Spin-orbit coupling and spin waves in ultrathin ferromagnets: The spin-wave Rashba effect

We present theoretical studies of the influence of spin-orbit coupling on the spin-wave excitations of the Fe monolayer and bilayer on the W(110) surface. The Dzyaloshinskii-Moriya interaction is active in such films by virtue of the absence of reflection symmetry in the plane of the film. When the magnetization is in plane, this leads to a linear term in the spin-wave dispersion relation for propagation perpendicular to the magnetization, to produce a dispersion curve similar in nature to that found for electrons on semiconducting surfaces when the Rashba coupling is active. We also show spin-polarized electron-loss spectroscopy response functions that illustrate the role of spin-orbit coupling in such measurements. In addition to the modifications of the dispersion relations for spin waves, the presence of spin-orbit coupling in the W substrate leads to a substantial increase in the linewidth of the spin-wave modes. The formalism we have developed applies to a wide range of systems, and the particular system explored in the numerical calculations provides us with an illustration of phenomena which will be present in other ultrathin ferromagnet/substrate combinations.