Topological properties and polarization states of magnetostatic modes in a hollow ferromagnetic sphere

Using the solution for magnetostatic modes in a hollow sphere, it is possible to determine the dynamic magnetization configurations through the use of Topology concepts. The results were obtained in the case where the solutions have azimuthal symmetry. As a result, two configurations were obtained. One is that magnetization has two singularities and manifests itself at the poles of the hollow sphere. The other situation reflects the case in which there are three singularities, with flux leakage in the sphere’s equator region and those mentioned in the previous case with flux concentration at the sphere’s poles. These results were possible by exploring topology concepts combined to the solutions of magnetostatic modes in hollow sphere by means of the solution of the Walker’s equation.