Evolution of the Domain Topology in a Ferroelectric

Topological materials, including topological insulators, magnets with Skyrmions and ferroelectrics with topological vortices, have recently attracted phenomenal attention in the materials science community. Complex patterns of ferroelectric domains in hexagonal ${\mathrm{REMnO}}_{3}$ (RE: rare earths) turn out to be associated with the macroscopic emergence of ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{3}$ symmetry. The results of our depth profiling of crystals with a self-poling tendency near surfaces reveal that the partial dislocation (i.e., wall-wall) interaction, not the interaction between vortices and antivortices, is primarily responsible for topological condensation through the macroscopic breaking of the ${Z}_{2}$ symmetry.