  Topological defects have been playgrounds for many emergent phenomena in
complex matter such as superfluids, liquid crystals, and early universe.
Recently, vortex-like topological defects with six interlocked structural
antiphase and ferroelectric domains merging into a vortex core were revealed in
multiferroic hexagonal manganites. Numerous vortices are found to form an
intriguing self-organized network. Thus, it is imperative to find out the
magnetic nature of these vortices. Using cryogenic magnetic force microscopy,
we discovered unprecedented alternating net moments at domain walls around
vortices that can correlate over the entire vortex network in hexagonal ErMnO3
The collective nature of domain wall magnetism originates from the
uncompensated Er3+ moments and the correlated organization of the vortex
network. Furthermore, our proposed model indicates a fascinating phenomenon of
field-controllable spin chirality. Our results demonstrate a new route to
achieving magnetoelectric coupling at domain walls in single-phase
multiferroics, which may be harnessed for nanoscale multifunctional devices.
