  Correlated band theory is employed to investigate the magnetic and electronic
properties of different arrangements of oxygen di- and tri-vacancy clusters in
SrTiO$_3$. Hole and electron doping of oxygen deficient SrTiO$_3$ yields
various degrees of magnetization as a result of the interaction between
localized magnetic moments at the defected sites. Different kinds of Ti atomic
orbital hybridization are described as a function of the doping level and
defect geometry. We find that magnetism in SrTiO$_{3-\delta}$ is sensitive to
the arrangement of neighbouring vacancy sites, charge carrier density, and
vacancy-vacancy interaction. Permanent magnetic moments in the absence of
vacancy doping electrons are observed. Our description of the charged clusters
of oxygen vacancies widens the previous descriptions of mono and
multi-vacancies and points out the importance of the controled formation at the
atomic level of defects for the realization of transition metal oxide based
devices with a desirable magnetic performance.
