Search

The appropriate framework for the study of magnetization dynamics induced by spin-polarized current injection is the nonlinear dynamical system theory and its branch known as the bifurcation theory. The chapter systematically applies the methods and concepts of nonlinear dynamical system theory to the analysis of large magnetization motions governed by the Landau-Lifshitz equation. The chapter deals with the theoretical aspects of Landau-Lifshitz dynamics. The phenomenological derivation of the Landau-Lifshitz equation as a dynamic constitutive relation consistent with micromagnetics constraints is explained. Landau-Lifshitz dynamics is treated as a nonlinear dynamical system defined on a sphere. The phase portraits of this dynamical system, its noncanonical Hamiltonian structure, and the nature of dissipation are discussed. The chapter further discusses precessional switchings of magnetization and spin-polarized current-induced phenomena. Precessional switchings of magnetization for longitudinal and perpendicular media are discussed for rectangular field pulses, and expressions for critical fields and pulse durations are derived. Finally, the magnetization dynamics driven by spin-polarized current injection are discussed. It is demonstrated that this dynamics can be treated as a perturbation of the conservative dynamics caused by intrinsic damping and spin transfer. By using this central idea as well as the bifurcation theory for nonlinear dynamical systems, complete stability diagrams are obtained for the case when injected spin-polarized currents and external magnetic fields are simultaneously present.

This chapter discusses the problem of the existence of spatially uniform magnetization modes under far-from-equilibrium conditions. When magnetization dynamics is spatially uniform, a system governed by the Landau-Lifshitz-Gilbert (LLG) equation is reduced to a nonlinear dynamical system evolving on the surface of the unit sphere and a number of remarkable conclusions can be drawn from this fact by means of topological arguments. The chapter investigates small-amplitude non-uniform deviations from large uniform motions. This study leads to far-from-equilibrium generalizations of the notions of magneto-static mode and of spin wave. The chapter emphasizes on the analysis of generalized spin waves. Itdiscusses the progressive alteration of the spin wave spectrum and the associated dispersion relation when the external field excitation becomes increasingly strong. The results presented in this chapter concern the periodic magnetization response to time-harmonic excitations that eventually sets in after all transients have died out. The transient response is the feature of main interest when the aim is to investigate the switching phenomena.