Bachelor Thesis - Calculation of spin-wave eigenmodes in confined nanostructures using a dynamic matrix approach

This is my bachelor thesis, as submitted to my university.

Numerical micromagnetic simulations have been proven to be a powerful tool to
obtain the spatial mode profiles and frequencies of spin waves, the elementary
excitations of magnetic systems. To simulate these spin waves in arbitrary confined
geometries, usually a dynamic simulation approach is implemented using a time
integration of the Landau-Lifshitz-Gilbert (LLG) equation, followed by a Fourier
transform to obtain mode profiles and frequencies. Although this method is very
versatile, it cannot resolve degenerate modes and requires a-priori knowledge of the
mode profiles. An alternative method is the dynamic matrix approach, which consists
of a diagonalization of the linearized LLG equation and directly yields mode profiles
and frequencies. In this thesis, such an approach is implemented in a program called
TetraEigen, which builds upon TetraMag, an already existing micromagnetic code
for finite element dynamical simulations. The implementation of the exchange and
dipolar interactions, as well as magnetic anisotropy and external field is carried out
and verified. Then, TetraEigen is applied to calculate the spin-wave modes in a disk
with a displaced vortex and a vortex-state hemisphere. The results are compared to a
flat vortex-state disk.