Effect of Ga-doping and oxygen vacancies on the ferromagnetism of TiO₂thin films

In this paper, we combine first principles calculations and experiments to investigate the influence of Ga-doping and oxygen vacancies on the magnetic properties of rutile TiO₂films. Ga-doped TiO₂with few oxygen vacancies exhibits ferromagnetism at room temperature with a T_Cnear 350 K, which can be explained using a modified magnetic polaron model. The number of Ti³⁺ions increases with increasing the oxygen vacancies concentration, which results in a larger magnetic moment along with a higher T_Cin TiO_2−δfilm with the ferromagnetic and antiferromagnetic coupling. The saturation magnetic moment is enhanced in Ga-doped TiO_2−δdue to the absence of antiferromagnetic coupling after Ga-doping. More electrons occupy nearby Ti sites giving rise to the Ti³⁺moments. Our theoretical calculations suggest that the modified magnetic polaron model works well for the ferromagnetism of doped and undoped-TiO_2−δ. Experimental results clearly show that the T_Cis related to the oxygen vacancies concentration, which is a verification of the polaron percolation theory.