Local negative permittivity and topological phase transition in polar skyrmions

Topological solitons such as magnetic skyrmions have drawn attention as stable quasi-particle-like objects. The recent discovery of polar vortices and skyrmions in ferroelectric oxide superlattices has opened up new vistas to explore topology, emergent phenomena and approaches for manipulating such features with electric fields. Using macroscopic dielectric measurements, coupled with direct scanning convergent beam electron diffraction imaging on the atomic scale, theoretical phase-field simulations and second-principles calculations, we demonstrate that polar skyrmions in (PbTiO 3 ) n /(SrTiO 3 ) n superlattices are distinguished by a sheath of negative permittivity at the periphery of each skyrmion. This enhances the effective dielectric permittivity compared with the individual SrTiO 3 and PbTiO 3 layers. Moreover, the response of these topologically protected structures to electric field and temperature shows a reversible phase transition from the skyrmion state to a trivial uniform ferroelectric state, accompanied by large tunability of the dielectric permittivity. Pulsed switching measurements show a time-dependent evolution and recovery of the skyrmion state (and macroscopic dielectric response). The interrelationship between topological and dielectric properties presents an opportunity to simultaneously manipulate both by a single, and easily controlled, stimulus, the applied electric field. Polar skyrmions are topologically protected structures that can exist in (PbTiO 3 ) n /(SrTiO 3 ) n superlattices. Here, it is shown that they have negative permittivity at the surface, and that they can undergo a reversible phase transition with large dielectric tunability under an electric field.