Theoretical approach to ferroelectricity in hafnia and related materials

Hafnia ferroelectrics combine technological promise and unprecedented behaviors. Their peculiarity stems from the many active extrinsic mechanisms that contribute to their properties and from a continuously growing number of novel intrinsic features. Partly because of their unconventional nature, basic questions about these materials remain open and one may wonder about the pertinence of some frequent theoretical assumptions. Aided by first-principles simulations, here we show that, by adopting an original high-symmetry reference phase as the starting point of the analysis, we can develop a mathematically simple and physically transparent treatment of the ferroelectric state of hafnia. The proposed approach describes hafnia as a uniaxial ferroic, as suggested by recent studies of (woken-up) samples with well developed polarization. Also, it is compatible with the occurrence of polar soft modes and proper ferroelectric order. Further, our theory provides a straightforward and unified description of all low-energy polymorphs, shedding light into old questions (e.g., the prevalence of the monoclinic ground state), pointing at exciting possibilities (e.g., an antiferroelastic behavior) and facilitating the future development of perturbative theories (from Landau to second-principles potentials). Our work thus yields a deeper understanding of hafnia ferroelectrics, improving our ability to optimize their properties and induce new ones.