Ab initio and Effective field Study of V doped TiO2

Using the effective field theory (EFT), the Curie temperature of V- doped rutile TiO2 has been determined. The exchange coupling used in the calculation has been deduced from first principal calculation based on the density functional theory with the local spin density approximation (LSDA). We also showed that V- doped rutile TiO2 is half metallic and the hybridization is between the V 3d states and the nearest-neighbouring O 2p states. The results from ab initio calculation showed that for weak holes concentrations the ferromagnetism is due to the double exchange, while, for higher hole concentration it comes from the RKKY exchange interaction. In addition, we show via effective field theory calculations that the transition from the nonmagnetic (NM) to the ferromagnetic (FM) phase is marked by the magnetic percolation. Magnetization as a function of the temperature for different values of the hole concentration, nc, is also given