Effective magnetic permeability of Ni and Co micro- and nanoparticles embedded in a ZnO matrix

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 $\gamma –{\mathrm{Fe}}_2{\mathrm{O}}_3∕\mathrm{Zn}\mathrm{O}$ 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 $0.01–10\mathrm{GHz}$ . 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 $\gamma –{\mathrm{Fe}}_2{\mathrm{O}}_3∕\mathrm{Zn}\mathrm{O}$ composites. Interestingly, the $\mathrm{Ni}∕\gamma –{\mathrm{Fe}}_2{\mathrm{O}}_3$ type-$N$ composites exhibit a composition dependence of the effective permeability which is quite different from the $\mathrm{Co}∕\mathrm{Zn}\mathrm{O}$ and $\mathrm{Ni}∕\mathrm{Zn}\mathrm{O}$ 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.