Energetic stabilization of the Mizoguchi structure for magnetite by band-structure effects

We show that the Mizoguchi structure is energetically stabilized over the Verwey structure for magnetite by electron hopping on the B sublattice. We use the one-band Cullen-Callen model Hamiltonian for the electronic band structure taking the nearest-neighbor and the second-neighbor Coulomb interactions, ${\mathit{U}}_{1}$ and ${\mathit{U}}_{2}$, into account. There is a competition between the Coulomb and the band-structure energies. The Coulomb energy tends to favor the Verwey structure while the band-structure energy tends to favor the Mizoguchi structure. We find that for ${\mathit{U}}_{1}$\ensuremath{\lesssim}0.25 eV, the kinetic-energy (band-structure energy) term dominates making the Mizoguchi structure energetically favorable over the Verwey structure. For a larger value of ${\mathit{U}}_{1}$, the band-structure effect alone is insufficient, making it necessary to invoke other mechanisms such as the electron-phonon coupling earlier proposed by other authors, to stabilize the Mizoguchi structure. The energy of a single ``reversed-ring'' excitation in the Mizoguchi structure is calculated to be of the order of a few meV. The small energy is consistent with Cullen's explanation of the absence of cell doubling in the ${\mathit{C}}_{\mathit{a}}$ plane as observed in diffraction experiments. The Mizoguchi order is unstable with respect to the formation of reversed-ring excitations if only ${\mathit{U}}_{1}$ is present, but is stabilized by a small value of ${\mathit{U}}_{2}$.