Multiple Ordering in Magnetite

We present results of a self-consistent band calculation of the ground-state energy and charge orderings based on a tight-binding scheme in magnetite. The calculation is greatly simplified by making use of the large intra-atomic Coulomb interactions between electrons on the Fe ions, previous estimates of the crystal field splittings, and the magnetic ordering. We find that below a critical value ({~}2.2) of the ratio of interatomic Coulomb energy U to bandwidth w the lowest-energy state has no order. Between this critical value and 2.5, the preferred state is multiply ordered (three nonzero order parameters). For larger values of this ratio, the Verwey-symmetry state (one order parameter) is stable, but the value of the order parameter approaches 1 (ionic Verwey order) only in the limit of U/w→∞.