  TThe magnetism and electronic structure of Li-doped SnO$_{2}$ are
investigated using first-principles LDA/LDA$+U$ calculations. We find that Li
induces magnetism in SnO$_{2}$ when doped at the Sn site but becomes
non-magnetic when doped at the O and interstitial sites. The calculated
formation energies show that Li prefers the Sn site as compared with the O
site, in agreement with previous experimental works. The interaction of Li with
native defects (Sn V$_\mathrm{Sn}$ and O V$_\mathrm{O}$ vacancies) is also
studied, and we find that Li not only behaves as a spin polarizer, but also a
vacancy stabilizer, i.e. Li significantly reduces the defect formation energies
of the native defects and helps the stabilization of magnetic oxygen vacancies.
The electronic densities of states reveals that these systems, where the Fermi
level touches the conduction (valence) band, are non-magnetic
(magnetic).cancies. The electronic densities of states reveal that those
systems, where the Fermi levels touch the conduction (valence) band, are
non-magnetic (magnetic).
