Kibble–Zurek mechanism of Ising domains

Our postdoctoral researcher Fernando J. Gómez-Ruiz, in collaboration with a distinguished team of researchers from Rutgers University, Pohang University of Science and Technology, Institute for Basic Science – Korea, Argonne National Laboratory, University of Luxembourg, and Donostia International Physics Center, has unveiled a significant breakthrough in the study of Ising domains. Groundbreaking research published in Nature Physics (DOI: 10.1038/s41567-023-02112-5) on June 26, 2023, this study marks the first-ever experimental investigation of Ising domains within the renowned Kibble-Zurek framework.

Phase transitions and the emergence of symmetry-breaking induced domain formations are fundamental phenomena in modern statistical mechanics and condensed matter physics. While the static aspects of continuous transitions have been extensively studied in textbooks, the dynamic behavior of phase transitions away from equilibrium has remained elusive. The Kibble-Zurek mechanism (KZM), a pioneering theory, sheds light on the universal nature of these nonequilibrium dynamics and predicts the density of topological defects that arise following the transition. Intriguingly, KZM can now be tested in laboratory settings, despite its original proposal in the cosmological realm. This captivating aspect has spurred extensive research interest in recent decades, leading to investigations of various condensed matter systems to uncover different facets of KZM.

However, an essential piece of the KZM puzzle has remained unexplored until now. Ising-type domains, characterized by two degenerate scalar order parameters, represent the most fundamental and prevalent types of order in both theoretical and experimental condensed matter physics. Surprisingly, these domains had never been experimentally investigated within the framework of KZM, primarily due to the scarcity of appropriate material systems, despite the ubiquity of Ising domains in condensed matter. The search for an ideal Ising system that enables easy imaging and comparison of domain populations across a wide range of cooling rates has proven challenging.

This groundbreaking research overcomes these obstacles by carefully selecting and fabricating emerging materials that host structural Ising domains. Specifically, clockwise (CW)/counter-clockwise (CCW) ferro-rotation domains in NiTiO3 and up/down polar domains in BiTeI were studied. Through the use of high-quality synthesized crystals, the researchers introduced innovative domain imaging techniques with large fields of view and efficient data analysis approaches. These advancements enabled extensive measurements required for testing KZM. By comparing the experimentally obtained results with theoretically computed KZM exponents in 3D Ising models, the researchers successfully confirmed that fundamental Ising-type domains indeed adhere to the general predictions of KZM. Moreover, they made a fascinating discovery: the presence of weak long-range interactions dramatically reduces the dynamical critical exponent z, leading to an increased KZM exponent. These findings not only validate the prevalence of Ising domains within the 3D Ising universality class, a critical aspect of KZM, but also highlight the significant role of possible long-range interactions in determining the KZM exponent in real systems. This pioneering work will serve as a reference for future applications in quantum science and technology, statistical mechanics, and the exploration of novel paradigms in quantum materials.


  • Kai Du, Xiaochen Fang, Choongjae Won, Chandan De, Fei-Ting Huang, Wenqian Xu, Hoydoo You,
    Fernando J. Gómez-Ruiz, Adolfo del Campo & Sang-Wook Cheong
    Nat. Phys. (2023) 10.1038/s41567-023-02112-5. on arXiv:2306.15821