Book Description

In this dissertation, we study two fundamental issues in nonlinear magnetism: the nonlinear dynamics of nanoparticles and the nonlinear dynamics of exchange-coupled thin-films. The behavior of a uniformly magnetized domain of ellipsoidal shape subject to a static external field and oscillatory external driving field is analyzed near bifurcation events. The analysis includes the effects of both linear and circularly polarized driving fields and is performed using numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equation. Under a linearly polarized driving field, the LLG equation is a nonautonomous differential equation which can lead to complex magnetization motions, such as bistability, multi-periodic orbits, quasiperiodicity and chaos. Under a circular polarized driving field, the LLG equation can be written in autonomous form by transforming to the frame rotating with the driving field. The autonomous nature allows one to perform a fixed point analysis of the system for select demagnetization factors. Similarities and differences between the driven systems are highlighted through, bifurcation diagrams, phase portraits, basins of attraction and Lyapunov exponents. Magnetization switching, prolonged transients, quasiperiodicity, and chaos are observed with both linear and circularly polarized driving fields in the magnetic systems investigated. We also investigate the dynamics of exchange-coupled ferromagnetic films in the nonlinear limit and find a number of interesting features. These include the following: 1) A power-dependent localization of the magnetization oscillations; 2) A nonlinear mixing of the acoustic and optic modes in the antiferromagnetically coupled system leads to quasiperiodic and multi-periodic composite modes; 3) Ferromagnetic resonance experiments will show new absorption peaks (in the 20-50 GHz range) which have a rapid increase in strength with input power. As with the case of the uniformly magnetized domain, the results are calculated through linearization techniques and numerical solutions of the LLG equation. The nonlinear (and linear) behavior is illustrated through Poincare section bifurcation diagrams and power absorption curves.