Kibble-Zurek Mechanism of Ising Domains

The Kibble–Zurek mechanism (KZM) is a pioneering theory that describes the universality of such nonequilibrium dynamics and predicts the density of topological defects after the transition. A crucial part of KZM is still missing to date. Specifically, 2D and 3D Ising-type domains with two degenerate scalar order parameters have never been investigated experimentally in terms of KZM even though they are the most fundamental and popular types of order in both theoretical and experimental condensed matter physics. This is primarily due to the lack of appropriate material systems despite the ubiquity of Ising domains in condensed matter systems. The search for the ideal Ising system whose domain populations can be easily imaged and compared in a wide range of cooling rates remains challenging.

In this work, we overcome these obstacles by selecting and fabricating proper emerging materials hosting structural Ising domains--3D clockwise (CW)/counter-clockwise (CCW) ferro-rotation domains in NiTiO3 and 2D up/down polar domains in BiTeI. With synthesized high-quality crystals, we also introduce innovative domain imaging techniques with large fields of view and efficient data analyzing approaches, which essentially enable extensive measurements required for the test of KZM. With comparisons to theoretically computed KZM exponents in 3D and 2D Ising models, we managed to confirm that fundamental Ising-type domains do follow the general prediction of KZM. Moreover, we also reveal that the dynamical critical exponent z can be dramatically reduced with the presence of weak long-range interactions, leading to an increased KZM exponent. Our results not only validate ubiquitous Ising domains in the 2D and 3D Ising universality class as an important aspect of intriguing KZM but also demonstrate the critical role of possible long-range interactions in determining KZM exponent in real systems.