Vacancy mediated ferromagnetic interaction in TiO2 doped with magnetic ions

We extend the model of ferromagnetic superexchange in dilute magnetic semiconductors to the ferromagnetically ordered highly insulating compounds (dilute magnetic dielectrics). The intrinsic ferromagnetism without free carriers is observed in oxygen-deficient films of anatase TiO2 doped with the transition metal impurities in cation sublattice. We suppose that ferromagnetic order arises due to superexchange between the complexes [oxygen vacancies+magnetic impurities], which are stabilized by a charge transfer from the vacancies to impurities. The Hund rule controls the superexchange via the empty vacancy related levels in the energy gap, so that it becomes possible only for the parallel orientation of impurity magnetic moments. The percolation threshold for magnetic ordering is determined by the radius of vacancy levels, but the exchange mechanism does not require free carriers. The crucial role of the nonstoichiometry in the formation of the ferromagnetism makes the Curie temperature extremely sensitive to the methods of sample preparation.