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

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