Jeffrey Rau
In this tutorial I will give an overview of the effect of magnon-magnon interactions in spin-wave theory, going beyond the linear theory. I will first outline the perturbative treatment of these interactions, including number non-conserving terms, and how the magnon Green's function and related quantities like the dynamical structure factor can be computed. Next, I will describe how spin-wave excitations can be renormalized and broadened due to these interactions and highlight several relevant material examples of where these effects have been observed. I will focus on two signatures of interaction effects: the opening of pseudo-Goldstone gaps and the appearance of spontaneous decay. Finally, I will discuss the impact of these non-linear interactions on the topological properties and responses of the linear theory and under what conditions this topology is robust.