Theory of Spin-Wave Resonance in Thin Films

A new theory of spin-wave resonance, based upon the assumption that the saturation magnetization varies linearly across the thickness of the film, is described. The characteristic equation for the normal modes has been solved both for free and for strongly pinned surface spins. According to this theory the lower-order modes are approximately equally spaced, their separation in magnetic field being given by δH≃1.5 (H0′)⅔D⅓, where H0′ is the field gradient and D=2A/M0 a phenomenological exchange constant (A = Landau-Lifshitz constant, M0 = saturation magnetization). The theory agrees remarkably well with the experimental data of Nisenoff and Terhune on Permalloy films.