Charge and Orbital Order inFe3O4

Charge and orbital ordering in the low-temperature monoclinic structure of magnetite (${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$) is investigated using the local spin density approximation with Coulomb interaction correction method. While the difference between $t_{2g}$ minority occupancies of ${\mathrm{F}\mathrm{e}}_B^{2+}$ and ${\mathrm{F}\mathrm{e}}_B^{3+}$ cations is large and gives direct evidence for charge ordering, the screening is so effective that the total $3d$ charge disproportion is rather small. The charge order has a pronounced [001] modulation, which is incompatible with the Anderson criterion. The orbital order agrees with the Kugel-Khomskii theory.