We investigate two-dimensional electric dipole sheets in the superlattice made of ${\mathrm{BaTiO}}_3$ and ${\mathrm{BaZrO}}_3$ using first-principles-based Monte Carlo simulations and density functional calculations. Electric dipole domains and complex patterns are observed and complex dipole structures with various symmetries (e.g., $Pma2,Cmcm$, and $Pmc{2}_1$) are further confirmed by density functional calculations, which are found to be almost degenerate in energy with the ferroelectric ground state of the $Amm2$ symmetry, therefore strongly resembling magnetic sheets. More complex dipole patterns, including vortices and antivortices, are also observed, which may constitute the intermediate states that overcome the high-energy barrier of different polarization orientations previously predicted by A. I. Lebedev [Phys. Solid State 55, 1198 (2013)]. We also show that such system possesses large electrostrictive effects that may be technologically important.

• Received 2 September 2014
• Revised 12 November 2014

DOI:https://doi.org/10.1103/PhysRevB.91.014105