Role of oxygen states in square planar d9-delta nickelates.

The discovery of superconductivity in square planar $d^{9-\delta}$ nickelates has ignited a vigorous debate regarding their essential electronic properties: Do these materials have appreciable oxygen charge-transfer character akin to the cuprates or are they in a distinct Mott-Hubbard regime where oxygen plays a minimal role? Here, we resolve this question using O $K$-edge \gls*{RIXS} measurements of the $d^{9-\delta}$ nickelate La$_{4}$Ni$_{3}$O$_{8}$ and a prototypical cuprate La$_{2-x}$Sr$_{x}$CuO$_{4}$ ($x=0.35$), interpreting the results with exact diagonalization calculations. As expected, the cuprate lies deep in the charge-transfer regime of the Zaanen-Sawatzky-Allen (ZSA) scheme. The nickelate, however, is not well-described by either limit of the ZSA scheme and is found to be of mixed charge-transfer / Mott-Hubbard character with the Coulomb repulsion $U$ of similar size to the charge transfer energy $\Delta$. Nevertheless, the transition-metal-oxygen hopping is larger in La$_{4}$Ni$_{3}$O$_{8}$ than in La$_{2-x}$Sr$_{x}$CuO$_{4}$, leading to a significant superexchange interaction and an appreciable hole occupation of the ligand O orbitals in La$_{4}$Ni$_{3}$O$_{8}$ despite its larger $\Delta$. Our results clarify the essential characteristics of $d^{9-\delta}$ nickelates and put strong constraints on theoretical interpretations of superconductivity in these materials.