Effects of inter-site Coulomb interactions on ferromagnetism: Application to Fe, Co and Ni

TL;DR

This paper investigates how inter-site Coulomb interactions influence metallic ferromagnetism, using tight-binding and Hartree-Fock methods to analyze transition metals Fe, Co, and Ni, revealing significant effects on magnetic properties.

Contribution

It introduces a generalized Stoner criterion considering inter-site Coulomb interactions and applies a realistic tight-binding model to explain ferromagnetism in 3d transition metals.

Findings

Inter-site Coulomb interactions modify ferromagnetic conditions.

The model agrees well with density functional calculations.

Hopping integral renormalization impacts magnetic properties.

Abstract

We reanalyze the condition for metallic ferromagnetism in the framework of the tight-binding approximation and investigate the consequences of the inter-site Coulomb interactions using the Hartree-Fock approximation. We first consider a non-degenerate $s$ band and we show that the inter-site interactions modify the occurrence of ferromagnetism, and we derive a generalized Stoner criterion. We analyze the main effects due to the renormalization of the hopping integrals by the inter-site Coulomb interactions. These effects are strongly dependent on the relative values of the inter-site electron-electron interactions and on the shape of the density of states as illustrated by a study of cubic crystals from which we establish general trends. We then investigate a realistic $spd$ tight-binding model, including intra (Coulomb and exchange) and inter-site charge-charge Coulomb integrals. This model is used to study the electronic structure (band structure, densities of states, magnetic moment) of bulk ferromagnetic 3d transition metals Fe(bcc), Co(hcp and fcc) and Ni(fcc). An excellent agreement with local spin density functional calculations is obtained for the three metals, in particular concerning the relative widths of the majority and minority spin bands. Thus our tight-binding Hartree-Fock model provides a consistent interpretation of this effect.