Kibble-Zurek mechanism of Ising domains

The formation of topological defects after a symmetry-breaking phase transition is an overarching phenomenon that encodes rich information about the underlying dynamics. Kibble-Zurek mechanism (KZM), which describes these nonequilibrium dynamics, predicts defect densities of these second-order phase transitions driven by thermal fluctuations. It has been verified as a successful model in a wide variety of physical systems, finding applications from structure formation in the early universe to condensed matter systems. However, whether topologically-trivial Ising domains, one of the most common and fundamental types of domains in condensed matter systems, also obey the KZM has never been investigated in the laboratory. We examined two different kinds of three-dimensional (3D) structural Ising domains: clockwise (CW)/counter-clockwise (CCW) ferro-rotation domains in NiTiO3 and up/down polar domains in BiTeI. While the KZM slope of ferro-rotation domains in NiTiO3 agrees well with the prediction of the 3D Ising model, the KZM slope of polar domains in BiTeI surprisingly far exceeds the theoretical limit, setting an exotic example where possible weak long-range dipolar interactions play a critical role in steepening the KZM slope of non-topological quantities. Our results demonstrate the validity of KZM for Ising domains and reveal an enhancement of the power-law exponent and a possible reduction of the dynamic critical exponent z for transitions with long-range interactions.