Ferromagnetic Resonance Frequency Shift in Yttrium Iron Garnet

Abstract

Calculations and measurements have been made of the shift of the ferromagnetic resonance frequency in the presence of excited magnons. The calculations were carried out by retaining terms in the Hamiltonian up to fourth order in the spin-wave variables and by treating these terms in a random phase approximation. The frequency shift depends linearly on the number of excited $k=0\mathrm{}$ and $k\ne 0$ magnons, with a $k$-dependent proportionality factor. Measurements of this shift therefore can be used to determine the magnon distribution at resonance, and such measurements have been used to study the effect of surface preparation of the sample on the magnon distribution. The results show considerable agreement with the surface pit model; namely, the linewidth and the number of $k\ne 0$ magnons increase with increased surface roughness, the surface-induced scattering from the $k=0\mathrm{}$ mode occurs to a localized group of degenerate $k\ne 0$ spin waves, and the effective wavelength of the spin wave to which scattering occurs increases with increased surface roughness. The data are not consistent with the theory that there is a rapid equilibration of the degenerate spin waves. The frequency shift was also observed at power levels above the critical value for the onset of nonlinearities. The results cannot be explained simply by invoking the instability of ${\theta }_k=0\mathrm{}$ spin waves. Possible alternate explanations are offered.