  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.
