  We examine the experimental absence of standing spin wave modes in thin
magnetic films, by means of atomistic spin dynamics simulations. Using Co on
Cu(001) as a model system, we demonstrate that by increasing the number of
layers, the "optical" branches predicted from adiabatic first-principles
calculations are strongly suppressed, in agreement with spin-polarized electron
energy loss spectroscopy measurements reported in the literature. Our results
suggest that a dynamical analysis of the Heisenberg model is sufficient in
order to capture the strong damping of the standing modes.
