Contributions to polarization and polarization switching in antiphase boundaries of SrTiO3 and PbZrO3

We use a recently developed method—based on layer group analysis combined with the Landau theory—to investigate the polar properties of antiphase boundaries (APBs) in SrTiO 3 and PbZrO 3. For SrTiO 3, we find that, in addition to the biquadratic, Houchmandazeh-Laizerowicz-Salje (HLS) coupling b i j k l P i P j ϕ k ϕ l in the Landau-Ginzburg free energy expansion, additional rotopolar terms of the form W i j k l P i ϕ k ∂ ϕ l ∂ x j contribute considerably to the polarization of antiphase boundaries in these materials. The rotopolar terms can be split into a symmetric flexoelectric part and an antisymmetric one. The antisymmetric Lifshitz term leads to a macroscopic polarization of APBs, which can be switched by application of an external electric field. For PbZrO 3, the observed polarization profiles [Wei et al., Mater. Res. Bull. 62, 101 (2015)] are fully compatible with the symmetries of the corresponding layer groups. Unlike in SrTiO 3, there exists no Lifshitz invariant W i j k l P i η k ∂ η l ∂ x j for the order parameter η i ( i = 1 , … , 12 ) describing the displacements of lead atoms. However, a detailed group theoretical treatment indicates that the polarity of APBs in PbZrO 3 is driven by higher order interactions between polarization P i, order parameter η k, and order parameter gradients ∂ η l ∂ x j.