Spin Waves in Ultrathin Ferromagnets: Intermediate Wave Vectors
Our earlier papers explore the nature of large wave vector spin waves in ultrathin ferromagnets, and also the properties and damping of spin waves of zero wave vector, at the center of the two dimensional Brillouin zone, with application to FMR studies. The present paper explores the behavior of spin waves in such films at intermediate wave vectors, which connect the two regimes. For the case of Fe films on Au(100), we study the wave vector dependence of the linewidth of the lowest frequency mode, to find that it contains a term which varies as the fourth power of the wave vector. It is argued that this behavior is expected quite generally. We also explore the nature of the eigenvectors of the two lowest lying modes of the film, as a function of wave vector. Interestingly, as wave vector increases, the lowest mode localizes onto the interface between the film and the substrate, while the second mode evolves into a surface spin wave, localized on the outer layer. We infer similar behavior for a Co film on Cu(100), though this evolution occurs at rather larger wave vectors where, as we have shown previously, the modes are heavily damped with the consequence that identification of distinct eigenmodes is problematical.