  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.
