Interest in filled polymers has expanded in recent years as investigators have recognized the great flexibility allowed by these materials to suit particular properties such as electrical, mechanical, and/or coupling between these properties. This article describes the work undertaken to investigate the microwave response of two different types of samples: one with carbon black or silica particles embedded in a linear low-density polyethylene, and the other with carbon black particles or carbon fibers embedded in an epoxy resin. We report broad-band (30 MHz–14 GHz) measurements of the complex permittivity of these materials obtained by measuring the scattering parameters (S parameters) of a microstrip line loaded with a rectangular sample of the test material. The experimental results presented give access to data which can be rationalized in terms of a combination of Bruggeman’s self-consistent model with Jonscher’s phenomenological analysis. This analytical approach yields data that are in good correspondence with experimental data in terms of the concentration dependence of inclusions within the polymeric matrixes and demonstrates large practical capabilities for analyzing the electromagnetic properties of these materials at microwave frequencies because it allows one to make an explicit connection between these properties and the experimentally accessible parameters.

Current trends in the miniaturization of microwave devices have prompted considerable interest in studying electromagnetic transport in nanoscale systems. Understanding the effect of physical structure and the role of interfaces is critical for gaining insight into the electromagnetic and magnetic properties of nanostructures and their behavior in microwave devices such as circulators and isolators. Previously, we have described the electromagnetic characteristics at microwave frequencies and the static magnetic properties of γ–Fe2O3∕ZnO micro- and nanocomposites fabricated via powder processing. Here we present systematic effective permeability measurements of magnetically structured granular systems composed of magnetic grains embedded in a nonmagnetic matrix using broadband microwave spectroscopy. Using the transmission∕reflection waveguide method, the effective complex permeability was measured in the frequency range of 0.01–10GHz. The results were compared for composites consisting of micrometer-sized (type-M) and nanometer-sized (type-N) Co and Ni particles embedded in a ZnO matrix. Results show that the type-N composite samples display a prominent gyromagnetic resonance in the gigahertz region of frequency which can have a complex structure. In contrast, this resonance is not observable for the type-M composite samples. These results are in agreement with the previous observations for the γ–Fe2O3∕ZnO composites. Interestingly, the Ni∕γ–Fe2O3 type-N composites exhibit a composition dependence of the effective permeability which is quite different from the Co∕ZnO and Ni∕ZnO type-N composites. From the microwave data collected, it is found that a mean-field approach (effective-medium approximation) is appropriate for understanding the permeability of composite materials characterized by submicrometer inclusion length scales. The relevance of the Bruggeman and McLachlan models are tested against experimental data over a large range of composition. From these comparisons, although there are some systematic discrepancies to a certain extent, we conclude that the overall agreement of the spectral dependence of the complex permeability of Ni nanocomposites with the Landau–Lifshitz–Gilbert prediction is fairly good in view of the simple assumption. It seems that this phenomenology is also applicable to Co nanocomposites by assuming a double Lorentzian form for the gyromagnetic resonance. Analysis of the gyrorcsonance linewidths strongly suggests a large dispersion in the local field which presumably reflects the disordered physical nanostructure.

We have measured the composition and frequency-dependent complex effective permittivities and permeabilities in zero applied field of a series of ZnO and ferrimagnetic γ-Fe2 O3 composites prepared by powder pressing. The overall features of the room temperature electromagnetic properties of these diluted magnetic semiconductor composites exhibit a strong dependence on the powder size of the starting materials. For instance, electromagnetic spectroscopy over the frequency range (300 MHz–10 GHz) shows that composites made of nanoparticles (N-type samples) display a strong increase of the real and imaginary parts of the permeability compared to composites made of micron-sized particles (M-type samples). The observed dielectric behavior as a function of composition is manifestly at odds with the predictions from the simple property-averaging continuum model of Bruggeman. Additionally, a gyromagnetic resonance in the gigahertz region of frequency has been established for N-type samples which is not observable in M-type samples. Examination of the dynamics of the magnetization distribution in N-type samples shows that the usual Landau–Lifshitz–Gilbert (LLG) equation can represent satisfactorily the gyromagnetic resonance line. Two important features of the data are the slight increase of the resonance frequency and the more important decrease of the width at half height of the gyromagnetic resonance line as the content of the magnetic phase is increased. It appears also that the value of the damping constant, characterizing the dynamics of magnetization, extracted from the fit of the gyromagnetic resonance line is consistent with previous experimental determinations. We attribute the remaining deviations in the fit and the discrepancies in the damping constant estimates namely to two approximations in our approach. First, the mean-field model considered here neglects composition fluctuations. Another source of the corrections are those due to the polydispersity of the nanoparticles. In contrast to the permittivity results, the comparison of the experimental values of the effective permeability, as a function of composition, with the analytical model combining the LLG and Bruggeman equations shows a good agreement. Given that the volume fraction of the organic binder has an effect on the shape of the gyromagnetic resonance line, we investigate also how this parameter affects the characteristics of the resonance mode. The analysis of the hysteretic behavior of these multiphase granular materials at room temperature indicates that the coercivity and the saturation magnetization normalized to the content of Fe2O3 in the sample is strongly dependent on particle size, but remain practically constant over the entire Fe2O3 volume fraction range investigated. Furthermore, the reduced remanence ratio is found much smaller than the Stoner and Wohlfarth’s prediction concerning randomly distributed single domain particles without interaction. Possible origins for this difference have been analyzed. The suggestion, through Chen et al.’s analysis [C. Chen, O. Kitakami, and Y. Shimada, J. Appl. Phys. 84, 2184 (1988)], that the surface anisotropy is responsible for the coercivity behavior is quantitatively consistent with the experimental data concerning N-type samples.

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