The interplay between dopants and oxygen vacancies in the magnetism of   V-doped TiO2
  Density functional theory calculations indicate that the incorporation of V into Ti lattice positions of rutile TiO2 leads to magnetic V4+ species, but the extension and sign of the coupling between dopant moments confirm that ferromagnetic order cannot be reached via low-concentration doping in the non-defective oxide. Oxygen vacancies can introduce additional magnetic centres, and we show here that one of the effects of vanadium doping is to reduce the formation energies of these defects. In the presence of both V dopants and O vacancies all the spins tend to align with the same orientation. We conclude that V doping favours the ferromagnetic behaviour of TiO2 not only by introducing spins associated with the dopant centres but also by increasing the concentration of oxygen vacancies with respect to the pure oxide. 
Ricardo Grau-Crespo and Udo Schwingenschl\"ogl
cond-mat.mtrl-sci