Charge-orbital ordering in low-temperature structures of magnetite:: GGA+U investigations

The atomic and electronic structure of magnetite (Fe3O4) in the four possible low-temperature structures, namely, P2/c-Pmca (I), Pmca (II), Pmc2(1) (III), and Cc (IV), have been investigated by generalized gradient approximation+Hubbard U (GGA+U) electronic structure and structural optimization calculations. Charge-orbital ordering is found to exist in all the four structures. The charge-orbital ordering and hence the Verwey metal-insulator transition is shown to be driven by the on-site Fe d-electron correlation. The theoretical charge-orbital ordering patterns in the I, II, and III structures do not satisfy the Anderson criterion but are consistent with recent neutron and x-ray diffraction experiments. The IV (Cc) structure is found to be the ground state structure. In the IV structure, the charge-orbital ordering on 3/4 of the tetrahedra does not satisfy the Anderson condition, while on 1/4 of the tetrahedra it does. The observed entropy change at the Verwey transition, which has been a long standing puzzle, is analyzed and found to be consistent with the charge-orbital orders obtained here.