Investigation of the Nonlinearity Thresholds of Magnetic Nanostructures by Computing the Bifurcation Points at Microwave Frequencies

摘要

The bifurcation analysis of the threshold for collective behavior, due to the instabilities (the parametric excitation) of magnetostatic waves (MSW) and dipole-exchange spin-waves (SW) in 3D magnetic nanostructures, is developed. The numerical method is applied to determine the bifurcation points of the nonlinear Maxwell operator (the nonlinear Maxwell equations with electrodynamic boundary conditions complemented by the Landau-Lifshitz equation including the exchange term). The original computational algorithm is improved by combining it with a qualitative method of analysis, based on Lyapunov stability theory. The threshold magnitudes of the pumping electromagnetic waves (EMWs) in the magnetic particle arrays are determined by computing the bifurcation point for different size nanoparticles and for various separations. This technique, based on the bifurcation theory, is a pioneering approach in nano-electrodynamics, taking into account the constrained geometries.