Quantum theory of spin waves: magnons

Abstract

The classical treatment of spin waves presented in the previous chapter provides only a limited view of their properties. Spin waves are quantum objects and several phenomena involving them require that they are treated as such. In this chapter, we present a quantum approach of spin waves based on the Holstein–Primakoff transformation from the spin operators into magnon operators. This formalism is not restricted to low temperatures and, as we will show in the rest of the book, it can be used to explain quantitatively several magnonic phenomena observed experimentally. Next, we present the properties of magnons, and show that coherent magnon states are the quantum states that describe classical spin waves. The three- and four-magnon interactions, that are conveniently treated with the Holstein–Primakoff formalism, are used to calculate magnon relaxation mechanisms and energy renormalization. The quantum treatments of magnetoelastic waves and inelastic light scattering are also presented. The last section is devoted to details of magnons in yttrium iron garnet and the calculation of its magnetic thermodynamic properties.