Ferromagnetic Resonance in Thin Films. II. Theory of Linewidths

The ferromagnetic-resonance linewidth $\Delta H$ from two-magnon processes in thin films is calculated. The results are quite different from those in spheroidal samples in general, since both the densities of states and the scattering Hamiltonians are different. It is shown that it should be possible to choose the radius and thickness of a ferromagnetic insulator thin film in such a way to make the frequency of the main-resonance mode lie well below the frequencies of all other magnetic modes. The resulting small $\Delta H\text{'}\mathrm{s}$ make the films important for studying ferromagnetic-resonance linewidths and afford a useful low-loss system. For scattering centers (such as pits and scratches on the surface of the sample or etch pits extending through the sample thickness) which are smaller than the film thickness, the results are similar to those of Sparks, Loudon, and Kittel (SLK) for a spherical sample. A modification of the SLK result is given which removes the divergence in $\Delta H$ at parallel resonance and also makes $\Delta H$ go smoothly to zero at perpendicular resonance. For scattering centers which are larger than the film thickness, $\Delta H$ has a rather large maximum at an angle approximately one-half way between perpendicular and parallel resonance, in contrast to the small-scattering-center result of a maximum at parallel resonance. In addition to these results for the main-resonance mode, it is shown that the mode-number-$n$ dependence of the two-magnon linewidths of exchange modes (having negligible microwave demagnetization energy) varies in a rather complicated way from $\Delta H\sim n^3$ for small $n$ to $\Delta H\sim n^2$ and $\Delta H\sim n$ for intermediate $n$ to $\Delta H\sim n^0$ for large $n$.