Based on a recently developed combination of layer group analysis with order-parameter symmetry, we study the polarity of antiphase domain boundaries (APBs) and ferroelastic twin boundaries (TBs) in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. In addition to the celebrated layer group analysis of domain twins, the present method allows us to investigate tensor properties of domain walls also for the case where order-parameter variables other than the spontaneous ones are active. We find that antiphase boundaries in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ can carry a polarization if in addition to the spontaneous order parameter $(0,0,{\varphi }_s)$ a second component, i.e., $({\varphi }_1,0,{\varphi }_s)$, develops within the domain wall. This result, which is solely based on symmetry arguments, strongly suggests that polarization in APBs is possible if a phase transition from an Ising-type wall to a Néel- or Bloch-like wall occurs. This is in very good agreement with previous calculations based on Landau-Ginzburg free energy expansions including biquadratic ($\propto P_i{P}_j{\varphi }_k{\varphi }_l$) [A. K. Tagantsev et al. Phys. Rev. B 64, 224107 (2001)] and flexoelectric ($\propto P_k\frac{\partial u_{ij}}{\partial \xi }$) coupling terms [A. N. Morozovska et al. Phys. Rev. B. 85, 094107 (2012)]. The present results also unveil a close connection between the recently discovered macroscopic polarization in antiferrodistortive cycloids of ferroelastic domain walls of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ and a mechanism for explaining polarization of APBs.

• Received 7 August 2020
• Revised 29 September 2020
• Accepted 20 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.184101