Vacancy ordering and electronic structure of γ-Fe₂O₃ (maghemite): a theoretical investigation.

The crystal structure of the iron oxide γ-Fe₂O₃ is usually reported in either the cubic system (space group P4(3)32) with partial Fe vacancy disorder or in the tetragonal system (space group P4(1)2(1)2) with full site ordering and c/a≈3. Using a supercell of the cubic structure, we obtain the spectrum of energies of all the ordered configurations which contribute to the partially disordered P4(3)32 cubic structure. Our results show that the configuration with space group P4(1)2(1)2 is indeed much more stable than the others, and that this stability arises from a favourable electrostatic contribution, as this configuration exhibits the maximum possible homogeneity in the distribution of iron cations and vacancies. Maghemite is therefore expected to be fully ordered in equilibrium, and deviations from this behaviour should be associated with metastable growth, extended anti-site defects and surface effects in the case of small nanoparticles. The confirmation of the ordered tetragonal structure allows us to investigate the electronic structure of the material using density functional theory (DFT) calculations. The inclusion of a Hubbard (DFT + U) correction allows the calculation of a band gap in good agreement with experiment. The value of the gap is dependent on the electron spin, which is the basis for the spin-filtering properties of maghemite.