  We study the magnetic and electronic properties of defects in SnO$_{2}$ using
pseudopotential and all electron methods. Our calculations show that bulk
SnO$_{2}$ is non-magnetic, but it shows magnetism with a magnetic moment around
4.00 $\mu_{B}$ due to Sn vacancy (V$_\mathrm{Sn}$). The magnetic moment comes
mainly from O atoms surrounding V$_\mathrm{Sn}$ and Sn atoms, which couple
antiferromagnetically with the O atoms in the presence of V$_\mathrm{Sn}$. The
coupling between different Sn vacancies is also studied and we find that these
defects not only couple ferromagnetically but also antiferromagnetically and
ferrimagnetically. Our calculations demonstrate that the experimentally
observed giant magnetic moment of transition metal doped SnO$_{2}$ can be
attributed to V$_\mathrm{Sn}$.

Materials Science