Ferroelectric annular domains in hexagonal manganites

Experimental observations and theoretical simulations for the ferroelectric (FE) domains in multiferroic RMnO₃ (R=Ho-Lu, Y, and Sc) demonstrate that annular domains can appear in the topological Kosterlitz-Thouless (KT) phase in coexistence with the "cloverleaf" vortices. Moreover, the annular domains often adopt the multilayered structures as indexed by the annular number. The double-layered FE domains, an energetically favored structure, are commonly found in RMnO₃. Thermal annealing experiments directly show exchanges between large annular domains and cloverleaf vortices above the trimerization-structural transition temperature T_c. The temperature evolution of the FE domains has been analyzed by using the six-state clock model through Monte Carlo simulations. Based on careful in situ SEM observations, the dynamic properties of annular domains and interplay among domain walls have been briefly discussed.