Kibble–Zurek mechanism of Ising domains

The formation of topological defects after a symmetry-breaking phase transition is an overarching phenomenon that encodes the underlying dynamics. The Kibble–Zurek mechanism (KZM) describes these non-equilibrium dynamics of second-order phase transitions and predicts a power-law relationship between the cooling rates and the density of topological defects. It has been verified as a successful model in a wide variety of physical systems, including structure formation in the early Universe and condensed-matter materials. However, it is uncertain if the KZM mechanism is also valid for topologically trivial Ising domains, one of the most common and fundamental types of domain in condensed-matter systems. Here we show that the cooling rate dependence of Ising domain density follows the KZM power law in two different three-dimensional structural Ising domains: ferro-rotation domains in NiTiO 3 and polar domains in BiTeI. However, although the KZM slope of NiTiO 3 agrees with the prediction of the 3D Ising model, the KZM slope of BiTeI exceeds the theoretical limit, providing an example of steepening KZM slope with long-range dipolar interactions. Our results demonstrate the validity of KZM for Ising domains and reveal an enhancement of the power-law exponent for transitions of non-topological quantities with long-range interactions. The Kibble–Zurek mechanism is shown to apply to structural Ising domains in three-dimensional materials. Long-range interactions modify the critical exponents away from theoretical predictions.