Verwey transition in magnetite: Mean-field solution of the three-band model

The nature of the Verwey transition in magnetite (Fe3O4) within a three-band spinless model Hamiltonian is examined. These bands, which arise from the minority-spin t2g orbitals on the Fe(B) sublattice, are occupied by half an electron per Fe(B) atom. The Verwey order–disorder transition is studied as a function of the ratio of the intersite Coulomb repulsion U1 and the bandwidth W. It is found that the electrons are ordered beyond the critical value of U1/W≊0.25 in essential agreement with the results of the one-band Cullen–Callen model. For larger values of U1/W, a Verwey-like order is exhibited where the electrons occupy alternate (001) planes. The model predicts a transition from the metallic to the semiconducting state with the band gap increasing linearly with U1 beyond the transition point.