Three-dimensional domain identification in a single hexagonal manganite nanocrystal

The three-dimensional domain structure of ferroelectric materials significantly influences their properties. The ferroelectric domain structure of improper multiferroics, such as YMnO₃, is driven by a non-ferroelectric order parameter, leading to unique hexagonal vortex patterns and topologically protected domain walls. Characterizing the three-dimensional structure of these domains and domain walls has been elusive, however, due to a lack of suitable imaging techniques. Here, we present a multi-peak Bragg coherent x-ray diffraction imaging determination of the domain structure in single YMnO₃ nanocrystals. We resolve two ferroelectric domains separated by a domain wall and confirm that the primary atomic displacements occur along the crystallographic c-axis. Correlation with atomistic simulations confirms the Mexican hat symmetry model of domain formation, identifying two domains with opposite ferroelectric polarization and adjacent trimerization, manifesting in a clockwise arrangement around the hat’s brim.