We present theoretical evidence for local magnetic moments on ${\text{Ti}}^{3+}$ ions in oxygen-deficient anatase and rutile ${\text{TiO}}_2$ observed in a recent experiment [S. Zhou et al., Phys. Rev. B 79, 113201 (2009)]. Results of our first-principles $\text{GGA}+U$ calculations reveal that an oxygen vacancy converts two ${\text{Ti}}^{4+}$ ions to two ${\text{Ti}}^{3+}$ ions in anatase phase, which results in a local magnetic moment of $1.0{\mu }_B$ per ${\text{Ti}}^{3+}$. The two ${\text{Ti}}^{3+}$ ions, however, form a stable antiferromagnetic state, and similar antiferromagnetism is also observed in oxygen-deficient rutile phase ${\text{TiO}}_2$. The calculated results are in good agreement with the experimentally observed antiferromagneticlike behavior in oxygen-deficient Ti-O systems.

• Received 21 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.033202