Theory of Ferromagnetic Resonance Line Shape outside the Spin-Wave Manifold

In the usual ferromagnetic resonance experiment the uniform precession lies within the magnon manifold, that is, there are long-wavelength magnons degenerate with the uniform precession. Several recent experiments have been performed with the uniform precession driven outside the magnon manifold. In this paper we calculate the line shape ${\chi }^{\prime \prime }$ as a function of applied field) for these experiments. Specifically, the relaxation frequency $\eta$ of the uniform precession and the line shift $\delta H$ (deviation of the uniform precession frequency from the Kittel frequency) are calculated. For relatively large $\eta$ ($\eta \ll \gamma 4\pi M$ not satisfied) the line shift $\delta H$ is at least as important as $\eta$ in determining the line shape. Explanations are given for the three interesting observations of Liu and Shaw that: (1) The relaxation frequency has the large value of the order of 150 Oe when the uniform precession is driven below the bottom of the spin-wave manifold; (2) The relaxation frequency drops sharply as the uniform precession passes below the bottom of the spin-wave manifold; and (3) The relaxation frequency within the spin-wave manifold is relatively independent of applied field. Examination of several possible sources of the 150-Oe relaxation frequency (1) indicates that the 150 Oe arises from the magnon manifold being modified by nonmagnetic voids in the sample in such a way as to allow two-magnon scattering below the magnon manifold of a perfectly dense sample. The field independence of relaxation frequency within the manifold (2) is in apparent agreement with the two-magnon scattering theory of Sparks, Loudon, and Kittel; Seiden; and Seiden and Sparks.