Ferromagnetic-Resonance Field and Linewidth in an Anisotropic Magnetic Metallic Medium

We have calculated the ferromagnetic-resonance (FMR) field and linewidth in an anisotropic metallic medium in contrast to previous calculations done by others for an isotropic medium or for polycrystalline materials. The Landau-Lifshitz equation of motion of the magnetization with an additional effective anisotropic field of cubic symmetry is coupled with Maxwell's equations. The solution yields a generalized secular equation which is quartic in $k^2$, where $k$ is the propagation constant. We assume two limiting cases of the dynamic component of the magnetization $\overrightarrow{\mathrm{m}}$ at the surface: (i) $\overrightarrow{\mathrm{m}}$ is "free" to precess around the magnetic field $\overrightarrow{\mathrm{H}}$ at the disk surface and (ii) $\overrightarrow{\mathrm{m}}$ is totally constrained in precessing around $\overrightarrow{\mathrm{H}}$. As an example, results are given for a (100) Ni disk and for $\overrightarrow{\mathrm{H}}$ in the plane of the disk and at various angles with respect to the $〈100〉$ axis. At 300 °K the FMR field ($\frac{{\omega }_{\sigma }}{\gamma }$) is greater than its insulator value of 3072 Oe by 92 and 89 Oe, for $H$ along the $〈100〉$ and $〈110〉$ axes, respectively; the linewidth is nearly isotropic and equal to 262 Oe. However, at 77 °K, where the anisotropy fields have a greater influence, the FMR fields are 341 and 207 Oe greater than the isotropic insulator value; the linewidth is anisotropic and equal to 660 and 424 Oe for the two respective directions. For the above cases, $\overrightarrow{\mathrm{m}}$ is assumed to be pinned at the surface. The results which are also given for unpinned surface spins do not differ qualitatively. All the results have been obtained for two different frequencies, 9.4 and 24.0 GHz. Contrary to intuitive feelings, the anisotropy in the linewidth is inversely proportional to frequency. This is due to the fact that the anisotropy field becomes comparable to the resonant field as the frequency is lowered. We have thus found that, although exchange-conductivity effects are small at room temperature, they are quite significant in determining the resonance parameters at moderately low temperatures.