Oxygen deficiency and valency reconstruction in multiferroic V-doped HfO2

The interplay of oxygen deficiency and vanadium multiple valency in the candidate multiferroic V-doped Pca21 hafnia HfO2 is studied by first-principles calculations. Low-lying V majority gap states accept electrons from oxygen-vacancy donors, reducing their formation energy, and converting nominal V4+ centers into V3+. The resulting local magnetization and screening changes are reflected in the calculated V core-level shifts, which are consistent with the experimentally observed x-ray photoelectron spectroscopy signatures. The calculated V3+/V4+ population ratio determined by oxygen vacancies only matches experiment in reducing conditions, suggesting that additional electron reservoirs may contribute under atomic-layer-deposition growth conditions. A similar scenario also seems to apply to the recently observed multiferroicity in Cr-doped hafnia, where oxygen deficiency is expected from the synthesis route.