Spin Waves in Ferromagnets: Semiclassical Approach

Abstract

In Chap. 1, we considered only the case of the magnetization dynamics that is uniform in space. The more general situation consists of a magnetization that varies in space, with elementary excitations that are called spin waves, the quanta of which are magnons. In this chapter, we shall treat spin waves considering that the spins are classical vectors with motion governed by the classical equation for the torque. We begin with a study of spin waves in an one-dimensional chain of classical spins. Then we present a macroscopic view of long-wavelength spin waves in a 3-dimensional ferromagnet, with an approach based on the Landau–Lifshitz equation of motion for the magnetization. Then we consider that the magnetization interacts with the lattice vibrations giving origin to coupled spin and elastic waves, called magnetoelastic waves, and discuss the conservation laws involved. We also present the concept of coupled spins and electromagnetic waves, called magnetic polaritons. Finally, we present two of the most important experimental techniques to study magnetoelastic waves, microwave excitation, and Brillouin light scattering.