Modeling and calculation of RKKY exchange coupling to explain Ti-vacancy-induced ferromagnetism in Ta-doped TiO2

We present a theoretical study on Ti-vacancy-induced ferromagnetism in anatase TiO2. A recent experimental study has revealed room temperature ferromagnetism in Ta-doped anatase TiO2thin films (Rusydi et al., 2012) [7]. Ta doping assists the formation of Ti vacancies which then induce the formation of localized magnetic moments around the Ti vacancies. As neighboring Ti vacancies are a few unit cells apart, the ferromagnetic order is suspected to be mediated by itinerant electrons. We propose that such an electron-mediated ferromagnetism is driven by Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction. To examine our hypothesis, we construct a tight-binding based model Hamiltonian for the anatase TiO2 system. We calculate the RKKY exchange coupling constant of TiO2 as a function of distance between local magnetic moments at various temperatures. We model the system by taking only the layer containing a unit of TiO2, at which the Ti vacancy is believed to form, as our effective two-dimensional unit cell. Our model incorporates the Hubbard repulsive interactions between electrons occupying Ti d orbitals treated within mean-field approximation. The density of states profile resulting from the model captures the relevant electronic properties of TiO2, such as the energy gap of ~3.4 eV and the n-type character, which may be a measure of the adequacy of the model. The calculated RKKY coupling constant shows that the ferromagnetic coupling extends up to 3-4 unit cells and enhances slightly as temperature is increased from 0 to 400 K. These results support our hypothesis that the ferromagnetism of this system is driven by RKKY mechanism.