Vacancy-induced magnetism in SnO$_{2}$: A density functional study

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$_\mathrm{Sn}$.