  Hexagonal manganites REMnO3 (RE, rare earths) have attracted significant
attention due to their potential applications as multiferroic materials and the
intriguing physics associated with the topological defects. The two-dimensional
(2D) and 3D domain and vortex structure evolution of REMnO3 is predicted using
the phase-field method based on a thermodynamic potential constructed from
first-principles calculations. In 3D spaces, vortex lines show three types of
topological changes, i.e. shrinking, coalescence, and splitting, with the
latter two caused by the interaction and exchange of vortex loops. Compared to
the coarsening rate of the isotropic XY model, the six-fold degeneracy gives
rise to negligible differences with the vortex-antivortex annihilation
controlling the scaling dynamics, whereas the anisotropy of interfacial energy
results in a deviation. The temporal evolution of domain and vortex structures
serves as a platform to fully explore the mesoscale mechanisms for the 0-D and
1-D topological defects.
