Magnetization Dynamics

This chapter provides a concise introduction to magnetization dynamics in single magnetic domains, with an emphasis on behavior in ferromagnetic metal thin films. The material presented here underpins micromagnetics, which consists of coupled equations of motion for single magnetic domains, and spin torque, which adds additional terms to the equation of motion for a single domain. In Section 4.1, we provide motivation and formalism for the fundamental equation of motion of magnetization, the Landau–Lifshitz–Gilbert (LLG) equation. Small‐angle solutions of the LLG equation are developed in Section 4.2.1. We emphasize how materials parameters have been extracted from experiments, particularly from ferromagnetic resonance experiments, in Section 4.2.2 and tabulate some materials parameters in Section 4.2.3. Approaches to calculate large‐angle dynamics are developed in Section 4.3; we show quasistatic aspects of switching and a short example of how to integrate the nonlinear LLG equation for a switching experiment. Finally, in Section 4.4, we describe how spin torque terms modify the LLG equation and outline some simple consequences
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