As analogies to magnetic skyrmions, polar skyrmions in ferroelectric superlattices and multilayers have garnered widespread attention for their non-trivial topology and novel properties like negative capacitance and nonlinear optical effect. So far, they have only been theoretically predicted to be able to assemble ordered hexagonal skyrmion lattices (SkLs) in ferroelectric thin films. Here, based on phase-field simulations, we report the critical roles of flexoelectricity playing in the stabilization and transformation of polar SkLs. Different polar SkL patterns can emerge in the ferroelectric thin films, including tetragonal-SkL, and hexagonal-SkLs with diverse orientations, as summarized by phase diagrams. These emergent SkL states are attributed to the material anisotropy modified by the flexoelectric effect. Interestingly, we further found that the hexagonal-SkLs can be rotated by applying strain gradient or in-plane electric field to the films. Moreover, a nonreciprocal bending response of tetragonal-SkL is also induced by the flexoelectric effect. Our results provide useful guidelines for the implementation of polar skyrmion lattices in experiments.

与磁性斯格明子类似，铁电超晶格和多层膜中的极性斯格明子因其非凡的拓扑结构和负电容和非线性光学效应等新颖特性而受到广泛关注。到目前为止，他们只是在理论上预测能够在铁电薄膜中组装有序的六方斯格明子晶格（SkL）。在这里，基于相场模拟，我们报告了挠曲电在极性 SkL 的稳定和转变中发挥的关键作用。正如相图所总结的，铁电薄膜中可以出现不同的极性 SkL 图案，包括具有不同方向的四方-SkL 和六方-SkL。这些新出现的 SkL 态归因于挠曲电效应改变的材料各向异性。有趣的是，我们进一步发现，通过对薄膜施加应变梯度或面内电场，可以旋转六角形SkL。此外，挠曲电效应还引起四方-SkL的不可逆弯曲响应。我们的结果为在实验中实现极性斯格明子晶格提供了有用的指导。