Charge-ordered insulating state of ${\mathrm{Fe}}_3$${\mathrm{O}}_4$ from first-principles electronic structure calculations

The charge-ordered insulating state of ${\mathrm{Fe}}_3$${\mathrm{O}}_4$ below the Verwey transition temperature has been studied by the modified local density approximation with Coulomb interaction correction method. The charge ordering is found to be a stable solution with an energy gap value of 0.34 eV (the experimental value is 0.14 eV) in contrast to a uniform metallic state given by the standard local spin-density approximation. The calculated effective intersite Coulomb interaction is well screened (V=0.18 eV). It was shown that the change in electrostatic potential associated with the transition to a completely disordered state can close an energy gap leading to a metallic state. © 1996 The American Physical Society.