Multi-meron interactions and statistics in two-dimensional materials

As a fundamental type of topological spin textures in two-dimensional (2D) magnets, a magnetic meron carries half-integer topological charge and forms a pair with its antithesis to keep the stability in materials. However, it is challenging to quantitatively calculate merons and their dynamics by using the widely used continuum model because of the characteristic highly inhomogeneous spin textures. In this work, we develop a discrete method to address the concentrated spin structures around the core of merons. We reveal a logarithmic-scale interaction between merons when their distance is larger than twice their core size and obtain subsequent statistics of meron gas. The model also predicts how these properties of single and paired merons evolve with magnetic exchange interactions, and the results are in excellent agreement with the Monte Carlo simulations using the parameters of real 2D van der Waals magnetic materials. This discrete approach not only shows equilibrium static statistics of meron systems but also is useful to further explore the dynamic properties of merons through the quantified pairing interactions.