Two-magnon contribution to the ferromagnetic resonance linewidth in amorphous ferromagnetic metals

The wave-number- and frequency-dependent susceptibility χ(k,ω) for a ferromagnet in the presence of two-magnon scattering processes, and including intrinsic damping of the Gilbert form, has been calculated using first-order perturbation theory. A simple model was used for the two-magnon scattering: driven magnons of wave vector k and frequency ω were assumed to be scattered only into states ${\mathrm{k}}_l$ for which ‖${\mathrm{k}\mathrm{-}\mathrm{k}}_l$‖≤Q. The susceptibility χ(k,ω) was used to calculate the surface impedance of the metal, and hence to obtain the magnetic field dependence of the absorption of microwave radiation. The theory is expected to be valid for those cases in which the line broadening due to two-magnon scattering is small compared with the line broadening due to intrinsic processes. A numerical calculation was carried out using magnetic parameters appropriate for the amorphous ferromagnet ${\mathrm{Fe}}_{82}$ ${\mathrm{B}}_{18}$. The two-magnon scattering contributed an amount to the linewidth which varied slowly with frequency. Thus the two-magnon scattering mechanism may be the origin of the nearly frequency-independent ferromagnetic resonance line broadening which has been observed for many amorphous metallic ferromagnets.