Multivariate statistical characterization of charged and uncharged domain walls in multiferroic hexagonal YMnO₃ 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 ₃ 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 c-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 ₅ bipyramids, the very core mechanism of multiferroicity of the material, is evaluated.