Strain effects on stability of topological ferroelectric polar configurations in (PbTiO₃)_n/(SrTiO₃)_n superlattices

The (PbTiO₃)_n/(SrTiO₃)_n (PTO/STO) superlattice system has been shown to exhibit interesting topological phases (e.g., vortices and skyrmions) in addition to normal ferroelectric domain states. Existing studies are mostly focused on the dependence of topological polar distributions and properties of PTO/STO superlattice on its periodicity. Here, we study the strain effect on the topological phase transitions and ferroelectric domain structures employing phase-field simulations. We summarized in an isotropic strain (in-plane misfit strain along the x direction is equal to that along the y direction) periodicity phase diagram displaying the stability regions of different polar topological states, including normal ferroelectric twins, vortices, skyrmions, and mixtures of vortices and twins. We also analyzed the polarization configurations under anisotropic in-plane strains (in-plane misfit strain along the x direction is not equal to that along the y direction) and demonstrated that the strain anisotropy can be used to tune the directions of vortex arrays along either the [100] _pc or [010] _pc directions or labyrinth vortex arrays. This work offers guidance to manipulating polar structures in the PTO/STO superlattices via strain engineering.