Deterministic ordering of polar skyrmions into a hexagonal crystal in ferroelectric ultrathin films via anisotropic strain

Summary Polar skyrmions are nanoscale topological solitons in ferroelectric polarization fields whose robustness and density render them attractive for low-power electronics and neuromorphic applications. Unlike magnetic skyrmions, which readily form long-range-ordered skyrmion crystals, ferroelectric skyrmions typically appear as disordered glasses, limiting collective dynamics and device integration. Using phase-field simulations of epitaxial PbZr0.2Ti0.8O₃ thin films, we demonstrate that uniform in-plane anisotropic strain provides the critical symmetry breaking required to deterministically order polar skyrmions into hexagonal skyrmion lattices. Specifically, we identify two parallel ordering mechanisms: converting strain-aligned stripes into a lattice via an electric field and crystallizing a field-induced skyrmion glass via strain. Both pathways are substantiated by reciprocal-space pattern evolution from diffuse rings to discrete 6-fold peaks, establishing a robust protocol for tailoring topological order. The applied strain simultaneously shrinks ferroelectric skyrmions and elicits an anomalous negative Poisson's ratio response. These insights provide a playground for strain-engineered, deterministic, and low-power control of polar topologies in ferroelectrics, potentially enabling reproducible creation of high-density, highly ordered, and highly directional skyrmion lattices for ferroelectric topological nanoelectronics.