First-principles study of magnetic properties of stoichiometric and O deficient low-index surfaces of rutile SnO2 and TiO2

In consideration of experimental evidences of O vacancies or/and surface state as the possible origin of d0 ferromagnetism in SnO2 and TiO2, the electronic structure and magnetic properties of stoichiometric and O deficient (110), (100), (101) and (001) surfaces of rutile SnO2 and TiO2 are investigated using first-principles calculations. The calculations show that the stoichiometric (110), (100), (101) and (001) surfaces of rutile SnO2 and TiO2 are nonmagnetic. The O vacancy at these low-index surfaces of SnO2 do not induce magnetic moment due to extended character of 5s and 5p orbitals of the reduced Sn atom, while the vacancy at the low-index surfaces of TiO2 produce spin splitting defect states in the band gap, resulting in the formation of magnetic moment of 2.0 μB. The induced magnetic moment by surface O vacancy is mainly contributed by partially filled 3d orbitals of the reduced Ti atoms. It is noticed that the magnetic coupling between magnetic moments induced by two O vacancies at the low-index surfaces of rutile TiO2 are long-range ferromagnetic, which can be explained by the overlap of spin density around the common Ti or O atoms among reduced Ti atoms produced by two O vacancies.