  Magnonics, an emerging field of Magnetism, studies spin waves (SWs) in
nano-structures, with an aim towards possible applications. As information may
be eventually transmitted with efficiency stored in the phase and amplitude of
spin waves, a topic of interest within Magnonics is the propagation of SW
modes. Thus, understanding mechanisms that may influence SW propagation is of
interest. Here the effect of localized surface geometric defects on
magnetostatic surface modes propagation is studied in ferromagnetic films and
semi-infinite media. Theoretical results are developed that allow to calculate
the scattering of these surface or Damon-Eshbach (DE) modes. A Green-Extinction
theorem is used to determine the scattering of incident surface modes, through
the determination of phase shifts of associated modes that are symmetric and
anti-symmetric under inversion in the same geometry with geometric defects.
Choosing localized symmetric depressions as geometric defects, scattering
transmission coefficients are determined that show perfect transmission at
specific frequencies or wave-lengths, that we associate with resonances in the
system. Interestingly the system shows the appearance of localized modes in the
depression regions, with associated discrete frequencies immersed in the
continuum spectrum of these surface DE modes. These localized modes have a
short wave-length content, and appear similarly in semi-infinite surfaces with
depressions. The latter indicates that these types of scattering effects should
appear in all surfaces with roughness or more pronounced geometric defects.
