An application of resonant inelastic x-ray scattering technique for studying of optical scale excitations in electron-correlated materials is discussed. Examples are given including data obtained for 3d transition metal, lanthanide, and actinide systems. In some cases, the data are compared with the results of crystal-field multiplet and Anderson impurity model calculations. Advantages of this technigue are pointed out, such as an ability to probe an extended multiplet structure of the ground state configuration, which is not fully accessible by other spectroscopies, an extreme sensitivity of spectral profiles to the chemical state of the element in question and to the crystal-field strength, and a great potential in probing the ground state character (for example, ground state J-mixing in rare-earths) due to the technique's elemental selectivity and strict selection rules. Issues are addressed, such as a possible deviations from the linear dispersion of inelastic scattering structures, corresponding to charge-transfer excitations, with varying excitation energies and an estimation of values for model parameters, involved in the description of charge-transfer processes.
Technique and modelsTo successfully describe various physical properties of a system in question it is necessary to obtain knowledge about the ground state and low-energy excited states of this system. For 3d transition element, lanthanide, and actinide compounds with a partly filled d or f shell, strong correlation effects, when the dispersional part of d or f bandwidth is smaller than the on-site Coulomb interaction U between localized electrons, break down a single-particle picture and an atomic-like approach to characterize the electronic structure of these compounds is more appropriate.In this case a state of the system without a core hole is described in terms of intra-atomic neutral excitations (a multiplet structure of the ground state electronic configuration due to electrostatic, exchange, crystal field, spin-orbit interactions, etc.) and/or inter-atomic charge-transfer excitations. The latter are the result of electron hopping from delocalized states to a localized state and are treated by short-range models, such as an Anderson impurity model [1], using a set of parameters. The models are represented by the HamiltonianImportant physical quantities included in this Hamiltonian are the delocalized-and localizedstate energies ε kα and ε m , hopping matrix element V kαm , and U . Here k, α, σ, and m denote a wave vector, an index of the energy level in the valence band, a spin index, and an azimutal quantum number, respectively. For the description of core spectroscopies a further term is added to the Hamiltonian to account for coupling between localized electron and a core hole. The values of model parameters are optimized by fitting both high-energy spectroscopic and low-energy transport data and then employed to describe the character of the ground state, different ground-state properties, the nature and size of the band gap in insulat...