Multiphysics Time-Domain Modeling of Nonlinear Permeability in Thin-film Magnetic Material

A fast-converging one-dimensional (1-D) finite-difference time-domain (FDTD) algorithm has been proposed based on reduction strategy of unknowns in electromagnetic (EM) fields. The proposed algorithm solves simultaneously Max-well's equations and Landau-Lifshitz-Gilbert (LLG) equation with nonlinear effects. Therefore, the proposed algorithm can predict the dynamic interaction between magnetic spins and EM fields. The accuracy of the modeling has been validated by 1. a standard magnetic switching process under static magnetic fields, and 2. the dispersive permeability of a PEe-backed continuous ferrite film with a 3 $\pmb{\mu} \mathbf{m}$ -thickness, under dynamic electric excitation. The simulated permeability agrees with the theoretical prediction, under both linear and nonlinear circumstances. Specifically, the algorithm has fully revealed numerically that sufficiently large RF power can decrease the ferromagnetic resonance (FMR) frequency and suppress the permeability.