# Theory of ferromagnetic resonance line shape outside the spin-wave manifold

## Abstract

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 as a function of applied field) for these experiments. Specifically, the relaxation frequency of the uniform precession and the line shift H (deviation of the uniform precession frequency from the Kittel frequency) are calculated. For relatively large (4M not satisfied) the line shift H is at least as important as 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. © 1965 The American Physical Society.