BSc defense by Rasmus Kristiansen

Titel: Spin-waves and Two-Magnon Scattering Heisenberg Models

Abstract: The Heisenberg model is a well-known model of localized magnetism where spins interact with their neighbors via an exchange interaction. At low temperatures the ordered state of spins can exhibit excitations called spin-waves (magnons).

One important experimental procedure for the study of spin-waves is inelastic neutron scattering where the magnon dispersion is directly accessible via the scattering function/dynamical structure factor. The calculations to lowest order using linear spin-wave theory is well known, however the higher order corrections are rarely discussed in the literature.

In this project I investigate how the higher order corrections up to fourth order contribute to the dynamical structure factor and plot the result for the two-dimensional models; triangular antiferromagnet and square altermagnet. The corrections firstly produce a constant spin reduction coming from the finite deviation of the spins from vertical. A further small correction is identified, which vanishes in multiple models with parallel spins, but is finite for the triangular lattice. Secondly, fourth order $zz$-correlation is responsible for two-magnon scattering, which I conclude is primarily relevant for systems with parallel spins.

In the square two-dimensional altermagnet considered, the splitting of the dispersion relation into branches from the broken symmetry produces a splitting of the resonance peaks into multiple peaks, which are of the same magnitude. This provides a way to identify altermagnets if the splitting is larger than the experimental resolution.