Scaling Behavior and Beyond Equilibrium in the Hexagonal Manganites

We show that the improper ferroelectric phase transition in the multiferroic hexagonal manganites displays appropriate symmetry-breaking characteristics for testing the Kibble-Zurek mechanism originally proposed to describe early-universe phase transitions. We present an analysis of the Kibble-Zurek theory of topological defect formation applied to the hexagonal manganites, discuss the conditions determining the range of cooling rates in which Kibble-Zurek behavior is expected, and show that recent literature data are consistent with our predictions. Finally, we explore experimentally the crossover out of the Kibble-Zurek regime and find a surprising reversal of the scaling behavior.