Finite-temperature properties of the antiferroelectric perovskite PbZrO3 from a deep-learning interatomic potential

The prototypical antiferroelectric perovskite ${\mathrm{PbZrO}}_{3}$ (PZO) has garnered considerable attention in recent years due to its significance in technological applications and fundamental research. Many unresolved issues in PZO are associated with large length- and time-scales, as well as finite temperatures, presenting significant challenges for first-principles density functional theory studies. Here, we introduce a deep-learnining interatomic potential of PZO, enabling investigation of finite-temperature properties through large-scale atomistic simulations. Trained using an elaborately designed dataset, the model successfully reproduces a large number of phases, in particular, the recently discovered 80-atom antiferroelectric $Pnam$ phase and ferrielectric $Ima2$ phase, providing precise predictions for their structural and dynamical properties. Using this model, we investigated phase transitions of multiple phases, including $Pbam\text{/}Pnam, Ima2$, and $R3c$, which show high similarity to the experimental observation. Our simulation results also highlight the crucial role of free energy in determining the low-temperature phase of PZO, reconciling the apparent contradiction: $Pbam$ is the most commonly observed phase in experiments, while theoretical calculations predict other phases exhibiting even lower energy. Furthermore, in the temperature range where the $Pbam$ phase is thermodynamically stable, typical double polarization hysteresis loops for antiferroelectrics were obtained, along with a detailed elucidation of the structural evolution during the electric-field induced transitions between the nonpolar $Pbam$ and polar $R3c$ phases.