Resonant inelastic x-ray scattering spectra for electrons in solids

Resonant inelastic x-ray scattering (RIXS) has recently been a subject of remarkable progress due to the advent of high-brilliance synchrotron radiation sources. The authors present a review of both experimental and theoretical investigations of electrons in solids using this second-order optical process, in which there is coherent absorption and emission of x rays at resonance with electronic excitations. The review starts with some of the fundamental aspects of RIXS, after which are presented typical experimental data and their theoretical interpretation for various materials. The first class of materials considered is semiconductors and insulators (Si, C, and BN), which are typical systems with weak electron correlation, and the data are interpreted based on electronic states described by an energy-band model. Effects of symmetry of electronic states and electron momentum conservation are discussed. At the opposite extreme are rare-earth systems (metals and oxides), in which the $4f$ electrons are almost localized with strong electron correlation. The observations are interpreted based on the effects of intra-atomic multiplet coupling and weak interatomic electron transfer, which are well described with an Anderson impurity model or a cluster model. In this context a narrowing of spectral width in the excitation spectrum, polarization dependence, and the magnetic circular dichroism in ferromagnetic materials are discussed. The authors then consider transition-metal compounds, materials with electron correlation strengths intermediate between semiconductors and rare-earth systems. In these interesting cases there is an interplay of intra-atomic and interatomic electronic interactions that leads to limitations of both the band model and the Anderson impurity model. Finally, other topics in resonant x-ray emission studies of solids are described briefly.