  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.
