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

Abstract

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.

Generalization of Snoek’s law to ferromagnetic films and composites

“…Microwave composites made of a magnetic spherical powder dispersed in a dielectric matrix are widely used as microwave materials 33,34,35 and magnetic absorbers. 6,7,15 In most cases, the radius of the particles is significant as compared to the skin depth.…”

Synthesis, magnetic and electrical characteristics of poly(2-thiophen-3-yl-malonic acid)/Fe3O4 nanocomposite

“…This dependence can be often conveyed as a slope in logarithmic conductivity versus reciprocal temperature graphs. So, this behavior can be attributed to the temperature-induced transition from three dimensional hopping conduction in a network of weakly interconnected nanoparticles to thermally activated behavior [41,42], where the physical meaning of the one fourth exponent in Mott's law can be ascribed to the reciprocal of the effective dimensionality of four (three spatial plus one energy) [43]. Here, it should be emphasized that due to ferrites' semiconducting nature, the conductivity increases with increasing temperature.…”

Controlled extrinsic magnetoelectric coupling in BaTiO3/Ni nanocomposites: Effect of compaction pressure on interfacial anisotropy

“…4 The debate over the origin of the ME effect continues today, with some researchers suggesting to probe the magnetoelastic coupling between the magnetostrictive and piezoelectric phases from the measurement of the effective complex permittivity and magnetic permeability since these quantities are the standard source of information on the response to external electric and magnetic fields. [2][3][4][5][6][12][13][14][15]24 field: the strength of the coupling between polarization and magnetization mechanisms and the role of interface.…”

“…1,10,11 From the experimental standpoint, frequency-domain spectroscopy and broadband ferromagnetic magnetic resonance have proved to be useful tools in characterizing the gigahertz frequency electromagnetic response of ME NCs and the dynamical aspect of the ME coupling. [2][3][4][5][6][12][13][14][15] Possible implementation of device applications relies upon a significantly improved understanding and ability to dynamically control this response. Although most of the contemporary activity has been focused in understanding the ME properties of laminate inhomogeneous materials, 1,[16][17][18][19] recently the interest has shifted toward granular two-phase nanostructures where the electric polarization and the magnetic moment are intrinsic to the two different phases, but coupled by interfacial strain.…”