Band Theory of Multiple Ordering and the Metal-Semiconductor Transition in Magnetite

A tight-binding calculation of the band structure of magnetite with Verwey ordering alone does not, for any strength of interatomic Coulomb energy, yield insulating behavior; for this, additional orderings in transverse directions are required. Below the Verwey temperature TV, iron B-site charge densities are fractional (nonionic), continuous functions of T, and the gap is probably indirect with T-dependent band extrema (TTV). There is semimetallic behavior above TV. Multiple orderings allow a natural description of the extra M\"ossbauer spectra and neutron- and electron-diffraction patterns recently observed.