fluctuations as the Cooper pairing mechanism we calculate the doping dependence of the resonance peak seen in inelastic neutron scattering and the magnetic coherence effect. Most importantly, we find that the resonance peak in the magnetic susceptibility, ${Im}χ({\bf q},ω)$, appears {\it only} in the superconducting state, that it scales with $T_c$, and that magnetic coherence is a result of a d-wave order parameter. We further analyze the structure of ${Im}χ$ below $T_c$, the position of the peak at $ω_{res}$ and the consequences for photoemissi…
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.
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…
The theory for the dynamical spin susceptibility within the t-J model is developed, as relevant for the resonant magnetic peak and normal-state magnetic response in superconducting (SC) cuprates. The analysis is based on the equations of motion for spins and the memory-function presentation of magnetic response where the main damping of the low-energy spin collective mode comes from the decay into fermionic degrees of freedom. It is shown that the damping function at low doping is closely related to the c-axis optical conductivity. The analysis reproduces doping-dependent features of the reson…
Using resonant inelastic x-ray scattering (RIXS) at the Cu $L$-absorption edge, we have observed intense, dispersive spin excitations in highly overdoped Tl$_2$Ba$_2$CuO$_{6+δ}$ (superconducting $T_c =6$ K), a compound whose normal-state charge transport and thermodynamic properties have been studied extensively and shown to exhibit canonical Fermi-liquid behavior. Complementary RIXS experiments on slightly overdoped Tl$_2$Ba$_2$CuO$_{6+δ}$ ($T_c =89$ K) and on Y$_{1-x}$Ca$_{x}$Ba$_2$Cu$_3$O$_{6+δ}$ compounds spanning a wide range of doping levels indicate that these excitations exhibit energi…
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…
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.
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…
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, …
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 show that, contrary to common lore, in resonant inelastic x-ray scattering (RIXS) at the copper L- and M-edge direct spin-flip scattering is in principle allowed. We demonstrate how this possibility can be exploited to probe the momentum dependent magnetic properties of cuprates such as the high Tc superconductors and compute in detail the relevant local and momentum dependent magnetic scattering amplitudes, which we compare to the elastic and $dd$-excitation scattering intensities. For cuprates these results put RIXS as a technique on the same footing as neutron scattering.
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 $U= 3.0 \…
We analyze resonant inelastic x-ray scattering (RIXS) at the Cu K edge in a typical orbital-ordered compound KCuF3 on the basis of a microscopic theory. Spectral shape and its dependence on polarization direction and momentum transfer of photons are explained consistently with experimental data within our microscopic calculation. According to our microscopic orbital-resolving analysis, high-energy spectral weights (above 5 eV) originate from charge-transfer excitations related to the Cu-dγorbitals, while the low-energy weights (below 2 eV) originate from the d-d orbital excitations among the f…
Using the three-orbital Hubbard model, we investigate the low-energy excitation spectra in the antiferromagnetic phase of Ca$_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 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.
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…
