Charge disproportionation without charge transfer in the rare-earth nickelates as a possible mechanism for the metal-insulator transition

TL;DR

This paper models the metal-insulator transition in rare-earth nickelates as driven by charge disproportionation without actual charge transfer, involving lattice distortions and a new type of charge ordering.

Contribution

It introduces a model showing that charge disproportionation can occur without charge transfer, driven by lattice distortions and negative charge transfer energy.

Findings

A gap opens at large lattice distortions, leading to insulating behavior.

The insulating state involves charge ordering without charge movement.

The transition is associated with a superstructure observed in experiments.

Abstract

We study a model for the metal-insulator (MI) transition in the rare-earth nickelates RNiO$_3$, based upon a negative charge transfer energy and coupling to a rock-salt like lattice distortion of the 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 ground state of predominantly $d^8\ligand$ character, where $\ligand$ denotes a ligand hole. For sufficiently large distortions ($\delta d_{\rm Ni-O} \sim 0.05 - 0.10\AA$), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with $(d^8\ligand^2)_{S=0}(d^8)_{S=1}$ character, where $S$ is the total spin. Thus the MI transition may be viewed as being driven by an internal volume "collapse" where the 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 a new type of charge ordering achieved without any actual movement of the charge.