The role of transition metal impurities and oxygen vacancies in the   formation of ferromagnetism in Co-doped TiO2
  We have investigated the role of transition metal impurities and oxygen vacancies in the formation of ferromagnetism in Co-doped TiO2 using LSDA+U approach which takes into account strong on-cite Coulomb correlations for electronic structure calculations. Several model systems such as supercells of rutile TiO2 with Co{+2} ion in high-spin state substituted into titanium cite and with oxygen vacancies were considered. We found that exchange interaction of Co magnetic ions is ferromagnetic, but very weak due to the large average impurity-impurity distance. However, its strength becomes three times stronger when there is a magnetic vacancy nearby. The magnetic moment values are 3\mu_B for Co{2+} and 1\mu_B for vacancy with the opposite directions of them. Our investigation showed that exchange interaction energy of Co and vacancy moments varies from 330meV to 40meV depending on the distance between them in the supercell. We suppose that strong interaction between Co and vacancy moments should be taken into account for the explanation of high Curie temperature value in Co-doped TiO2. 
V.I. Anisimov, M.A. Korotin, I.A. Nekrasov, A.S. Mylnikova, A.V.   Lukoyanov, J.-L. Wang, and Z. Zeng