Charge ordered structure of magnetiteFe3O4below the Verwey transition

The crystal structure of highly stoichiometric magnetite $\left({\mathrm{Fe}}_3{\mathrm{O}}_4\right)$ below the Verwey transition has been refined from high-resolution neutron and synchrotron x-ray powder-diffraction data. The refined model has a monoclinic $P2/c$ symmetry cell with orthorhombic Pmca pseudosymmetry constraints on the atomic positions, and contains four independent octahedral B site iron atoms. Charge ordering is evidenced by the presence of expanded and contracted $B{\mathrm{O}}_6$ octahedra, and by the distribution of B-B distances resulting from unequal Coulombic repulsions between the different B site charges. The B-B distances are inconsistent with dimer formation. Competition between the $B-\mathrm{O}$ and B-B interactions results in polar displacements of two of the B site cations. The charge ordering has a predominant [001] density modulation, which relieves a nesting instability in the electronic density of states, but a second $\left[00\frac{1}{2}\right]$ phase modulation also occurs. The monoclinic distortion at the Verwey transition is consistent with a macroscopic rhombohedral magnetostriction, driven by the localization of orbitally degenerate ${\mathrm{Fe}}^{2+},$ coincident with the microscopic charge ordering distortions that have an orthorhombic lattice symmetry.