Collective magnetism at multiferroic vortex domain walls

Cross-coupled phenomena of multiferroic domains and domain walls are of fundamental scientific and technological interest. Using cryogenic magnetic force microscopy, we find alternating net magnetic moments at ferroelectric domain walls around vortex cores in multiferroic hexagonal ErMnO₃, which correlate with each other throughout the entire vortex network. This collective nature of domain wall magnetism originates from the uncompensated Er³⁺ moments at domain walls and the self-organization of the vortex network. Our results demonstrate that the collective domain wall magnetism can be controlled by external magnetic fields and represent a major advancement in the manipulation of local magnetic moments by harnessing cross-coupled domain walls.