Coupling Electromagnetic Waves to Spin Waves: A Physics-Based Nonlinear Circuit Model for Frequency-Selective Limiters

A physics-based nonlinear circuit model is developed for frequency-selective limiters (FSLs) based on thin-film magnetic materials. The equivalent circuit model is structured and its parameters are determined rigorously from the fundamental physics of electromagnetic waves and spin waves. The spin motions as well as the ferromagnetic resonance (FMR) are modeled by RLC parallel circuits with parameters derived from Polder's tensor and Kittel's equations. The exchange coupling between spins is modeled by an inductor added between adjacent RLC circuits based on quantum spin theory. The nonlinear crossfrequency coupling from signal at ω to spin waves at ω/2 is represented by a nonlinear coupled inductor model that follows the mathematics of a pendulum motion to represent the parametric oscillations of spins. The circuit units are cascaded to describe the spin-wave propagation inside the magnetic material, and transmission line parameters are added finally to describe the electromagnetic wave propagation. An FSL device described in the literature is used as an example to validate the circuit model, and the model successfully predicts the power-dependent insertion loss as well as the threshold power level, time delay, and frequency selectivity of the power limiting effect.