Hafnia HfO2 is a proper ferroelectric

We clarify the nature of hafnia as a proper ferroelectric and show that there is a shallow double well involving a single soft polar mode as in well-known classic ferroelectrics. Using symmetry analysis, density functional theory structural optimizations with and without epitaxial strain, and density functional perturbation theory, we examine several important possible hafnia structures derived ultimately from the cubic fluorite structure, including baddeleyite (P21/c), tetragonal antiferroelectric P42nmc, Pbca (nonpolar and brookite), ferroelectric rhombohedral (R3m and R3), Pmn21, and Pca21 structures. The latter is considered to be the most likely ferroelectric phase seen experimentally and has an antiferroelectric parent with space group Pbcn, with a single unstable polar mode and a shallow double well with a well depth of 24 meV/atom. Strain is not required for switching or other ferroelectric properties, nor is coupling of the soft mode with any other modes within the ferroelectric Pca21, Pmn21, R3m, or R3 phases.