Inhomogeneous Broadening of Ferromagnetic Resonance Lines

A general theory of ferromagnetic resonance is developed assuming that the local, effective magnetic field is inhomogeneous. The scattering processes induced by the inhomogeneity may be classified as "primary" processes (which couple the uniform mode to nonuniform modes) and "secondary" processes (which couple nonuniform modes). In previous work only the primary processes were taken into account. The effect of secondary processes upon the susceptibility is calculated in the present paper. A perturbation series for the complex, effective resonant frequency of the uniform mode is derived. It is shown that the important terms of this infinite series can in part be generated by a self-consistency condition for the complex effective resonant frequency of spin waves. An approximate solution of this self-consistency condition is derived. Applied to polycrystals with cubic crystal structure, the theory predicts a linewidth of $\simeq 2.07\frac{{H_a}^2}{4\pi M_0}$ for spherical samples and $H_a\ll 4\pi M_0$ but $\simeq 0.87H_a$ for $H_a\gtrsim 4\pi M_0$. Here $H_a$ is the anisotropy field and $M_0$ the saturation magnetization. The off-resonance absorption is characterized by the existence of a "strong absorption" region. When the intrinsic damping of the spin waves is assumed to approach zero the absorption goes to zero in the exterior of this region but to a finite value in its interior. If the Fourier spectrum of the inhomogeneity has significant components only at long wavelength and the inhomogeneity is weak, the strong absorption region coincides with the dc field interval in which the signal frequency is degenerate with resonant frequencies of long-wavelength spin waves. With increasing inhomogeneity, the width of the strong absorption region increases by approximately twice the width of the resonance line.