Visualizing domain wall magnetism and domain magnetoelectricity in multiferroic hexagonal manganites

Summary form only given. Multiferroics are insulating materials with coexisting magnetic and ferroelectric orders. The cross-coupling between two ferroic orders can result in strong magnetoelectric effect [1-4], which holds promise for conceptually novel electronic devices such as electric field controlled magnetic memory and compact magnetic field sensors. However, the existence of domains and defects in these ferroic materials strongly influences their macroscopic responses. Therefore, it is of both fundamental and technological interests to visualize cross-coupled domains and domain walls in magnetoelectrics and multiferroics. Recently, intriguing topological defects with six interlocked structural antiphase and ferroelectric domains merging into a vortex core were revealed in multifer-roic hexagonal REMnO₃ (RE=rare earths) [5, 6]. Many emergent phenomena, such as enhanced conduction and unusual piezoelectric response, were observed in charged ferroelectric domain walls protected by these topological defects [7-9]. Using cryogenic magnetic force microscopy (MFM), we discovered alternating uncompensated magnetic moments at structural domain walls in hexagonal manganites, which directly demonstrates the cross-coupling between ferroelectric and antiferromagnetic orders [10]. To probe the local magnetoelectric responses in multiferroics, we developed a novel Magnetoelectric Force Microscopy (MeFM) technique that combines MFM with in-situ modulation of high electric fields [11, 12]. This method allows us to image the magnetoelec-tric response of the domain patterns in hexagonal manganites directly. We find that this response changes sign at each structural domain wall, a result that is corroborated by symmetry analysis and phenomenological modeling [13], and provides compelling evidence for a lattice-mediated magne-toelectric coupling. The direct visualization of magnetoelectric domains at mesoscopic scales opens up explorations of emergent phenomena in mu- tifunctional materials with multiple coupled orders [14-19].