The rotational relaxations exist in magnetic nanoparticles (MNPs) exposed to AC excitation magnetic field, including Brownian rotational relaxation and Neel rotational relaxation. The magnetization of MNPs exposed in AC magnetic field may be affected by rotational relaxation (Brownian relaxation play a dominated role when frequency is less than 1 kHz), and phase lag of magnetization harmonics are existed. In this paper, we employ a Fokker-Planck Equation, which describe accurately AC magnetization dynamic (dominated by Brownian rotational relaxation), analyze the difference of AC magnetization based on Fokker-Planck Equation and Langevin Function, study magnetization harmonic and phase lag dependence on Brownian rotational relaxation, impose a simple, empirical harmonic model. The simulation and experiment results show that the harmonic model can describe accurately AC magnetization when the Brownian rotational relaxation is dominated in MNPs. It is expected to be useful for improving MPI and MNPT.
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