Time Quantified Monte Carlo Algorithm for Interacting Spin Array Micromagnetic Dynamics

TL;DR

This paper critically evaluates the time quantified Monte Carlo method for simulating stochastic dynamics of interacting magnetic nanoparticles, comparing it with Langevin dynamics and validating through numerical analysis.

Contribution

It derives and compares Fokker-Planck coefficients for TQMC and LLG, providing a justified time quantification factor and validating the approach with numerical simulations.

Findings

TQMC accurately reproduces Langevin dynamics for interacting spins.

Derived Fokker-Planck coefficients for both TQMC and LLG.

Validated TQMC method through spin-wave dispersion analysis.

Abstract

In this paper, we reexamine the validity of using time quantified Monte Carlo (TQMC) method [Phys. Rev. Lett. 84, 163 (2000); Phys. Rev. Lett. 96, 067208 (2006)] in simulating the stochastic dynamics of interacting magnetic nanoparticles. The Fokker-Planck coefficients corresponding to both TQMC and 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.