Long Range Charge Ordering in Magnetite Below the Verwey Transition

The crystal structure of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ below the 122 K Verwey transition has been refined using high-resolution x-ray and neutron powder diffraction data. The refinements give direct evidence for charge ordering (CO) over four independent octahedral Fe sites, two with a charge of $+2.4\mathrm{}$ and the other two of $+2.6\mathrm{}$. CO schemes consistent with our model do not meet the widely accepted Anderson condition of minimum electrostatic repulsion. Instead we propose that CO is driven primarily by a [001] electronic instability, which opens a gap at the transition through a charge density wave mechanism.