Sym4state.jl: An efficient computation package for magnetic materials

Abstract

Exploring magnetic configurations of magnets often involves utilizing the four-state method to obtain the magnetic interaction matrix, and Monte Carlo method to simulate spin textures and phase transition processes. However, computing the interaction matrix between magnetic atoms using the four-state method requires plenty of individual calculations. Despite manual simplifying the number of individual calculations based on material's symmetry is possible, there remains a necessity for an automated approach to streamline the process for high-throughput screening of magnetic materials. Meanwhile, the traditional sequential Monte Carlo simulation encounters challenges of low efficiency and long time consuming in dealing with large systems. Furthermore, the prior parallelism in the Heisenberg model was limited to parallel computation of the system's energy or run several replicas in parallel. Hence, in our pursuit of comprehensive parallelization for the Heisenberg model, we have introduced a novel adaptation of the checkerboard algorithm, enabling a fully parallelizable simulation of the Heisenberg model. To address these problems, we have developed Sym4state.jl, a program specifically designed to simplify the computation of magnetic interaction matrix and simulate spin textures under various environmental conditions. This program, available as a Julia package, can be freely accessed at https://github.com/A-LOST-WAPITI/Sym4state.jl.

Program summary

Program title: Sym4state.jl

CPC Library link to program files: https://doi.org/10.17632/s6dkmgrjfw.1

Developer's repository link: https://github.com/A-LOST-WAPITI/Sym4state.jl

Licensing provisions: MIT

Programming language: Julia

Nature of problem: Employing the four-state method to calculate magnetic interaction matrix for magnetic materials can be simplified based on material symmetry, however, there is a lack of automated approach to streamline the simplification. Additionally, the commonly used Metropolis method for simulating magnetic texture can only make parallel computation of the system's energy or run several replicas in parallel, which could hardly boost the performance when simulating the large-scale magnetic textures.

Solution method: We simplify the four-state method calculations by utilizing the principles of energy invariance under symmetry operations and time reversal operations. To enhance the efficiency of the Metropolis algorithm, we have designed a strategy to divide the entire 2D lattice into multiple domains. We then execute the Metropolis algorithm in parallel for each individual domain, thereby improving the overall computational efficiency.

Additional comments including restrictions and unusual features: While the methods aimed at simplifying the four-state method and parallelizing the Metropolis algorithm are applicable to both 2D and 3D systems, the current program is specifically designed for the calculation and simulation of magnetism in 2D materials. As a result, compatibility with 3D systems has not yet been implemented.