A 2D ferroelectric vortex lattice in twisted BaTiO3 freestanding layers

The wealth of complex polar topologies recently found in nanoscale ferroelectrics result from a delicate balance between the materials intrinsic tendency to develop a homogeneous polarization and the electric and mechanic boundary conditions imposed upon them. Ferroelectric dielectric interfaces are model systems where polarization curling originates from open circuit like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux closure domains that evolve into vortex like structures at the nanoscale. Interestingly, while ferroelectricity is known to couple strongly to strain (both homogeneous and inhomogeneous), the effect of mechanical constraints on thin film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles opens an unprecedented opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated to the twisting. Interestingly, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding opens exciting opportunities to create two-dimensional high density vortex crystals that would allow us to explore novel physical effects and functionalities.