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.