Inner structure of topological defects in hexagonal manganites

The diverse opportunities inspired by the properties of topological defects in solid-state systems have triggered the broad interest in this rapidly evolving field. Particularly promising are topological defects in electrically and magnetically ordered materials -- robust nanoscale objects that can readily be controlled by external fields, opening innovative pathways in active nanoelectronics and related areas. Hexagonal manganites (RMnO$_3$, R = Sc, Y, In, Dy -- Lu) host an explicitly large variety of topological defects, including neutral and charged domain walls, multiferroic vortices, thus providing new fertile ground for the investigation of topology-related phenomena. Despite the growing interest, very little is known about the inner structure and local symmetry of the topological defects in RMnO$_3$. In this work, we quantify the vortices and domain walls emerging in these systems combining the scanning transmission electron microscopy and Landau-theory-based analytical calculations. Thus we observe and reproduce key novel features of the topological defects such as the emergence of a continuous U(1) symmetry at the vortex cores, and link these features to fundamental properties characterizing the material such as the correlation lengths.