A snapshot of domain evolution between topological vortex and stripe in ferroelectric hexagonal ErMnO₃

Hexagonal manganites exhibit three distinct domain patterns: stripe, loop, and vortex. Due to the high ferroelectric phase transition temperature and the lack of reliable visualization methods, it is still a mystery about the evolution and the formation of vortex networks. In this study, we managed to capture the coexistence of vortices, loops, and stripes by accurately controlling the annealing temperature right at Tc. We proposed a merging process between the V-AV pair and the stripe, which result in two different forms of vortex networks, namely, the normal vortex and the zigzag vortex. In addition, the connection between the density of stripes and the orientation of V-AV pairs is analyzed, which are both influenced by self-straining of the crystal. The mystery of evolution of the vortex network is unveiled by capturing the snapshot, and the experimental database provided calls for more analysis to understand the evolution of different domain topologies.