Magnetic imaging of domains and walls in multiferroic ErMnO$_{3}$

Multiferroic hexagonal rare-earth manganities $R$MnO$_{3}$ ($R$ = Ho{\ldots} Lu, Y, Sc) have generated great interest because of the coexistence of ferroelectric and magnetic orders. Herein we conducted low temperature magnetic force microscopy (LT-MFM) studies on flux-grown ErMnO$_{3}$ single crystals. The ferroelectric transition T$_{C}$ is $\sim $1300 K while antiferromagnetic transition T$_{N}$ is $\sim $ 80 K. We observed intriguing behaviors of magnetic domains {\&} walls in ErMnO$_{3}$ from the temperature and magnetic field dependence of local magnetic contrast. In addition, we will present results of comparison between LT-MFM images and room temperature piezoresponse force microscopy (PFM) images of the same sample to understand the mechanism of cross-coupling between ferroelectricity {\&} magnetism in $R$MnO$_{3}$.