Time-quantified Monte Carlo algorithm for interacting spin array micromagnetic dynamics

In this paper, we reexamine the validity of using time-quantified Monte Carlo (TQMC) method [Phys. Rev. Lett. 84, 163 (2000); 96, 067208 (2006)] in simulating the stochastic dynamics of interacting magnetic nanoparticles. The Fokker-Planck coefficients corresponding to both TQMC and the Langevin dynamical equation (Landau-Lifshitz-Gilbert, LLG) are derived and compared in the presence of interparticle interactions. The time quantification factor is obtained and justified. Numerical verification is shown by using TQMC and Langevin methods in analyzing spin-wave dispersion in a linear array of magnetic nanoparticles.