Ferromagnetic Resonance Magnon Distribution in Yttrium Iron Garnet

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Abstract
The presence of excited magnons results in a shift of the ferromagnetic resonance frequency. Calculations of this frequency shift have been made by retaining terms in the Hamiltonian up to fourth order in the spin wave variables. The shift can be expressed in terms of the number of excited k=0 magnons and k≠0 magnons. Determination of this shift can then be used to study the magnon distribution during resonance. This frequency shift has been measured in four single-crystal yttrium iron garnet spheres at 9 Gc. The shifts are observed to be directly proportional to the rf power absorbed by the sample, positive when the dc magnetic field is in [100] direction, and negative when the dc magnetic field is in the [111] direction. These results require a distribution of k≠0 magnons dominated by magnons with 48°<Θk<60°. If it is assumed that the k≠0 magnons are degenerate with the k=0 magnons, the total number of k≠0 magnons is approximately equal to the number of k=0 magnons, and magnons in the region centered about k=1−2×105 cm−1 dominate. This result is in agreement with a prediction of the surface pit scattering model; namely, the relaxation of the k=0 magnons results in the production of k≠0 magnons with wavelength approximately equal to the pit size. The results are in disagreement with any model requiring a uniform distribution of degenerate modes.