The onset of antiferromagnetism in the Hubbard model

Abstract

The antiferromagnetic phase of a narrow energy band material with one electron per atom is studied using the Hubbard model in the 'alloy analogy'. An electron of a particular spin sees the potential due to a 'frozen' configuration of the electrons of opposite spin, these being distributed on two sublattices with probabilities 1/2(1+or-m), where m is the antiferromagnetic order parameter. This problem of a partially ordered alloy is treated within the coherent potential approximation. The order parameter m is determined self-consistently and the detailed calculations are given for an alternant lattice with a semicircular density of states. It is found that, contrary to Hartree-Fock calculations, antiferromagnetism appears only when the intra-atomic Coulomb interaction U exceeds a critical value. The metal-insulator transition occurs at a lower value of U so that antiferromagnetism does not appear in the metallic state. The general features of the electronic density of states in the antiferromagnetic phase are discussed.