First-principles LDA+U calculations were performed to study the effects of oxygen vacancies (Vo) on the electronic structure and magnetism in undoped rutile TiO2-x. Instead of treated as an adjustable parameter, the value of U was determined by constrained-density-functional calculations. The calculated electronic structure revealed that the valence electrons released by Vo would occupy mainly the neighbouring Ti:3d orbital which then becomes spin-polarized due to intra-atomic exchange interaction, thereby giving rise to the half-metallic ferromagnetism. The magnetization induced by Vo in rutile TiO2-x was almost proportional to the Vo concentration (x) for x > 0.0625, and becomes 0 for x-values of up to 0.0417.

Oxygen Vacancy Induced Ferromagnetism in Rutile TiO2-x. Han, G.B., Hu, S.J., Yan, S.S., Mei, L.M.: Physica Status Solidi - Rapid Research Letters, 2009, 3[5], 148-50