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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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It has been observed that the magnetic anisotropy direction of certain thin Permalloy films prepared by the thermal decomposition of nickel and iron carbonyls can be rotated through 90 deg at room temperature by fields less than 10 oe. The experimental conditions under which these films were prepared suggest that this phenomenon is due to the presence of carbon. The relaxation time for the rotation of the anisotropy axis was calculated from the time dependence of the induction and found to be 10 msec. A simple model has been developed which relates the anisotropy rotation to specific domain wall configurations and to the establishment of a “directional order” among interstitial carbon atoms.

Articles you may be interested inShifts of frequency and bandwidth of quartz crystal resonators coated with samples of finite lateral size A polished, ellipsoidal, single crystal, yttrium iron garnet sample with rotation axis along a [ 1ooJ direction and tJ.fl = 1.0 oe was prepared. X -band measurements of the microwave resonant frequency were made as a function of rf power. The resonant frequency was found to shift at the rate of 41 Mc/ w. The shift of the resonant frequenc), was related to the number of k:::110 magnons (" 0) and the number of k~O magnons ( Il k) by means of spin-wave theory. From this relation and the experimental data the value of 11 1.:/11 0 was determined to be 2.7.

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.

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