Finite-temperature properties of antiferroelectric ${\mathrm{PbZrO}}_3$ from atomistic simulations

Antiferroelectrics are under extensive reexamination owing to their unique properties and technological promise. Computationally, they pose a challenge for predictive modeling as they often do not possess well-defined localized electric moments and exhibit a delicate energetic balance between polar and antipolar phases. We propose a first-principles-based atomistic model for the prototype antiferroelectric ${\mathrm{PbZrO}}_3$ that captures accurately a wide range of its properties. Application of the model to study finite-temperature properties of ${\mathrm{PbZrO}}_3$ under external electric field and hydrostatic pressure aids in achieving a coherent picture of this intriguing material. In particular, our simulations predict (i) the existence of a strong coupling between the antiferrodistortive motion of oxygen octahedra and the antipolar distortion in a wide range of temperatures and electric fields; (ii) a linear temperature dependence for the critical field associated with the antiferroelectric to ferroelectric phase transition; and (iii) a stabilizing effect of the hydrostatic pressure on the phase transition in ${\mathrm{PbZrO}}_3$.

Figure 1

Amplitude of structural distortions of different symmetry in the ground state of ${\mathrm{PbZrO}}_3$ (shown by rectangles) and the cumulative energy gain (shown by circles) due to addition of each distortion. The energy of undistorted cubic structure is taken as the reference point.

Figure 2

Dependence of the components of the AFE order parameter (a), the AFD order parameter (b), and the lattice distortion $1-c/a$ (c) on the temperature. Experimental data in (c) are from Refs. [25, 53, 54]. They are rescaled to match the experimental and computation transition temperatures. The order parameters are in the units of ${\mathrm{PbZrO}}_3$ cubic lattice constant.

Figure 3

The field evolution of FE, AFE, and AFD, and strain order parameters as follows: FE order parameter (a) and (e); AFE order parameter (b) and (f); AFD order parameter (c) and (g); strain (d) and (h). The AFE and AFD order parameters are in the units of ${\mathrm{PbZrO}}_3$ cubic lattice constant.

Figure 4

The temperature evolution of the [110] electric-field-induced double hysteresis loops (a). Temperature dependence of the critical field (b), and of the saturation polarization and strain (c).

Figure 5

Dependence of the magnitudes of the AFE and AFD modes at 300 K (a) and transition temperature (b) on the hydrostatic pressure. The transition temperatures are normalized by their zero pressure value. AFE and AFD modes are in the units of ${\mathrm{PbZrO}}_3$ cubic lattice constant.