Charge ordering and lattice distortion inFe3O4

An ordered state is proposed for ${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$ which explains both the half-integer and mixed-integer diffraction peaks. The consequences of this state are discussed in terms of a model which includes both electrostatic and distortion-induced interactions. An Ewald-method calculation for the various possible ordered states does not find lowest electrostatic energy for the experimentally observed ordered state, implying that the electronphonon interaction is crucially important in stabilizing the ordered state.