Vortices and antivortices in antiferroelectric PbZrO₃

Ferroelectric materials are characterized by a parallel arrangement of electric dipoles, but at the nanoscale they can present vortices and other non-trivial topological structures^1-9 that combine small size and topological protection, rendering them functionally attractive^10-13. The driving force for the appearance of vortices in ferroelectrics is the need to minimize the depolarizing fields at interfaces^3-5,14; by making the polarization rotate, depolarization fields vanish^4,5,8,9. Antiferroelectrics, by contrast, are defined by an antiparallel arrangement of electric dipoles¹⁵. A priori, therefore, they lack the depolarization fields that drive the appearance of non-trivial topologies in ferroelectrics. At the atomic scale of the dipoles, however, we find that polar discontinuities can still happen, driving the appearance of topological singularities at ferroelastic domain walls.