Theory of large-wave-vector spin waves in ultrathin ferromagnetic films: Sensitivity to electronic structure

We present a series of theoretical studies of short wavelength spin waves in ultrathin ferromagnetic films, with attention to sensitivity of their dispersion relation to aspects of the electronic structure of the films. Our emphasis is on the influence of the magnitude of the intra-atomic Coulomb interaction U within the 3d shell. The calculations we report focus on eight layers of ferromagnetic Co adsorbed on the Cu(100) surface, a system whose spin wave dispersion relation has been studied experimentally for wave vectors throughout the surface Brillouin zone. We find the frequency of the short wavelength spin waves to be very sensitive to U. Appropriate values of this parameter produce a dispersion relation in very good accord with experiment, and a remarkably quantitative account of both the width and shape of the single feature in the spectral density found in the experiments. We have argued previously that in these systems, the adiabatic approximation (the "frozen magnon" approximation) breaks down qualitatively, with the consequence that our dynamical theory produces a single very broad feature in the spectral density at large wave vector, in contrast to the predictions of "frozen magnon" calculations, where a sequence of standing wave modes of infinite lifetime is predicted. In the present paper, we use adiabatic theory to calculate exchange constants for the ultrathin Co film adsorbed on Cu, and compare explicitly the predictions of "frozen magnon" theory with our dynamical calculations. The comparison provides insight into the origin of the broad features found in the dynamical calculations.