A universal framework for metropolis Monte Carlo simulation of magnetic Curie temperature

Abstract Recent research of two-dimensional magnetism intrigues rapidly growing attention and broadens the prospects for utility in nano-devices. However, understanding the new magnetic phenomena and the behavior of magnetic centers is still one of the challenges. The Heisenberg model with the Metropolis Monte Carlo method provides an accurate description with continuous degrees of freedom while effective and universal spin update algorithms remain highly desirable. In this study, we propose algorithms for the magnetization switching in the classical Heisenberg model based on the concept of Euler angles and quaternion, which update the spins simply by a rotation matrix and convert to sphere and Cartesian coordinates in a very convenient way. The proposed methods are fully tested and validated by comparisons with the benchmarks of both the two-dimensional square lattice Ising model and the three-dimensional cubic lattice Heisenberg model. As an application example of the two-dimensional ferromagnetic material of CrI3, the simulated Curie temperature is about 42 K, which is in good agreement with the experimental value of 45 K. The update algorithms together with other configuration schemes are compiled into an easy-to-operate program named SEU-mtc, aiming to execute post-processing analysis of the spin microstates and greatly improve the efficiency of Curie temperature simulations based on ab initio methods.