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

Abstract

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 $T_{\mathrm{V}}$, iron $B$-site charge densities are fractional (nonionic), continuous functions of $T$, and the gap is probably indirect with $T$-dependent band extrema ($T\lesssim T_{\mathrm{V}}$). There is semimetallic behavior above $T_{\mathrm{V}}$. Multiple orderings allow a natural description of the extra Mössbauer spectra and neutron- and electron-diffraction patterns recently observed.