Charge and orbital ordering structure of Fe3O4 in the low-temperature phase as deduced from NMR study

The hyperfine fields of Fe ions in Fe3O4 have been investigated for a spherically shaped specimen at 4.2 K using NMR. From the angular dependence of the resonance frequencies on an external magnetic field, the numbers of the inequivalent sites on A- and B-sites are determined to be just eight and sixteen, respectively. The anisotropy in the hyperfine fields of A-sites reveals that one of the mirror symmetries in the high-temperature phase remains incomplete. A charge and orbital ordering structure, which is consistent with the crystallographic and electronic properties of Fe3O4 in the low-temperature phase, is proposed. A model of charge density waves above the metal-insulator transition temperature T-MI is also proposed. The charge ordering below T-MI is constructed by freezing the charge density waves at the lattice points of Fe ions. Two mechanisms are postulated to stabilize orbital ordering at the time of freezing, One is the repulsive Coulomb force between the electron clouds of the nearest-neighbor Fe ions and the other is the formation of bonding and anti-bonding orbitals between these Fe ions.