We present an ab initio study of pure and doped TiO2 in the rutile and anatase phases. The main purpose of this work is to determine the role played by different defects and different crystal structures in the appearance of magnetic order. The calculations were performed for varying impurity and vacancy concentrations in both TiO2 structures. For Co impurities the local magnetic moment remained almost independent of the concentration and distribution while for Cu this is not the case, there is magnetism for low concentrations that disappears for the higher ones. Impurity-impurity interactions in both structures favor linear ordering of them. Magnetism in un-doped samples appears for certain vacancy concentrations and structural strain.
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