Defect compensation, clustering, and magnetism in Cr-doped anatase TiO2

The origin of the magnetism in recently reported Cr doped anatase TiO2 is investigated with first principles full-potential linearized augmented plane wave calculations. Through a systematic study over a range of defect compensation, we predict a strikingly different behavior of Cr3+ (compensated species) and Cr4+ (noncompensated species): Cr3+ tends to distribute uniformly but contributes only to paramagnetism. By contrast, Cr4+ tends to form clusters which induces strong ferromagnetism. The same p-d hopping interaction found in Mn:GaAs also explains the presence or absence of ferromagnetism and its dependence on the compensation; this short-range bonding interaction is also one of the major sources for the predicted clustering of Cr4+. Our results thus contradict the experimental interpretation that oxygen vacancies induced the ferromagnetic coupling between Cr3+ through the F-center bound magnetic polaron (FCBMP) mechanism. We show that large size magnetic polarons cannot form in Cr:TiO2 and that the FCBMP mechanism does not apply.