  We present theoretical evidence for local magnetic moments on Ti3+ ions in
oxygen-deficient anatase and rutile TiO2 observed in a recent experiment [S.
Zhou, et al., Phys. Rev. B 79, 113201 (2009)]. Results of our first-principles
GGA+U calculations reveal that an oxygen vacancy converts two Ti4+ ions to two
Ti3+ ions in anatase phase, which results in a local magnetic moment of 1.0
$\mu_B$ per Ti3+. The two Ti3+ ions, however, form a stable antiferromagnetic
state, and similar antiferromagnetism is also observed in oxygen-deficient
rutile phase TiO2. The calculated results are in good agreement with the
experimentally observed antiferromagnetic-like behavior in oxygen-deficient
Ti-O systems.
