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 ErMnO 3 . The collective nature of domain wall magnetism originates from the uncompensated Er 3+ 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.
2Multiferroics are materials with coexisting magnetism and ferroelectricity 1 . The cross-coupling between two ferroic orders can result in giant magnetoelectric coupling for potential applications [2][3][4][5] . Because formation of domains is the hallmark of any ferroic order 6 , it is of both fundamental and technological interests to visualize cross-coupled domains or walls in multiferroics. Hexagonal (h-) REMnO 3 (RE = Sc, Y, Ho, … Lu) are multiferroics with coexistence of ferroelectricity (T C ≈ 1200 -1500 K) 7 and antiferromagnetism (T N ≈ 70 -120 K) 8 . The ferroelectricity is induced by structural instability called trimerization 9,10 , which lifts presumably the frustration of antiferromagnetic interactions of Mn 3+ spins on triangular lattice. Indeed, a 120º antiferromagnetic order of Mn 3+ spin in the ab-plane sets in below T N . Recently, an intriguing 6-state vortex domain structure in YMnO 3 is revealed by transmission electron microscopy, conductive atomic force microscopy and piezoresponse force microscopy (PFM) at room temperature [11][12][13] . The formation of 6-state vortices originates from the cyclic arrangement of 6 interlocked structural antiphase (α, β, γ) and ferroelectric (+/−) ground states (i.e. α + , β -, γ + , α -, β + , γ -) 11,14 . The intriguing network of vortex-antivortex pairs has a profound connection to graph theory, where 6-valent planer graphs with even-gons are two-proper-colorable 15 . Using second harmonic generation optics, it has been claimed that ferroelectric domain walls (DWs) in millimeter-size YMnO 3 tend to pin antiferromagnetic DWs, but free antiferromagnetic DWs also exist 16 . Thus, it is of great interest to find out the magnetic nature of vortex domains and DWs. However, this has been an experimental challenge, particularly due to the lack of suitable high resolution imaging technique of antiferromagnetic domains or DWs for h-REMnO 3 at low temperatures (...
