  A double-peaked structure was observed in the {\it in-situ} Brillouin Light
Scattering (BLS) spectra of a 6 \AA$ $ thick epitaxial Fe/GaAs(001) film for
values of an external magnetic field $H$, applied along the hard in plane
direction, lower than a critical value $H_c\simeq 0.9$ kOe. This experimental
finding is theoretically interpreted in terms of a model which assumes a
non-homogeneous magnetic ground state characterized by the presence of
perperpendicular up/down stripe domains. For such a ground state, two spin-wave
modes, namely an acoustic and an optic mode, can exist. Upon increasing the
field the magnetization tilts in the film plane, and for $H \ge H_{c}$ the
ground state is homogeneous, thus allowing the existence of just a single
spin-wave mode. The frequencies of the two spin-wave modes were calculated and
successfully compared with the experimental data. The field dependence of the
intensities of the corresponding two peaks that are present in the BLS spectra
was also estimated, providing further support to the above-mentioned
interpretation.
