Reversible Phase Transition between Vortex Lattice and Hexagonal Polar Skyrmion Crystals.

Polar skyrmions in oxide heterostructures have recently attracted extensive interest due to their unique physical properties and potential applications. Here, we report the formation of the vortex lattice and the nanoscale polar skyrmion crystals with two-dimensional hexagonal symmetry in PbTiO 3 /SrTrO 3 (PTO/STO) superlattices. Under an increasing external field, the system transitions from a vortex lattice phase to hexagonal polar skyrmion crystals (PSkC). The formation and annihilation process of the polar skyrmion crystals resemble the structural phase transition observed in atomic crystals. A temperature-electric field topological phase diagram is constructed, demonstrating stabilization of the vortex lattice and polar skyrmion crystals in a wide temperature and electric-field range. This study demonstrates the potential of manipulating the topological phase transition and its long-range order through an external field.