Calculation of Standing Spin-Wave Resonance Modes in Ferromagnetic Metal Films

We have combined Maxwell's equations with the Landau-Lifshitz equation for finite thickness metal plates of nickel and Permalloy with infinite plane symmetry, and have imposed the boundary conditions corresponding to a constant rf driving field and complete pinning of m at the surfaces. The objective is to evaluate the effect of including conductivity and other refinements of the calculated spin-wave spectra of ferromagnetic films. In order to compare results with simplified calculations and experiment, we have taken the case of perpendicular resonance and calculated the frequency derivative of the power absorption spectrum. We find that for plate thicknesses such that the modes do not overlap, the mode spacing is quadratic, as found by the simpler theories, but that the mode intensities and linewidths are significantly increased. Overlap of the modes does not simply linearize the spacing of the lower modes, as is often found experimentally.