A theoretical model is presented for the study of the scattering and the
localisation of spin-waves at an extended inhomogeneous structural and
magnetic boundary separating ultrathin Heisenberg ferromagnetic films. The
model system consists of two different magnetic materials A and B with
different thickness of two and three atomic layers, on either side of a
defect atomic step. The matching technique is used with nearest neighbour
magnetic exchange to analyse both the localisation and the scattering spin
dynamics. The localised spin states that manifest themselves as Rayleigh
branches, and the local densities of spin states are calculated on this
boundary. The coherent reflection and transmission scattering properties of
spin-waves incident from the interior of the ultrathin films on the
inhomogeneous boundary are also calculated. The numerical calculations are
applied in particular to a system of three Fe ferromagnetic atomic layers
and two Gd ferromagnetic atomic layers, across a defect atomic step. The
results illustrate the occurrence of Fano resonances in the transmitted
spectra due to the localised spin states on the inhomogeneous boundary. An
interesting physical effect is observed for this magnetic and atomic step
boundary, namely the frequency selective conductance of the spin-waves via
Fano resonances, by an appropriate choice of the angle of spin-wave
incidence on the boundary.