  We discuss, based on first principles calculations, the possibility to tune
the magnetism of oxygen vacancies at the (001) surface of strontium titanate
$(\mathrm{SrTiO_3}\!)$. The magnetic moment of single and clustered vacancies
stemming from Ti-O broken bonds can be both quenched and stabilized
controllably by chemical potential adjustment associated with doping the system
with electrons or holes. We discuss to what extent this route to magnetization
state control is robust against other external influences like chemical doping,
mechanical action and electric field. Such control of vacancy state and
magnetization can conceivably be achieved experimentally by using local probe
tips.
