Multivariate Statistical Characterization of Charged and Uncharged Domain Walls in Multiferroic Hexagonal YMnO<sub>3</sub> Single Crystal Visualized by a Spherical Aberration-Corrected STEM

A state-of-the-art spherical aberration-corrected STEM was fully utilized to directly visualize the multiferroic domain structure in a hexagonal YMnO<sub>3</sub> single crystal at atomic scale. With the aid of multivariate statistical analysis (MSA), we obtained unbiased and quantitative maps of ferroelectric domain structures with atomic resolution. Such a statistical image analysis of the transition region between opposite polarizations has confirmed atomically sharp transitions of ferroelectric polarization both in antiparallel (uncharged) and tail-to-tail 180° (charged) domain boundaries. Through the analysis, a correlated subatomic image shift of Mn–O layers with that of Y layers, exhibiting a double-arc shape of reversed curvatures, have been elucidated. The amount of image shift in Mn–O layers along the <i>c</i>-axis is statistically significant as small as 0.016 nm, roughly one-third of the evident image shift of 0.048 nm in Y layers. Interestingly, a careful analysis has shown that such a subatomic image shift in Mn–O layers vanishes at the tail-to-tail 180° domain boundaries. Furthermore, taking advantage of the annular bright field (ABF) imaging technique combined with MSA, the tilting of MnO<sub>5</sub> bipyramids, the very core mechanism of multiferroicity of the material, is evaluated.