  In view of the recent experimental reports of unexpected ferromagnetism in
HfO$_{2}$ thin films, we carried out first principles investigations looking
for magnetic order possibly brought about by the presence of small
concentrations of intrinsic point defects. {\it Ab initio} electronic structure
calculations using density functional theory (DFT) show that isolated cation
vacancy sites in HfO$_{2}$ lead to the formation of high spin defect states.
Furthermore these appear to be ferromagnetically coupled with a rather short
range magnetic interaction, resulting in a ferromagnetic ground state for the
whole system. More interestingly, the occurrence of these high spin states and
ferromagnetism is in the low symmetry monoclinic phase of HfO$_{2}$. This is
radically different from other systems previously known to exhibit point defect
ferromagnetism, warranting a closer look at the phenomenon.
