Phase transitions in HfO2 probed by first-principles computations

Ever since ferroelectricity was discovered in HfO2, the question of its origin remains controversial. Here, we probe this question using a combination of Landau theory of phase transitions and first-principles computations. In such an approach, the energy landscape associated with the phase transition between cubic and different experimentally demonstrated phases of HfO2 (tetragonal, monoclinic, orthorhombic Pbca, orthorhombic Pnma, and orthorhombic Pca21) is explored using density functional theory calculations. Computations revealed that stabilization of all but orthorhombic Pbca phase is driven by a single unstable zone-boundary antipolar mode X2−. When coupled with zone-center modes (Γ1+ and Γ3+), it stabilizes the tetragonal phase. Coupling with four additional modes (Γ5+, X3−, X5−, X5+) results in the monoclinic phase, which is the ground state of the material. If, however, Γ5+ mode is replaced with Γ4− mode, orthorhombic polar phase Pca21 is stabilized. The application of this framework to examine the effect of electric field on the ferroelectric phase of hafnia reveals that the field of 5 MV/cm is capable of stabilizing ferroelectric phase over the monoclinic one at 0 K.