Superexchange in Dilute Magnetic Dielectrics: Application to (Ti,Co)O_2
  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 TiO_2 doped with transition metal impurities in cation sublattice. We suppose that ferromagnetic order arises due to superexchange between complexes [oxygen vacancies + magnetic impurities], which are stabilized by charge transfer from vacancies to impurities. The Hund rule controls the superexchange via empty vacancy related levels 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 non-stoichiometry in formation of the ferromagnetism makes the Curie temperatures extremely sensitive to the methods of sample preparation. 
K. Kikoin and V. Fleurov