Surface properties of ferromagnetic films and spin wave modes

Ferromagnetic films are a fundamental platform in Magnonics, the area that studies spin wave propagation and its possible applications. These films have been studied for a long time experimentally and theoretically, either individually or as parts of multifilms structures. The present study delves into an issue of interest that remains to be studied in detail, which is the relation between the surface properties of these films and the spin wave propagation in them. The main idea of this work is that the frequencies of spin waves may be determined experimentally with precision and through their relation with surface properties one may theoretically validate and derive the main parameters of models that describe the behavior of the surfaces. Several parameters may be changed in the process of testing the relation between surface properties and spin waves, like an applied magnetic field orientation and strength, the angle of in-plane spin wave propagation, etc. This study uses a continuum micromagnetic model for the description of the magnetization dynamics, in this case, the surface properties enter through effective boundary conditions. Three models of surface properties are studied: uniaxial surface anisotropy, the latter combined with bulk uniaxial anisotropy, and surfaces with Dzyaloshinskii-Moriya interactions (DMI). In general, the boundary conditions affect the equilibrium magnetization in boundary layer regions close to the surfaces: an asymptotic analysis predicts their penetration lengths for reasonable surface anisotropies. For very thin films, this is quite relevant since the boundary layers are of the order of the film thickness, we propose this as a practical way to define what may be considered a very thin film. Effective physical parameters of thin films and very thin films clearly depend on the surface properties. The main effects of the surfaces on spin waves occur for angles of inclination of the applied magnetic field close to perpendicular to the plane, and they may be of significant magnitude. Several different numerical methods were used to solve for the spin waves, in the context of an orthogonality equation method.