Direct observation of the proliferation of ferroelectric loop domains and vortex-antivortex pairs.

We discovered stripe patterns of trimerization-ferroelectric domains in hexagonal REMnO(3) (RE=Ho,···,Lu) crystals (grown below ferroelectric transition temperatures (T(c)), reaching up to 1435 °C), in contrast with the vortex patterns in YMnO(3). These stripe patterns roughen with the appearance of numerous loop domains through thermal annealing just below T(c), but the stripe domain patterns turn to vortex-antivortex domain patterns through a freezing process when crystals cross T(c) even though the phase transition appears to not be Kosterlitz-Thouless-type. The experimental systematics are compared with the results of our six-state clock model simulation and also the Kibble-Zurek mechanism for trapped topological defects.