Spin Waves in Thin Films; Dipolar Effects

We have examined the spin-wave eigenfrequencies and eigenfunctions for a model ferromagnetic film, in the presence of both exchange and magnetic dipole interactions. A detailed computer study of spin waves in a thirty-layer film is presented for the case where the exchange and dipole interactions are of comparable strength. We discuss in detail both surface and "bulk" modes for this case. Also, the symmetry properties of the eigenvectors are discussed, along with a method for converting certain two-dimensional dipole sums to a rapidly converging form.