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 and ky^O magnons, with a ^-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^O magnons increase with increased surface roughness, the surface-induced scattering from the £=0 mode occurs to a localized group of degenerate kp^O 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 0£ = O spin waves.Possible alternate explanations are offered.

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“…For this latter requirement to hold at small k the spin wave energy gap must be large compared with the dipole-dipole interaction energy, so that a sufficiently large applied magnetic field or Ising-type exchange must bx included in the Hamiltonian. Calculations have also been carried out using Green function equation of motion methods (Haas et al 1963, Tanaka 1964, where only low order terms in the spin variables are retained and a RPA type of decoupling is employed. The disadvantage of this method is that the precise nature of the approximations is not known.…”