Impact of surface anisotropy on the spin-wave dynamics in a thin ferromagnetic film

The spin-wave dynamics in the thin CoFeB film in Damon-Eshbach geometry are studied in three cases of boundary conditions-free boundary conditions, symmetrical surface anisotropy, and one-sided surface anisotropy. The analytical model created by Wolfram and De Wames was extended to include perpendicular surface anisotropy in boundary conditions. Its comparison with numerical simulations demonstrates perfect agreement between the approaches. The analysis of the dispersion relation indicates that the presence of surface anisotropy increases the avoided crossing size between the Damon-Eshbach mode and perpendicular standing modes. Additionally, asymmetrical one-sided surface anisotropy induces nonreciprocity in the dispersion relation. In-depth analysis of the avoided crossing size is conducted for systems with different boundary conditions, different thicknesses, surface anisotropy constant values, and external magnetic fields. It shows the significant role of the strength of surface localization of the Damon-Eshbach mode and the symmetry of perpendicular standing modes in the avoided crossing broadening. Interestingly, for a specific set of parameters, the interaction between the particular modes can be suppressed, resulting in a mode crossing. Such a crossing, which occurs only for one direction of the wave vector in a one-sided surface anisotropy system, can be utilized in nonreciprocal devices.