Charge ordering in magnetite at low temperatures

The ordering of the Fe2+ and Fe3+ ions on the octahedral sites of magnetite (Fe3O4) at temperatures below the Verwey metal-insulator transition has been studied by quantitative high-energy transmission electron diffraction. We find that there are ten independent charge-ordering models (including the Verwey model) for the low-temperature structure that satisfy the Anderson condition if the symmetry is Cc (monoclinic). Dynamical electron diffraction patterns are simulated and compared with experiment for these charge-ordering models, using atomic coordinates obtained from neutron diffraction work. We find that one of these ten charge-ordering models agrees best with experiment and that the electrons in this model form a characteristic wave. Our calculations of electron correlation energy show that this model has the second lowest energy, while the Verwey model has the lowest. This indicates the importance of electron-phonon interactions in stabilizing the structure.