Charge Disproportionation without Charge Transfer in the Rare-Earth-Element Nickelates as a Possible Mechanism for the Metal-Insulator Transition

Abstract

We study a model for the metal-insulator ($M\text{\ensuremath{-}}I$) transition in the rare-earth-element nickelates $R{\mathrm{NiO}}_{3}$, based upon a negative charge transfer energy and coupling to a rocksaltlike lattice distortion of the ${\mathrm{NiO}}_{6}$ octahedra. Using exact diagonalization and the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with a ground state of predominantly ${d}^{8}L$ character, where $\underset{_}{L}$ denotes a ligand hole. For sufficiently large distortions ($\ensuremath{\delta}{d}_{\mathrm{Ni}\text{\ensuremath{-}}\mathrm{O}}\ensuremath{\sim}0.05--0.10\text{ }\text{ }\AA{}$), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with $({d}^{8}{\underset{_}{L}}^{2}{)}_{S=0}({d}^{8}{)}_{S=1}$ character, where $S$ is the total spin. Thus the $M\text{\ensuremath{-}}I$ transition may be viewed as being driven by an internal volume ``collapse'' where the ${\mathrm{NiO}}_{6}$ octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the ($1/2$, $1/2$, $1/2$) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of charge ordering achieved without any actual movement of the charge.