Chapter 2 - Basic Equations for Magnetization Dynamics

Abstract

This chapter deals with the origin of the Landau–Lifshitz (LL) equation, which is a dynamic constitutive relation that is compatible with micromagnetic constraints. The interactions with the thermal bath, which result in the physical phenomena of damping, are accounted for in the LL and Landau–Lifshitz–Gilbert (LLG) equations by introducing different damping terms. By using the appropriate linear combination of the LLG damping terms, the LL and LLG equations can be written in the mathematically equivalent form where the precessional term is the same as in the absence of the thermal bath. Equations for the free energy balance are also derived from the equations. Results show that the free energy is always a decreasing function of time when the external field is constant in time. The Bloch equation serves as an alternative to the LL and LLG equations in situations where the driving actions of applied magnetic fields are so strong that the magnetization magnitude is no longer preserved, at least during short transients before usual micromagnetic states have emerged. Micromagnetics is also reviewed.