Analogue Gravity for Magnons on a Spin Lattice

Abstract

Theoretical research into analogue gravity systems demonstrate promising results for observing gravitational phenomena. In this thesis we give an introduction of the theory behind analogue gravity and investigate the possibility of Cherenkov radiation occurring at a one dimensional magnonic black or white hole. We do this by determining the critical background spin velocity for an energetic instability to be possible and examening the behavour of magnons as they cross the event horizon where the background spin velocity exceeds this critical velocity. This way, we find expressions for the reflection and transmission coefficients of spin waves crossing the event horizon, which can be used to further explore this phenomenon.