Hafnia is a proper ferroelectric

The nature of ferroelectricity in hafnia is still unclear as some studies consider hafnia as an improper ferroelectric[1][2], whereas some experimental evidence and density functional theory calculations suggest otherwise[3][4]. We clarify and demonstrate that ferroelectricity in hafnia is indeed proper. Using symmetry analysis, DFT for structural optimization, and density functional perturbation theory we investigate the dynamical stability of the structures derived from fluorite cubic. We examine the group-subgroup relations between relevant hafnia phases and demonstrate that, upon adequately choosing the parent structure, all polar hafnia phases — Pca2₁, Pmn2₁, R3m and R3— result from the distortion of single, unstable polar mode of the parent structure as they all exhibit double-well potential that are relatively shallow.

[1] H.-J. Lee et al., Science 369, 1343 (2020)

[2] F. Delodovici, P. Barone, and S. Picozzi, Phys. Rev. Mater. 5, 064405 (2021).

[3] H. Arramberri and J. Íñiguez, arXiv:2302.00688.

[4] U.Schroeder et al., Advanced Electronic Materials 8, 2200265 (2022).