Tilt-driven antiferroelectricity in PbZrO₃

PbZrO₃ (PZO) is, by far, the best-known antiferroelectric (AFE) material. During its AFE phase transition, its atomic structure undergoes a complex set of distortions, resulting in the ↑↑↓↓ displacement pattern of Pb ions and in seemingly unrelated O₆ octahedra tilts. The physical origin of such complex antiferroelectricity in PZO has been a subject of debates over the last years. Here we combine ab-initio simulations with Landau theory modelling to study the physics behind the AFE phase transition in PZO. We show that the atomic distortions accompanying it condense during a locked-in incommensurate phase transition and are essentially spatial modulations of polarization, P, and of antiphase O₆ octahedra tilts, φ. We further demonstrate that the AFE state in PZO is stabilized by the trilinear rotopolar gradient coupling between the modulated P and φ, having form W Pφ(∇φ). Our theoretical framework combines the defining features of two main existing models of PZO into a single physical mechanism: locked-in incommensurate modulations and trilinear coupling between distortions. The proposed mechanism is promising for description of actual incommensurate phases observed in PZO-like perovskites, such as PLZST and PbHfO3.