Transport signature of the BKT transition in 2D easy-plane magnets

The theory of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition was formulated to describe the 2D phase transition of easy-plane magnets as well as 2D superconductors and superfluids. The BKT transition being topological in nature, i.e. not characterized by a local order parameter, its detection has been challenging. The BKT transitions in the latter cases have been observed in experiments, much of which involves transport signatures, such as the current-voltage relation being non-linear below the BKT temperature and linear above the BTK temperature. By contrast, the experimental study of the solid-state 2D magnetic material emerged only in the last few years. The accompanied recent development of spin-transport measurements offers a tantalizing opportunity to discover novel transport phenomena of spin, which should be expected as the spin, unlike the particle number, is not conserved. In this Letter, we show here that this non-conservation of spin in the 2D easy-plane magnets leads to a distinct spin transport signature at the BKT transition, the crossover between the infinitely long-range spin transport and the exponentially decaying spin transport. We also present how this can be detected in the van der Waals easy-plane magnetic materials such as the monolayer NiPS₃.