Finite-temperature properties of antiferroelectric perovskite $\rm PbZrO_3$ from deep learning interatomic potential

TL;DR

PbZrO$_3$ is a canonical antiferroelectric whose finite-temperature phase behavior is challenging to predict with conventional first-principles methods due to large system sizes. The authors develop a deep-learning interatomic potential (DeePMD-kit) trained on extensive first-principles data to enable large-scale MD and phonon analyses, capturing a wide range of phases including the recently identified $Pnam$-AFE80 and $Ima2$-FiE states. Their model reproduces temperature-driven phase transitions and yields a nearly ideal double $P$-$E$ hysteresis loop, while highlighting that free-energy dictates room-temperature phase selection more than static ground-state energies. This approach provides atomistic insight into phase competition, domain formation, and electric-field induced transitions in PbZrO$_3$, with implications for energy storage and multifunctional antiferroelectric materials.

Abstract

The prototypical antiferroelectric perovskite $\rm PbZrO_3$ (PZO) has garnered considerable attentions 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 learning 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 $Pbam$/$Pnam$, $Ima2$ 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 non-polar $Pbam$ and polar $R3c$ phases.

Figures (9)

• Figure 1: Schematic views of the structures of (a) $Pbam$-AFE40, (b) $Ima2$-FiE, and (c) $Pnam$-AFE80 phases of PZO. The $Pbam$-AFE40 phase is featured by an octahedra rotation pattern $a^-a^-c^0$ and a fourfold periodic Pb displacement pattern "$\uparrow \uparrow \downarrow \downarrow$" in the pseudocubic $[110]$ direction. The $Ima2$-FiE phase has a octahedra rotation pattern $a^-a^-c^0$ similar to that of the $Pbam$-AFE40 phase, but with a different threefold periodic Pb displacement pattern "$\uparrow \uparrow \downarrow$" in the pseudocubic [110] direction. In the $Pnam$-AFE80 phase, the Pb displacement pattern is similar to that of the $Pbam$-AFE40 phase, but there are additional octahedra rotations around the $c$-axis (pseudocubic $[001]$), alternating between in-phase and anti-phase rotations, i.e., two layers of clockwise rotations followed by two layers of anticlockwise rotations, and so on. We refer to this alternating in-phase and anti-phase $c$-rotation pattern as "$c^{+/-}$".
• Figure 2: Exploration of potential energy surface of PZO by first-principles calculations. (a) Phonon dispersions of PZO in the cubic reference structure. (b) Energies of various stationary phases of PZO, where the cubic phase is taken as the energy reference.
• Figure 3: Training set design. (a) Procedures of sampling the potential energy surface and constructing the training set. (b) Schematic plot of sampling the potential energy surface. (c) Energy distribution of the configurations in the training set.
• Figure 4: Model validations on (a-c) training set and (d-f) test set. Comparisons of (a, d) energy, (b, e) forces and (c, f) virials between DFT calculations and model predictions. The insets show the distributions of absolute errors.
• Figure 5: Model validations by structural relaxations of different phases, which are corresponding to the stationary points on the potential energy surface. Comparisons of (a) energy and (b) lattice distortions between DFT calculations and model predictions. The cubic phase is taken as the energy reference.