Domain wall dynamics in quasi one-dimensional nanostructures

The goal of this book is to give an overview about the dynamics of transverse domain walls. Therefore, it is necessary to understand first the underlying Heisenberg model which will be introduced in the first chapter. The quantum mechanical Heisenberg model can be used to describe single atoms, small clusters, and molecules. The classical Heisenberg model can be used to describe systems on the atomic and macroscopic (micromagnetism) scale. Within this book the description is restricted to the atomic scale and micromagnetic description and therefore, to the classical Heisenberg model. However, it will be shown that the corresponding equation of motion, the Landau-Lifshitz-Gilbert equation can be derived from quantum mechanics. Then, the Landau-Lifshitz-Gilbert equation will be used to describe the dynamics of domain walls.