Antiferromagnetic ordering of itinerant systems in modified mean-field theory

TL;DR

This paper develops a modified mean-field theory for itinerant antiferromagnetism, incorporating on-site and inter-site correlations, band degeneracy, and Green function techniques to explain antiferromagnetic ordering in high-temperature superconductors.

Contribution

It introduces a new approach combining CPA and modified Hartree-Fock approximations to explain antiferromagnetism in itinerant systems at half-filling.

Findings

Antiferromagnetic instability occurs at half-filling in the split band limit.

Correlation factors modify the shape of spin bands and reduce kinetic energy.

On-site and inter-site interactions cooperatively induce antiferromagnetism.

Abstract

This is an analysis of the itinerant model for antiferromagnetism, in which is included both on-site and inter-site electron correlations. We also consider the band degeneration, which brings into the Hamiltonian the on-site exchange interactions. The Green function technique is used and the coherent potential approximation (CPA) decoupling for the on-site Coulomb repulsion. This decoupling combined with the modified Hartree-Fock approximation for the inter-site interactions generates the change in shape of the spin bands with growing interaction constants, which is described by the correlation factors and which decreases the kinetic energy of the system. The effective Hartree field and the gain in kinetic energy due to the on-site and inter-site correlation factors drive the antiferromagnetism. The on-site and inter-site interactions act together towards the antiferromagnetism. Their cooperation decreases the interaction constants required for the antiferromagnetic ordering. This new approach allows for the antiferromagnetic instability in the purely itinerant model at the half-filling in the split band limit. This situation describes the high temperature superconducting cuprates.