Ferromagnetic Resonance in Metals. Frequency Dependence

Abstract

The FMR (ferromagnetic-resonance) measurements were performed in single crystals of silicon-iron, nickel-iron, nickel, and hcp cobalt in the frequency region 8-140 Gc/sec at room temperature. The samples, in the form of thin discs, were statically magnetized parallel to the plane of the disc. Their thickness was at least one order of magnitude greater than the penetration depth at microwave frequencies. The values of linewidths, magnetocrystalline anisotropy constants, and $g$ factors were obtained. A macroscopic theory of the resonance line shape was developed, including simultaneously the effects of skin penetration of microwave field, the pinning conditions of the surface spins, and the relaxation damping in the Landau-Lifshitz form. The linewidth frequency dependence of the materials with small values of magnetocrystalline and magnetostriction constants (s\'{\i}licon-iron and nickel-iron) can be fairly well explained assuming a small amount of surface spin pinning and a certain value of the frequency-independent Landau-Lifshitz damping constant. The possible origin of pinning and damping is discussed. The linewidths of highly magnetostrictive and anisotropic materials (cobalt and nickel) suggest a large inhomogeneous broadening, probably due to imperfections and inhomogeneities in crystal structure of the samples. The values of magnetocrystalline anisotropy constants agree mostly with the results of static measurements. The values of $g$ factors were found independent of frequency and in good agreement with the Kittel-Van Vleck theory.