Nonresonant Inelastic X-Ray Scattering Involving Excitonic Excitations: The Examples of NiO and CoO

TLDR: An accurate quantitative description based on a local many body approach, beyond local density approximation + Hubbard U approximations is presented, allowing for a determination of the local symmetry of the initial and final states in transition metal and rare earth compounds.

Abstract: In a recent publication Larson et al. reported remarkably clear $d\mathrm{\text{\ensuremath{-}}}d$ excitations for NiO and CoO with x-ray scattering. Here we present an accurate quantitative description based on a local many body approach, beyond local density approximation $+$ Hubbard U approximations. The magnitude of $\stackrel{\ensuremath{\rightarrow}}{q}$ determines which of the allowed multipoles contributes most to the spectra. The direction of $\stackrel{\ensuremath{\rightarrow}}{q}$ with respect to the crystal can be used as an equivalent to polarization similar to electron energy loss spectroscopy, allowing for a determination of the local symmetry of the initial and final states. This method is more generally applicable and could be a powerful tool for the study of local distortions and symmetries in transition metal and rare earth compounds.