Theory of low energy excitations in resonant inelastic x-ray scattering for rare-earth systems: Yb compounds as typical examples

Abstract

Theoretical predictions are given for low energy excitations, such as crystal field excitations and Kondo resonance excitations, to be detected by high-resolution measurements of resonant inelastic x-ray scattering (RIXS) of rare-earth materials with Yb compounds as typical examples. Crystal field excitations in the Yb $3d$ RIXS of a Yb${}^{3+}$ ion in the cubic crystal field are formulated, and the calculation of RIXS spectra for YbN is done. Kondo resonance excitations revealed in the Yb $3d$ RIXS spectra are calculated for mixed-valence Yb compounds, Yb${}_{1\ensuremath{-}x}$Lu${}_{x}$Al${}_{3}$, in the leading term approximation of the 1/${N}_{f}$ expansion method with a single impurity Anderson model. It is emphasized that the high-resolution RIXS with polarization dependence is a powerful tool to study the crystal field levels together with their symmetry and also the Kondo bound state in rare-earth compounds. Some in-depth discussions are given on the polarization effects of RIXS, including $4d$ and $2p$ RIXS spectra, the coherence effect of the Kondo bound states, and the importance of the high-resolution RIXS spectra for condensed matter physics under extreme conditions.