  The surface spin wave branches in ferromagnetic films are studied using a
microscopic theory which considers both magnetic dipole-dipole and Heisenberg
exchange interactions. The dipole terms are expressed in a Hamiltonian
formalism, and the dipole sums are calculated in a rapidly convergent form. The
Damon-Eshbach surface modes are analyzed for different directions of the
spin-wave propagation and also for different ratios of the strength of the
dipole interactions relative to the exchange interactions. Numerical results
are presented using parameters for Fe and GdCl$_3$.
