Proposal of hybrid-type simulation techniques for spherical magnetic nanoparticles with uniaxial anisotropy: A combination of Brownian dynamics and Monte Carlo methods achieving fast and scalable simulations

We developed a hybrid-type simulation method that combines the Brownian dynamics (BD) and Monte Carlo (MC) methods for spherical magnetic particles with uniaxial magnetic anisotropy. In this hybrid-type simulation method, the viscous translational and rotational motions of a magnetic particle are simulated using the BD method, where the direction of the magnetic moment of the particle is determined using the MC method instead of the stochastic Landau–Lifshitz–Gilbert (LLG) method. We addressed a single-particle system to investigate the orientational properties of both the particle and magnetic moment. In order to verify the validity of the hybrid-type method, the present results were compared with those obtained by solving a stochastic LLG equation. With respect to the magnetisation curve, the hybrid-type simulation method gives rise to a theoretical solution (Langevin function), just as in the stochastic LLG simulation method. The orientational characteristics of the particle and the magnetic moment, as a function of the value of the magnetic anisotropy and as a function of the magnetic field strength, agreed well between the two simulation methods. Even if the anisotropic factor is more dominant than the thermal motion, the magnetic particle behaves as a superparamagnetic particle in a sufficiently strong magnetic field. The developed hybrid-type simulation method provides significantly higher performance with respect to CPU time in comparison with the stochastic LLG method, which is the most appealing aspect of the present simulation method. This CPU time may be a definitive factor in determining the feasibility of a particle-based simulation method for a multi-particle system. We conclude that the present hybrid-type simulation method is remarkably effective and practical for simulations of a multi-particle system where the motion of both the particle and the magnetic moment are governing factors, for instance, in studies on magnetic hyperthermia.