Interfacial polarization and pyroelectricity in antiferrodistortive structures induced by a flexoelectric effect and rotostriction

Theoretical analysis based on the Landau-Ginzburg-Devonshire theory is used to show that the combined effect of flexoelectricity and rotostriction can lead to a spontaneous polarization and pyroelectricity in the vicinity of antiphase boundaries, structural twin walls, surfaces, and interfaces in the octahedrally tilted phase of otherwise nonferroelectric perovskites such as CaTiO${}_{3}$, SrTiO${}_{3}$, and EuTiO${}_{3}$. As an example, we numerically demonstrate a spontaneous polarization and pyroelectric response at the SrTiO${}_{3}$ antiphase and twin boundaries at temperatures lower than the antiferrodistortive structural phase transition temperature of ${T}_{S}\ensuremath{\sim}105$ K in agreement with previously unexplained experimental results. At temperatures lower than effective Curie temperature ${T}_{C}$${}^{*}$ ($\ensuremath{\sim}$25 K for twins and $\ensuremath{\sim}$50 K for antiphase boundaries) biquadratic coupling between oxygen octahedron tilt and polarization vectors essentially enhances the polarization induced by the combined flexoelectric and rotostriction effects near the hard domain wall. Biquadratic coupling cannot induce polarization inside easy twins and antiphase boundaries; their polarization and pyroelectricity originates below ${T}_{S}$ from the built-in flexoelectric field. The spontaneous polarization reaches the values $\ensuremath{\sim}$0.1--5 $\ensuremath{\mu}$C/cm${}^{2}$ at the SrTiO${}_{3}$ antiphase boundaries and twins without free charges. A principal difference between the influence of biquadratic and flexoelectric couplings on the interfacial polarization is the following: the biquadratic coupling induces bistable ferroelectric polarization inside hard antiphase boundaries and hard twins below ${T}_{C}$${}^{*}$, while the flexoelectric coupling induces improper spontaneous polarization via the flexoelectric field below ${T}_{S}$.