Effect of curvature on nonlinear magnetization dynamics in submicrometer-sized rings

This is my bachelor thesis, as submitted to my university. One of the interesting characteristics of spin waves, which are collective elementary excitations in magnetic materials, is their nonlinear interaction. Moreover, topological and curvatureinduced effects are gaining increasing attention in the emerging field of curvilinear magnonics. The aim of this thesis is to study the interplay between a topological effect, the Berry phase, and nonlinear dynamics such as three magnon scattering in a magnetic ring in the vortex state. Here, a Berry phase appears when a static external field perpendicular to the ring is applied. The influence on three magnon scattering is studied by first obtaining spin-wave eigenmodes for different external out-of-plane fields. Second, important characteristics, such as the damping of the modes, are calculated. With those results splitting coefficients and thresholds of the three-wave splitting are calculated in order to predict scattering channels and to estimate the splitting threshold. It is found that, along with the appearance of a Berry phase, certain selection rules of three-wave splitting in vortices are relaxed; moreover, the threshold microwave fields to excite nonlinear dynamics are drastically decreased