Band Gap in Magnetite above Verwey Temperature Induced by Symmetry Breaking

Magnetite exhibits a famous phase transition, called Verwey transition, at the critical temperature TV of about 120 K. Although numerous efforts have been devoted to the understanding of this interesting transition, up to now, it is still under debate whether a charge ordering and a band gap exist in magnetite above TV. Here, we systematically investigate the charge ordering and the electronic properties of magnetite in its cubic phase using different methods based on density functional theory: DFT+U and hybrid functionals. Our results show that, upon releasing the symmetry constraint on the density but not on the geometry, charge disproportionation (Fe2+/Fe3+) is observed, resulting in a band gap of around 0.2 eV at the Fermi level. This implies that the Verwey transition is probably a semiconductor-to-semiconductor transition and that the conductivity mechanism above TV is small polaron hopping.