Orbital polarization, charge transfer, and fluorescence in reduced-valence nickelates

Abstract

This paper presents a simple formalism for calculating x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) that has as input orbital-resolved density of states from a single-particle or many-body ab initio calculation and is designed to capture itinerant like features. We use this formalism to calculate both the XAS and RIXS with input from density functional theory (DFT) and $\mathrm{DFT}+\mathrm{DMFT}$ for the recently studied reduced valence nickelates ${R}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{8}$ and $R{\mathrm{NiO}}_{2}$ ($R=\text{rare earth}$), and these results are then contrasted with those for the cuprate ${\mathrm{CaCuO}}_{2}$ and the unreduced nickelate ${R}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}$. In contrast to the unreduced ${R}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}$, the reduced valence nickelates as well as the cuprate show strong orbital polarization due to the dominance of ${x}^{2}\ensuremath{-}{y}^{2}$ orbitals for the unoccupied $3d$ states. We also reproduce two key aspects of a recent RIXS experiment for ${R}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{8}$: (i) a charge-transfer feature between $3d$ and oxygen $2p$ states whose energy we find to decrease as one goes from $R{\mathrm{NiO}}_{2}$ to ${R}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{8}$ to the cuprate, and (ii) an energy-dependent polarization reversal of the fluorescence line that arises from hybridization of the unoccupied $3{z}^{2}\ensuremath{-}{r}^{2}$ states with $R 5d$ states. We end with some implications of our results for the nature of the $3d$ electrons in reduced valence nickelates.