Chapter 5 - Dissipative Magnetization Dynamics

Abstract

This chapter deals with dissipative magnetization dynamics, which has two distinct time scales: the fast time scale of the precessional dynamics and the relatively slow time scale of relaxational dynamics controlled by a small damping constant. The Landau–Lifshitz (LL) and Landau–Lifshitz–Gilbert (LLG) equations are written in terms of magnetization components that generally vary on the fast time scale. The slow and fast time scales of magnetization dynamics are mathematically decoupled in the problem of damping switching of uniaxial particles due to the unique symmetry properties of that problem. It is clear on physical grounds that the magnetic free energy varies on the slow time scale. In other words, the magnetic free energy is a slow variable whose time evolution is not essentially affected by the fast precessional dynamics. It is desirable to derive dynamic equations containing the magnetic free energy as a state variable, which can be accomplished by using two different techniques. One is based on two-time-scale reformulation and the averaging technique. The Poincare–Melnikov theory, which is conceptually similar to the averaging technique, is also discussed. This theory is instrumental for the identification of self- oscillations of magnetization dynamics when it is driven not only by applied magnetic fields but by other stationary forces as well.