Exchange narrowing of magnetic resonance linewidths in inhomogeneous ferromagnets

The theory of exchange narrowing of ferromagnetic and spin-wave resonance linewidths in ferromagnets with the randomly inhomogeneous magnetic anisotropy is developed. The calculation is carried out by the method of averaged Green functions in the framework of the coherent potential approximation (CPA). One- and three-dimensional inhomogeneities with an arbitrary correlation wave number $k_c$ are considered ($r_c=k_c^{-1}$ is the correlation radius of the inhomogeneities). The method of the approximate solution of the CPA equation is proposed which has the quick convergence. Effects of exchange narrowing of the magnetic resonance lines and shifts of these lines are calculated in the whole region of the values of the correlation wave number $k_c$. The approximate analytical expressions for the linewidth of the FMR in the limiting cases of the small and large $k_c$ are obtained. Large narrowing of the FMR and spin-wave linewidths with the decrease of the correlation radius of inhomogeneities is the substantiation of the main advantage of nanocrystalline and amorphous materials over usual polycrystals when they are used at high frequency devices.