Charge and orbital ordering in the low-temperature monoclinic structure of magnetite (Fe_3O_4) is investigated using LSDA+U. While the difference between t_{2g} minority occupancies of Fe^{2+}_B and Fe^{3+}_B 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.
@article{arxiv.cond-mat/0402363,
title = {Charge and orbital order in Fe_3O_4},
author = {I. Leonov and A. N. Yaresko and V. N. Antonov and M. A. Korotin and V. I. Anisimov},
journal= {arXiv preprint arXiv:cond-mat/0402363},
year = {2016}
}