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The wealth of complex polar topologies recently found in nanoscaleferroelectrics result from a delicate balance between the materials intrinsictendency to develop a homogeneous polarization and the electric and mechanicboundary conditions imposed upon them. Ferroelectric dielectric interfaces aremodel systems where polarization curling originates from open circuit likeelectric boundary conditions, to avoid the build-up of polarization chargesthrough the formation of flux closure domains that evolve into vortex likestructures at the nanoscale. Interestingly, while ferroelectricity is known tocouple strongly to strain (both homogeneous and inhomogeneous), the effect ofmechanical constraints on thin film nanoscale ferroelectrics has beencomparatively less explored because of the relative paucity of strain patternsthat can be implemented experimentally. Here we show that the stacking offreestanding ferroelectric perovskite layers with controlled twist angles opensan unprecedented opportunity to tailor these topological nanostructures in away determined by the lateral strain modulation associated to the twisting.Interestingly, we find that a peculiar pattern of polarization vortices andantivortices emerges from the flexoelectric coupling of polarization to straingradients. This finding opens exciting opportunities to create two-dimensionalhigh density vortex crystals that would allow us to explore novel physicaleffects and functionalities.

A 2D ferroelectric vortex lattice in twisted BaTiO3 freestanding layers