HfO$_2$: a new direction for intrinsic defect driven ferromagnetism

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.