Magnon focusing in thin ferromagnetic films

Abstract

We study the focusing of bulk and surface spin waves in thin ferromagnetic films. This is done by first solving the implicit dispersion relation obtained from the magnetostatic Maxwell equations. We then obtain slowness surfaces (constant frequency curves in $k$-space) for the first four bulk modes and one surface mode. The focusing pattern is obtained from the slowness surface by finding the normal to the slowness surface and then evaluating the curvature at each point on the surface. Numerical examples are given for two materials, yttrium iron garnet and iron. It is found that the bulk modes are focused in four to eight distinct directions depending on the frequency and the applied magnetic field. For magnetostatic modes, the surface waves are not focused as strongly as the bulk waves. Also, we study the effect of the exchange interaction on the focusing pattern of both the bulk and surface waves. This is carried out by numerically solving the magnetostatic Maxwell equations along with the equations of motion for the magnetization in thin film to obtain the slowness surface and the focusing pattern. It is found that while the bulk wave focusing is not substantially affected by the exchange interaction, the surface waves now become as strongly focused as the bulk waves. In both cases the focusing direction is tunable with the frequency and applied field.