Magnons (or spin waves) are the low-lying excitations that occur in ordered magnetic materials. The concept of spin waves was introduced by Bloch (1930), who envisaged some of the spins as deviating slightly from their ground-state alignment and this disturbance propagating with a wave-like behaviour through the solid. Because the spins are properly described by quantum-mechanical operators, the spin waves are also quantised with the basic quantum being referred to as the magnon (by analogy with the phonon for quantised lattice vibrations). Magnons can be studied through their contribution to thermodynamic properties (e.g. specific heat) or more directly by techniques such as light scattering, neutron scattering and magnetic resonance.

We begin this chapter by giving an introductory account of the theoretical models required to describe magnons in simple ferromagnets and antiferromagnets. Using the Heisenberg model we then present the theory of bulk magnons in infinite ferromagnets, as a preliminary to generalising the theory to semi-infinite ferromagnets and to ferromagnetic films. In the last two cases we show that surface magnons may occur localised near the surface(s) and that bulk-magnon properties are modified. After extending the theory to bulk magnons and surface magnons in Heisenberg antiferromagnets, we give a review of experimental results for surface magnons in Heisenberg magnetic materials.