Magnetic resonance in spherical Co-Ni and Fe-Co-Ni particles

Magnetic resonance is studied in absence of external field on composite materials made up with spherical and monodisperse fine Co–Ni and Fe–Co–Ni particles. The particle size range varies over one order of magnitude from 25 to 250 nm. In the frequency range studied [0.1–18 GHz] several resonance bands are generally observed attributed to nonuniform resonance modes. The resonance frequencies are found to depend on the magnetic particle size, only weakly for the lowest frequency mode, in a more pronounced manner for the following modes. A theoretical model based on a discrete treatment of the resonant effect in independent small spherical or cylindrical grains is proposed. It allows to compute the resonance frequencies, the spin-wave profiles, and the spin-wave intensities. The respective influences of particle geometry, surface pinning, crystalline anisotropy, and exchange parameter values are presented. According to this model it is found that the size dependence of the resonance frequencies is mainly related to the surface pinning and to the exchange parameter value. In all cases the size dependence of the lowest frequency mode is found weaker than that of the following modes and for large particles the frequency of the first mode is directly related to the crystalline anisotropy. The particle shape effect on resonance frequencies is weak whereas the spin-wave profiles of the first modes are found to depend on the particle geometry. This model enables us to describe the general shape of the experimental spectra and to infer the magnetocrystalline anisotropy constants ${(K}_1)$ from the experimental data, which are found in good agreement with bulk values. Moreover it shows that the weak size dependence of the lowest frequency mode is due to a weak pinning at the particle surface. Nevertheless, the effect of particle size on higher spin-wave modes requires us to account for the magnetic interactions between grains.