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

Abstract

The bifurcation analysis of the threshold for collective behavior, due to the instabil- ities (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 deter- mine the bifurcation points of the nonlinear Maxwell operator (the nonlinear Maxwell equations with electrodynamic boundary conditions complemented by the Landau-Lifshitz equation includ- ing 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 difierent 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. Magnetic nanocomposites of nanometer size magnetic particles embedded in a non-magnetic, insu- lating matrix provide a novel solution for low loss microwave materials up to mm wave frequencies. The electromagnetic properties of magnetic materials change drastically upon reducing the dimen- sions into the nano-range, including the early onset of nonlinear efiects, important for high power applications and non-linear signal processing. To investigate this efiect, the instability of para- metric excitation process of magnetostatic waves MSW and dipole-exchange spin-waves SW in 3D magnetic nanostructures should be simulated, taking into account the constrained geometries. In contrast to the bifurcation analysis of the instability of parametric excitation of electromag- netic oscillations in resonator structures with nonlinear planar ferrite inserts (1) and the parametric instability of MSW in thin fllm ferrite structures (2), in this work the parametric excitation of dipole-exchange SW in the arrays of magnetic nanoparticles is analyzed. For the analysis of non- linear phenomena (i.e., the parametric instability of SW) in magnetic nanoparticle systems the numerical method, developed by us earlier (3), is modifled here to determine the bifurcation points of the nonlinear Maxwell's operator including the Landau-Lifshitz equation with the exchange term.