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Spin-polarized surface state in Li-doped SnO$_{2}$(001)

Using LDA+$U$, we investigate Li-doped rutile SnO$_2$(001) surface. The surface defect formation energy shows that it is easier for Li to be doped at surface Sn site than bulk Sn site in SnO$_2$. Li at surface and sub-surface Sn sites has a magnetic ground state, and the induced magnetic moments are not localized at Li site, but spread over Sn and O sites. The surface electronic structures show that Li at surface Sn site shows $100%$ spin-polarization (half metallic), whereas Li at sub-surface Sn site does not have half metallic state due to Li-Sn hybridized orbitals. The spin-polarized surface has a ferromagnetic ground state, therefore, ferromagnetism is expected in Li-doped SnO$_2$(001) surface.