Polarization of domain boundaries in SrTiO3 studied by layer group and order-parameter symmetry

Abstract

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 $(0,0,{\ensuremath{\phi}}_{s})$ a second component, i.e., $({\ensuremath{\phi}}_{1},0,{\ensuremath{\phi}}_{s})$, 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 N\'eel- or Bloch-like wall occurs. This is in very good agreement with previous calculations based on Landau-Ginzburg free energy expansions including biquadratic ($\ensuremath{\propto}{P}_{i}{P}_{j}{\ensuremath{\phi}}_{k}{\ensuremath{\phi}}_{l}$) [A. K. Tagantsev et al. Phys. Rev. B 64, 224107 (2001)] and flexoelectric ($\ensuremath{\propto}{P}_{k}\frac{\ensuremath{\partial}{u}_{ij}}{\ensuremath{\partial}\ensuremath{\xi}}$) 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.