Effective one-band electron-phonon Hamiltonian for nickel perovskites

TL;DR

This paper develops a minimal microscopic model for nickel perovskites that captures charge, lattice, magnetic, and transport phenomena by analyzing hole motion and phonon coupling in $NiO_2$ planes.

Contribution

It introduces a generalized Holstein t-J Hamiltonian tailored for nickelates, incorporating complex hopping, spin interactions, and phonon coupling.

Findings

Model explains observed charge and lattice modulations.

Captures magnetic and electronic transport anomalies.

Provides a framework for understanding nickelate properties.

Abstract

Inspired by recent experiments on the Sr-doped nickelates, $La_{2-x}Sr_xNiO_4$, we propose a minimal microscopic model capable to describe the variety of the observed quasi-static charge/lattice modulations and the resulting magnetic and electronic-transport anomalies. Analyzing the motion of low-spin (s=1/2) holes in a high-spin (S=1) background as well as their their coupling to the in-plane oxygen phonon modes, we construct a sort of generalized Holstein t-J Hamiltonian for the $NiO_2$ planes, which contains besides the rather complex ``composite-hole'' hopping part non-local spin-spin and hole-phonon interaction terms.