  Time-resolved scanning transmission x-ray microscopy (TR-STXM) has been used
for the direct imaging of spin wave dynamics in thin film yttrium iron garnet
(YIG) with spatial resolution in the sub 100 nm range. Application of this
x-ray transmission technique to single crystalline garnet films was achieved by
extracting a lamella (13x5x0.185 $\mathrm{\mu m^3}$) of liquid phase epitaxy
grown YIG thin film out of a gadolinium gallium garnet substrate. Spin waves in
the sample were measured along the Damon-Eshbach and backward volume directions
of propagation at gigahertz frequencies and with wavelengths in a range between
100~nm and 10~$\mathrm{\mu}$m. The results were compared to theoretical models.
Here, the widely used approximate dispersion equation for dipole-exchange spin
waves proved to be insufficient for describing the observed Damon-Eshbach type
modes. For achieving an accurate description, we made use of the full
analytical theory taking mode-hybridization effects into account.
