Theory of the order-disorder and insulator-metal transformations in magnetite

Abstract

Electronic energy bands for Fe3O4 are calculated in the neighborhood of the Verwey transition temperature using a Hartree‐Fock decoupled Hamiltonian. Parameters appearing in the H‐F Hamiltonian are determined by minimizing the free energy in configuration space in the pair approximation of the cluster variation method. Four sublattice construction of the spinel structure, charge density of 1/2 electron per site, and the Verwey charge ordering along the c‐axis are assumed. The Verwey order parameter, effective exchange fields and the specific heat are calculated as functions of temperature. Those results are substituted into the H‐F Hamiltonian and four energy bands are obtained. At sufficiently low temperatures, those bands are split into two, almost doubly degenerate, bands separated by a large energy gap, corresponding to an insulator phase. As temperature approaches the Verwey transition point, the band width increases rapidly, accompanied by a narrowing of the energy gap. The lower filled bands and upper vacant bands eventually touch each other, changing the system into a metallic state. It is found that the insulator‐metal transition takes place at a temperature where the Verwey order is still finite, although very small. As long as the Verwey transition remains second order, the theory predicts two different transition temperatures, one for the insulator‐metal transition and the other for the order‐disorder transition.Electronic energy bands for Fe3O4 are calculated in the neighborhood of the Verwey transition temperature using a Hartree‐Fock decoupled Hamiltonian. Parameters appearing in the H‐F Hamiltonian are determined by minimizing the free energy in configuration space in the pair approximation of the cluster variation method. Four sublattice construction of the spinel structure, charge density of 1/2 electron per site, and the Verwey charge ordering along the c‐axis are assumed. The Verwey order parameter, effective exchange fields and the specific heat are calculated as functions of temperature. Those results are substituted into the H‐F Hamiltonian and four energy bands are obtained. At sufficiently low temperatures, those bands are split into two, almost doubly degenerate, bands separated by a large energy gap, corresponding to an insulator phase. As temperature approaches the Verwey transition point, the band width increases rapidly, accompanied by a narrowing of the energy gap. The lower filled bands and up...