Anisotropy Broadening of Ferromagnetic Resonance in Dense NiCo-Ferrites

Abstract

Measurements have been made at 9 GHz of the circularly polarized components of the susceptibility tensor in dense samples of Ni_1−xCo_xMn_0.05Fe_1.95O₄, where x=0, 0.015, 0.027, and 0.05. The materials were prepared from powders, obtained by spray drying a mixed solution of sulphate salts, and subsequent thermal decomposition of the dried mixture. After isostatic pressing and conventional sintering, porosities below 0.8% were obtained. The susceptibility data were interpreted in terms of the quantities¹ S and W, defined by χ₊ = M_s/(H−ω/γ+S+jW/2). The variation of S and W over the spinwave region is in quantitative agreement with Schlömann's theory,² although the predicted singularities were not found. Outside the spinwave region W has a constant value: at high field W is proportional to x (16 Oe per % Co); at low fields the values are higher and not linear in x. The absence of the predicted singularities cannot be explained by taking into account exchange or intrinsic damping. Another possible explanation is that the spinwave energies themselves are influenced by the variations in anisotropy field. For a simple variation of the internal field, as given by H_i=H₀+A_q cosq·r, the interaction between spinwaves parallel to q can be calculated (neglecting exchange interaction). The frequency of these spinwaves is broadened over an amount 2γA_q. In a random sample A_q can be taken to be independent of the direction of q. In order to express A_q in terms of the anisotropy constants K₁ and K₂, the rms value of the anisotropy field in this model is put equal to that in a random sample. Therefore ½A_q² = (16/21) [K₁²+ (2/11) K₁K₂+ (5/143) K₂²]/ M_s². Using this A value, and summing S and W over‐all directions of q, quantitative agreement is found with experiment.³