The electronic and magnetic properties of cation vacancies in $m\text{−}{\mathrm{HfO}}_2$ are predicted using density functional theory. The hafnium vacancy is found to introduce a series of charge transition levels in the range 0.76–1.67 eV above the valence band maximum associated with holes localized on neighboring oxygen sites. The neutral defect adopts a $S=2$ spin state, and we compute corresponding $g$ tensors to aid electron experimental identification of the defect by electron spin resonance spectroscopy. We find that separated vacancies exhibit weak ferromagnetic coupling and the interaction is highly anisotropic—being much stronger when mediated by planes of three-coordinated oxygen ions. Further, we characterize the process of thermal detachment of a hole from a neutral vacancy providing an atomistic model for the $p$-type conductivity observed experimentally at high temperature. These results provide invaluable information on the electronic and magnetic properties of cation vacancies in ${\mathrm{HfO}}_2$ and can aid future experimental identification of these complex defects.

• Received 26 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.205124

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Published by the American Physical Society