A Hybrid Brownian Dynamics-kinetic Monte Carlo Framework for Coupled Magnetic and Rotational Dynamics of Nanoparticles
Simulating the coupled magnetic and rotational dynamics of suspended magnetic nanoparticles (MNPs) over experimentally relevant timescales remains computationally demanding, particularly under low-frequency alternating magnetic fields. Here, we develop a hybrid Brownian Dynamics--kinetic Monte Carlo (BD--kMC) framework that combines thermally activated magnetic switching with particle rotation while retaining local fluctuations of the magnetic moment. These fluctuations are incorporated through Metropolis Monte Carlo (MC) sampling, allowing the moment to depart from the energy minima and thereby capturing the thermally averaged anisotropy torque that governs particle rotation. To preserve the distinction between local fluctuations and magnetic reversals, a barrier-trapping criterion confines MC trial moves to the current energy well, leaving thermally activated switching to the kMC process. For non-interacting single-domain MNPs, comparison with stochastic Landau--Lifshitz--Gilbert (LLG) simulations demonstrates agreement in the equilibrium torque and stationary easy-axis orientation, including the field-driven transition from predominantly perpendicular to parallel alignment. The resulting BD--kMC framework provides an efficient approach to coupled magnetic and Brownian Dynamics, reducing the computational cost of exploring the long timescales relevant to low-frequency magnetic applications.