Band Gap in Magnetite above Verwey Temperature Induced by Symmetry Breaking

Magnetite exhibits a famous phase transition, called Verwey transition, at the critical temperature T V 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 T V . 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 (Fe 2+ /Fe 3+ ) 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 T V is small polaron hopping.