  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 demonstrate perfect agreement between the approaches. The
analysis of the dispersion relation indicates that the presence of surface
anisotropy increases the avoided crossing size between 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 Damon-Eshbach mode and the symmetry of perpendicular
standing modes in the avoided crossing broadening. Interestingly, for specific
set of parameters the interaction between the particular modes can be
suppressed, resulting in a mode crossing. Such a crossing, which occurs only on
one side of the dispersion relation in a one-sided surface anisotropy system,
can be utilized in nonreciprocal devices.
