Collective Electron Theory of the Metal-Semiconductor Transition in Magnetite

Abstract

The Verwey transition in magnetite is described on a band model, with the electrons self-consistently breaking the symmetry by ordering in the self-induced Coulomb potential. The order parameter is the difference in occupation numbers on alternate sites. There is a gap in the single-particle excitation spectrum, and the gap and order parameter undergo a second-order phase transition. The theory is BCS-like, with the Verwey temperature being given in the weak-coupling limit by an exponential in the reciprocal of the density of states at the Fermi level.