Prediction of new metastable $$\hbox {HfO}_{2}$$ phases: toward understanding ferro- and antiferroelectric films

From first principles, we predict several yet-unknown, low-energy, dynamically stable phases of \(\hbox {HfO}_{2}\). One of the predicted metastable phases has a finite ferroelectric polarization and could be potentially responsible for the ferroelectric and/or antiferroelectric behavior recently reported in thin \(\hbox {(Hf,Zr)O}_{2}\)-based films. Other phases predicted here may potentially form as competing non-ferroelectric phases in thin films, and the possibility of their formation should be taken into account during analysis of experimental thin-film characterization data. These predictions are made possible by an explicit enumeration approach, designed for the case at hand. Our approach outperforms existing theoretical structure prediction methods, including evolutionary algorithms, which have been previously applied to the same problem yet have not identified most of the possible metastable phases found in this study. This suggests that structure enumeration techniques may be indispensable for practical structure prediction problems that seek to identify all low-energy metastable phases rather the single stable (lowest energy) phase.