Absence of charge ordering below the Verwey transition temperature in magnetite

The electronic state of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ below the Verwey transition has been studied by x-ray resonant scattering at the iron K edge of the forbidden (0 0 2) and (0 0 6) reflections. These reflections are permitted by the anisotropy of the iron anomalous scattering factor. The energy and the azimuthal angle dependence of the intensity of these reflections do not change above and below the transition temperature. Moreover, the spectrum at low temperature does not change upon orientation of the crystal c axis. The results clearly show that no charge ordering of ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{2+}$ occurs in the insulating phase of magnetite. We also discuss the possible charge ordering models, assuming the Cc symmetry and the Anderson condition. Only two models, out of ten analyzed, do not give any isotropic contribution to the forbidden reflections and could support a charge disproportionation. Nevertheless, it should be at most 25%.