Magnetic resonance in very fine ferrimagnetic powder

Abstract

As the conclusion the main results of this work will be presented. In spite of the fact that the results have been obtained by numerical solution of the simple model with the supposition of free surface and no anisotropy, it is believed that at least some of them could be applied more generally. Putting aside a common ferrimagnetic resonance occurring in the low frequency part of the spectra, in the spectrum of the two sublattice ferrimagnetic powder three relatively expressive absorption maxima can be expected — the exchange resonance and two surface modes. The frequency of the exchange resonance in very fine ferrimagnetic powder is (due to the surface) somewhat greater than that in the bulk material and with increasing roughness of the powder it converges to the bulk material value. The frequencies of both optically active surface modes are lower than the exchange resonance one and are nearly independent of the powder roughness. While the intensity of the exchange resonance increases approximately linearly with the decreasing SVR (surface to volume ratio), the intensity of the surface mode lines diminishes correspondingly. It has turned out that the surface modes are localized in the surface layer of the depth of about three lattice constants. The approximate sum rule (7) has been confirmed with good accuracy. In the framework of the model the ground state remains nearly antiparallel even for the smallest particles. The deviations are smaller for the greater particles. Extrapolating this dependence, the mean number of spin deviations in the infinite crystal can be estimated to be in the limits 0·065–0·075 for a single spin.