We report one algorithm for simulating oxygen $K$-edge RIXS for weakly correlated systems, using maximally localized Wannier functions as the basis set. The $N$-electron wavefunction is formulated using the single Slater determinant, and the many-body effect is treated explicitly at the dipole matrix element level. The simulated result of oxygen $K$-edge RIXS for solid state Li$_2$CO$_3$ matches well with the experimental data. Besides being efficient and reasonably accurate, this algorithm also shows potential to extent to more complex RIXS problems.
Systematic experimental data on resonant inelastic X-ray scattering (RIXS) in GaN near the N K-edge are presented for the first time. Excitation energy dependence of the spectral structures manifests the band structure effects originating from momentum selectivity of the RIXS process. This finding allows obtaining k-resolved band structure information for GaN crystals and nanostructures.
We investigate theoretically the resonant inelastic x-ray scattering (RIXS) at the $K$ edge of Si on the basis of an ab initio calculation. We calculate the RIXS spectra with systematically varying transfered-momenta, incident-photon energy and incident-photon polarization. We confirm the anisotropy of the experimental spectra by Y. Ma {\it et al}. (Phys. Rev. Lett. 74, 478 (1995)), providing a quantitative explanation of the spectra.
We present a formalism for the resonant inelastic x-ray scattering (RIXS) cross section. The resulting compact expression in terms of polarizability matrix elements, particularly lends itself to the implementation in an all-electron many-body perturbation theory (MBPT) framework, which is realized in the full-potential package exciting. With the carbon K edge RIXS of diamond and the oxygen K edge RIXS of $β-\mathrm{Ga_2 O_3}$, respectively, we demonstrate the importance of electron-hole correlation and atomic coherence in the RIXS spectra.
We present a novel derivation of resonant inelastic x-ray scattering (RIXS) which yields an expression for the RIXS cross section in terms of emission pathways between intermediate and final many-body states. Thereby electron-hole interactions are accounted for, as obtained from full diagonalization of the Bethe-Salpeter equation within an all-electron first-principles framework. We demonstrate our approach with the emission spectra of the fluorine K edge in LiF, and provide an in-depth analysis of the pathways that determine the spectral shape. Excitoninc effects are shown to play a crucial r…
The theory of incoherent nuclear resonant scattering of synchrotron radiation accompanied by absorption or emission of phonons in a crystal lattice is developed. The theory is based on the Maxwell's equations and time-dependent quantum mechanics under the condition of incoherent scattering of radiation by various nuclei. A concept of coherence in scattering processes, properties of the synchrotron radiation, and conditions of measurement are discussed. We show that employing the monochromator with a narrow bandwidth plays a decisive role.
We study the resonant inelastic x-ray scattering (RIXS) at the $K$ edge of Ge. We measure RIXS spectra with systematically varying momenta in the final state. The spectra are a measure of exciting an electron-hole pair. We find a single peak structure (except the elastic peak) as a function of photon energy, which is nearly independent of final-state momenta. We analyze the experimental data by means of the band structure calculation. The calculation reproduces well the experimental shape, clarifying the implication of the spectral shape.
We present a formula for the calculation of K-edge resonant inelastic x-ray scattering on transition metal compounds, based on a local interaction between the valence shell electrons and the $1s$ core hole. Extending a previous result, we include explicit momentum dependence and a basis with multiple core-hole sites. We apply this formula to a single-layered charge, orbital and spin ordered manganite, La$_{0.5}$Sr$_{1.5}$MnO$_4$, and obtain good agreement with experimental data, in particular with regards to the large variation of the intensity with momentum. We find that the screening in La$_…
High-resolution soft X-ray emission and absorption spectra near the N K-edge of wurtzite GaN are presented. The experimental data are interpreted in terms of band structure based full-potential electronic structure calculations. The absorption spectra, compared with calculations including core hole screening, indicate partial core hole screening in the absorption process. The resonant emission spectra demonstrate pronounced dispersions of the spectral structures, identifying effects of momentum conservation due to resonant inelastic X-ray scattering (RIXS) with anisotropic electronic structure…
This paper makes a comparison between x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) in the rare earths. Atomic calculations are given for 2p -> 4f and 2p -> 5d XAS. The latter calculation includes the contraction and expansion of the 5d orbitals resulting from the complete exchange interaction with the 4f electrons. The radiative decay of the XAS final states is described for the situations where the core hole created in the absorption process is filled by a valence electron or by an electron from a shallower core level. RIXS spectra, 4f^n -> _{3d} 4f^{n+1} -> 4f^n,inte…
A resonant inelastic x-ray scattering study of the electronic structure of the semiconductor cuprous oxide, $\rm Cu_2O$, is reported. When the incident x-ray energy is tuned to the Cu K-absorption edge, large enhancements of the spectral features corresponding to the electronic transitions between the valence band and the conduction band are observed. A feature at 6.5 eV can be well described by an interband transition from occupied states of mostly Cu 3d charactor to unoccupied states with mixed 3d, 4s and 2p character. In addition, an insulating band gap is observed, and the momentum depende…
Resonant inelastic X-ray scattering (RIXS) at the $L$-edge of transition metal elements is now commonly used to probe single magnon excitations. Here we show that single magnon excitations can also be measured with RIXS at the $K$-edge of the surrounding ligand atoms when the center heavy metal elements have strong spin-orbit coupling. This is demonstrated with oxygen $K$-edge RIXS experiments on the perovskite Sr$_2$IrO$_4$, where low energy peaks from single magnon excitations were observed. This new application of RIXS has excellent potential to be applied to a wide range of magnetic system…
A new method is presented for describing vibrational effects in x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) using a combination of the classical Franck-Condon (FC) approximation and classical trajectories run on the core-excited state. The formulation of RIXS is an extension of the semiclassical Kramers-Heisenberg (SCKH) formalism of Ref. {Ljungberg_2010} to the resonant case, retaining approximately the same computational cost. To overcome difficulties with connecting the absorption and emission processes in RIXS the classical FC approximation is used fo…
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.
We theoretically demonstrate that a resonant inelastic x-ray scattering (RIXS) with a sizable momentum transfer can be utilized to study valence band dispersion for broad band materials. We take RIXS at the Si K edge of 3C-SiC as a typical example. The RIXS spectra are calculated by systematically changing the transferred momentum, an incident photon polarization and an incident photon energy, on the basis of an ab initio calculation. We find that the spectra depend heavily on both the transferred momentum and the incident photon polarization, and the peaks in the spectra correspond to the ene…
Detailed information on the electronic states of both V and Mn 3d electrons in the ferrimagnet Mn2VAl is obtained by the bulk sensitive resonant inelastic soft x-ray scattering (SX-RIXS) excited with the circularly polarized light under an external magnetic field for the first time. The results under the V L-edge excitation have revealed the negligible partial density of states (PDOS) of the V 3d states around the Fermi energy as well as their rather localized character. Under the Mn L-edge excitation, on the other hand, the spectra are dominated by fluorescence with clear magnetic circular di…
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) 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.
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 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 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…
Resonant inelastic x-ray scattering at the N K edge reveals clearly resolved harmonics of the anion plane vibrations in the kappa-(BEDT-TTF)2Cu2(CN)3 spin-liquid insulator. Tuning the incoming light energy at the K edge of two distinct N sites permits to excite different sets of phonon modes. Cyanide CN stretching mode is selected at the edge of the ordered N sites which are more strongly connected to the BEDT-TTF molecules, while positionally disordered N sites show multi-mode excitation. Combining measurements with calculations on an anion plane cluster permits to estimate the sitedependent …
An unparalleled resolution is reported with an inelastic x-ray scattering instrument at the Cu K-edge. Based on a segmented concave analyzer, featuring single crystal quartz (SiO_{2}) pixels, the spectrometer delivers a resolution near 25 meV (FWHM) at 8981 eV. Besides the quartz analyzer, the performance of the spectrometer relies on a four-bounce Si(553) high-resolution monochromator and focusing Kirkpatrick-Baez optics. The measured resolution agrees with the ray tracing simulation of an ideal spectrometer. We demonstrated the performance of the spectrometer by reproducing the phonon disper…
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…
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 …
Using the tight-binding linear muffin-tin orbitals method, the soft x-ray fluorescence K-emission spectra of boron in MgB_2, excited close to the absorption edge, are estimated. In the calculations the angle of incidence between the direction of the incoming photon and the hexagonal axis of the specimen is 60 degrees and 75 degrees. Comparison with experiment is possible in the former case where good agreement is found. Furthermore, another resonant feature below the Fermi energy is predicted for the larger angle. This feature can be related to the excitations to the antibonding B pi-band in t…
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.
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…
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 present a study on the high-Tc superconductor (HTSC) YBa2Cu3O7-x (YBCO) using polarization-dependent X-ray absorption and resonant inelastic X-ray scattering. High-resolution measurements using synchrotron-radiation are compared with calculations using a quasi-atomic multiplet approach performed at the Cu 2p3/2-edge of YBCO. We use a multiplet approach within the single impurity Anderson model to reproduce and understand the character of the localized low-energy excitations in YBCO. We observe a distinct peak at about 0.5 eV in O K RIXS. This peak shows dependence on doping, incident energy…
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 propose a simple first-principles method to describe propagation of tightly bound excitons. By viewing the exciton as a composite object (an effective Frenkel exciton in Wannier orbitals), we define an exciton kinetic kernel to encapsulate the exciton propagation and decay for all binding energy. Applied to prototypical LiF, our approach produces three exciton bands, which we verified quantitatively via inelastic x-ray scattering. The proposed real-space picture is computationally inexpensive and thus enables study of the full exciton dynamics, even in the presence of surfaces and impurity …
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…
