Self-organization, condensation, and annihilation of topological vortices and antivortices in a multiferroic

The interaction among topological defects can induce novel phenomena such as disclination pairs in liquid crystals and superconducting vortex lattices. Nanoscale topological vortices with swirling ferroelectric, magnetic, and structural antiphase relationships were found in multiferroic h-YMnO ₃. Herein, we report the discovery of intriguing, but seemingly irregular configurations of a zoo of topological vortices and antivortices. These configurations can be neatly analyzed in terms of graph theory and reflect the nature of self-organized criticality in complexity phenomena. External stimuli such as chemistry-driven or electric poling can induce the condensation and eventual annihilation of topological vortex- antivortex pairs.