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Composite materials filled with ferromagnetic inclusions are useful in the development of various microwave devices. The performance of such devices is determined both by material properties (such as the saturation magnetization and the permeability) and by the demagnetization effects. The paper is devoted to the study of the demagnetization effect on the permeability measurements of composites under external magnetic bias. The microwave permeability of composites filled with flake sendust (Fe-Si-Al alloy) particles is measured as a function of frequency and the external magnetic field. The measurements are carried out by the Nicolson–Ross–Weir technique in a 7/3 coaxial line in the frequency range of 0.1 to 20 GHz by a vector network analyzer. It is found that the magnetic loss peak is split under external fields of more than 1.5 kOe. The main aim of this paper is to study the causes of this splitting and to interpret the observed magnetic loss peaks. To study this effect, the samples of various thicknesses and the samples with isotropic and anisotropic orientations of particles are measured. The particles in the anisotropic samples are oriented by a strong uniform magnetic field. At a small fraction of inclusions, the permanent magnetic field is demagnetized on the individual particles rather than the whole sample. The splitting of the magnetic loss peak of the isotropic sample is caused by different orientations of particles in the sample. At a high fraction of inclusions, the permanent magnetic field is demagnetized on the whole sample and the magnetic loss peak of the isotropic sample is not split. The saturation magnetization of the material is found by measurements under the external magnetic field of the anisotropic sample.

This paper presents a comparative analysis of the mixture models used in radio physics to describe the effective properties of composite materials and formulates the limits of their applicability and criteria for checking their correctness. Two of the most general models have been chosen, which take into account the transformation of the composite structure upon changes in its composition. The correspondence of the chosen model to the experimental results is considered. The effect of the composite structure on the frequency of the maximum and the shape of its dielectric absorption line is shown. The analysis shows that the complication of the models in comparison with those already known and an increase in the number of parameters determined from the experiment is inappropriate at the existing level of the composition and material parameters (permittivity and permeability) measuring error and due to a significant contribution of the size and surface effects, which is not taken into account in quasi-static mixture models.

Zn1−xNixFe2O4 ferrites up to x = 1.0 with Δx = 0.2 have been synthesized via solid state reactions and the sol–gel autocombustion technique with step-by-step co-firing. Data on the chemical composition and the surface morphology of the samples have been obtained using a scanning electron microscope. An X-ray powder diffractometer has been used to establish the phase purity and to determine the unit cell parameters. It has been found that the obtained samples had a spinel structure with the Fdm (No. 227) space group. The unit cell parameters decrease with increasing nickel concentration. The a unit cell parameter decreases almost linearly from ∼8.443 A for x = 0.0 down to ∼8.337 A for x = 1.0. The V unit cell volume decreases almost linearly from ∼601.72 A3 for x = 0.0 down to ∼579.52 A3 for x = 1.0. The magnetic characteristics of the obtained samples are determined and discussed. The Curie point of obtained samples varies in the range of 803.5–572.7 K. The maximum spontaneous magnetization of ∼74.6 emu g−1 at room temperature was fixed for the solid solution with x = 0.6. Ac-resistivity drops by more than 3 orders of magnitude in the frequency range 1–106 Hz. The composition with x = 0.6 has the minimum ac-resistivity of 5.3 kOm cm at a frequency of 106 Hz. The maximum value of the (μ′) real part of ∼11.2 and (μ′′) imaginary part of ∼5.2 of the permeability in the frequency range of 50 MHz–10 GHz is observed for the composition with x = 0.4. The composite samples for the microwave study were prepared by mixing of the ferrite powders with molten paraffin wax. The volume fraction of the ferrite filler in the composites was 25%. The largest value of the (μ′) real part of ∼3 and (μ′′) imaginary part of ∼0.63 of permeability is found for the x = 0.4 composite. The formation of the composite significantly reduces permeability.

The possibility of determining the magnetic susceptibility of metal inclusions from measured material parameters of binary composites using known mixing models is considered. A model is proposed that considers the inversion of the matrix structure of the Maxwell–Garnett model for a filler concentration close to the percolation threshold. It is determined that restructuring the composite occurs gradually in the region of transition concentrations the width of which is an additional parameter determined from the experiment. The proposed model is compared with the effective medium model in terms of the dependences of complex susceptibility on filling and frequency. The reliability of the model is illustrated by processing the material parameters of composites with carbonyl nickel as a filler measured in the frequency range 0.1–20 GHz.

Methods for measuring the microwave permittivity and permeability of materials are considered. The specific features and applicability conditions of measurement methods in transmission lines and in free space are shown, and the measurement errors are analyzed along with the calibration procedures applied for reducing the errors. Individual sections of the articles contain descriptions of scalar, resonance, quasistatic, and quasioptic methods. It has been determined that out of many existing techniques, the NicolsonRossWeir measurement method in a coaxial line and also the method for measuring the permeability of thin ferromagnetic films with the use of a shortcircuited strip cell are most widely applied. By using these methods, the majority of matters concerned with studying the microwave properties of materials can be solved.

—The magnetostatic and magnetodynamic properties of laminated materials based on glass-reinforced plastic laminate coated with magnetic (Co40Fe40B20)60(SiO2)40 nanocomposite are studied. The modified magnetic composite structural materials based on glass fiber are characterized by hysteresis with a low coercivity and magnetic shape anisotropy related to fiber geometry. No significant absorption of electromagnetic radiation was observed in the range of frequencies of natural ferromagnetic resonance, except for the bulk composite sample, where minor peaks at 3 and 5 GHz were detected. In the variation in the coefficient of electromagnetic radiation transfer versus frequency curves, the signal intensity is substantially attenuated at 6–12 GHz owing to dielectric loss in the composite film.

We present investigation of microwave permeability of thin supermalloy films deposited on a flexible substrate. The permeability measurements are performed by transmission-reflection technique in a coaxial line under external magnetic bias in the frequency range of 100 MHz–20 GHz. It is shown that demagnetization does not affect the measurements when bias is above 150 Oe. Magnetic characteristics of the films are determined by two approaches: (i) fitting of the resonant frequency dependence on magnetic bias by Kittel's equation and (ii) calculation of the parameters from the Landau–Lifshitz–Gilbert dispersion law. Both approaches give close results for values of magnetoelastic field, anisotropy field, saturation magnetization, and damping factor.

The frequency dependencies of microwave permeability of composites filled with flake-shaped sendust (Fe-Al-Si alloy) powder particles are measured. A technique for determining the physical mechanisms resulting in the appearance of magnetic loss peaks is proposed. The technique consists in analysis of the data on microwave permeability obtained under external magnetic field. It is shown that the mixing rule, which correctly retrieves the intrinsic permeability in the absence of the external field, is not valid under magnetic bias. Based on the measured data, the physical mechanisms leading to the appearance of loss peaks are determined, and the invalidity of mixing rules under magnetic bias is explained. It is shown that the main peak of magnetic loss is attributed to the Polder-Smith modes. An increase in the external field leads to vanishing of the domain structure and to an increase in the interaction between powder particles. The permeability under bias should be described by mixing rules that take into account the interaction between inclusions. The found frequencies of the Polder-Smith modes are in good agreement with the permeability data.

A new method of studying microwave magnetic properties of metal particles and films is developed. The method is based on measurements with swept frequency under magnetic bias in a coaxial line. Application of the technique is illustrated by the data obtained for two types of samples, washer-shaped rolls of thin ferromagnetic films and composites filled with flake Sendust particles. The treatment of the measured data is performed with an account for sample demagnetization and anisotropy. The values of the anisotropy field and the saturation magnetization of thin iron films are calculated considering demagnetization of the sample. Because of the anisotropy of the composite samples, permeability depends slightly on the length of samples, and the saturation magnetization and the anisotropy field cannot be determined.

Frequency dependencies of permittivity and permeability of composites filled with Permalloy powder with various concentrations and shapes of particles have been measured and discussed. The powder particles of various shapes were obtained by mechanical milling of industrial Permalloy powder in organic media. Paraffin wax was used as a matrix for producing the composites. A shape data of the particles were obtained with an electron microscope. The permittivity and permeability were measured in the frequency range of 0.1–20 GHz. It is shown that the shape of the particles changes from sphere to plate with increase of milling time. The change leads to a shift of the ferromagnetic resonance (FMR) frequency and the magnetic loss peak. It is shown that larger damping of the FMR is typical for larger particles. With increase of the concentration of Permalloy particles in composite, the magnetic loss peak shifts to lower frequencies. The measured frequency dependencies of the material parameters are discussed in terms of the theory of composites.

The microwave permeability of nickel is determined from constitutive parameters of paraffin–bound composites filled with nickel flakes or spheres. The metal permeability is calculated with account for skinning. The measurements of constitutive parameters are performed using the reflection–transmission coaxial-line within the frequency band of 0.001–20 GHz. The effects of filling factor, particle shape, and size on permittivity and permeability spectra are analyzed. The retrieval of inclusion permeability is based on the treatment of measured dependence of composite constitutive parameters on frequency and on volume fraction of inclusions. The retrieval procedure is based on the generalized Sihvola mixing model simplified for a single-dimension composite. The model describes the wide contrast of component susceptibility, accounts for inclusion shape and the Bergman–Milton spectral linewidth. The retrieved microwave permeability is close to the values reported for measurements with thick wires and foils.

Ferromagnetic resonance (FMR) and coaxial line techniques are employed for studying the high-frequency magnetic properties of thin Fe films deposited onto a flexible polymer substrate by magnetron sputtering. Multiple resonances are observed in the FMR spectra measured in X frequency range for films with thickness from 0.1 to 2.0 μm. The resonance magnetic fields are found to depend on of the film thickness and on the orientation of external magnetic field relative to the film plane. The variation of the FMR parameters with the layer thickness may be attributed to differences in the shape and size of nanocrystallites formed during the deposition of films of different thicknesses. Low-field resonance modes are found in addition to the homogeneous FMR of saturated magnetization. Qualitative agreement is observed between values of the resonance magnetic fields determined by FMR and coaxial line techniques.

A method to retrieve permeability of a metal inclusion from the measured constitutive parameters of a single composite sample of known structure and filling is developed. Treating constitutive parameters for a set of fillings increases accuracy of inclusion permeability determination and makes it possible to select the appropriate mixing model for the composite. The method is applied to determine microwave permeability of sendust inclusions from the measured permeability and permittivity spectra for a set of composites filled with sendust flakes and spheres. The calculations are performed for symmetric (Bruggeman type) and for matrix (Maxwell Garnett type) structures. The composites are shown to have the matrix structure. The retrieved permeability of inclusions is in good agreement with the data calculated with the parameters of generalized matrix mixing model that accounts for percolation threshold.

An investigation of the dependence of magnetic properties on the thickness of ferromagnetic films was completed. The study dealt with magnetostatic and microwave measurements of single-layer films of ferromagnetic metals (Fe, Co) and was aimed at revealing reasons for the deterioration of microwave magnetic performance with an increase in film thickness. Two types of variation of microwave permeability with the film thickness were distinguished for the films under study. One exhibited a noticeable deviation from maximal values and was observed for Co. The other case involved a gradual worsening of performance, and was observed for Fe. In the first case, the resonance frequency shifted lower when the film was thicker than 0.2–0.4 μm, and Acher’s coefficient fell by the factor of three. In the second case, the microwave performance worsened gradually, and a decrease of Acher’s coefficient was not large, approximately by 20%. The data analysis showed that the reason for the deterioration is an increase of out-of-plane anisotropy in the first case and sufficient growth of damping factor in the second case.

Composite materials are of great importance for both science and technology. In this work, the high-energy ball milling of carbonyl iron in the presence of polydienes of various structures (cis-polybutadiene, cis- and trans-polyisoprene) and surfactants (perfluorononanoic and stearic acid) is used to chemically modify the bulk and surface of iron particles. A comprehensive study of the particles was performed with the use of various experimental techniques. Mechanochemically activated iron surface favors the processes of decomposition and transformation of organic molecules that make up the milling medium, resulting in the accumulation of carbides in the particles bulk and the formation of modified organic layer on the surface. The composition and thickness of the modified layer as well as the arrangement of organic molecules in it was shown to be sensitive to variations in the chemical structure of the initial diene polymer and the type of surfactant added. The as-grown layers inhibit corrosive destruction of the resulting particles. Platelet-shaped particles prepared by surfactant-assisted ball milling can be used as fillers for magnetodielectric composites with high permittivity and permeability values.

The magnetic permeability of alsifer was restored from the frequency dependences of the dielectric and magnetic permeabilities of powder alsifer (AlSiFe alloy)–wax matrix composites. The permeabilities were measured using the coaxial line technique within a frequency range of 0.05–20 GHz. The effect of the concentration, shape, and size of powder particles on the microwave magnetic properties of composites was considered. A good agreement between the measurement results and the Maxwell–Garnett formula generalized with consideration for the particle shape, the percolation threshold, and the skin-effect was obtained. The found sizes of particles agreed with electron microscopy and granulometry data. Both the frequency and the ferromagnetic resonance line figure of merit (FOM) for lamellar particles proved to be higher than for spherical ones. Alsifer powders were shown to be promising fillers for radioabsorbing materials.

A resonant RLC circuit with a magnetic core has been investigated experimentally and theoretically as a promising metamaterial cell design. Laminates of multilayer ferromagnetic films serve as a magnetic core. The ferromagnetic resonance frequency of the bare laminate core is above 1 GHz. An intensive magnetic absorption peak is obtainable at lower frequencies due to a resonant wire coiled around the core. Such magnetic metamaterials seem promising for applications that require high magnetic loss at frequencies of hundreds of megahertz. This paper focuses on efficient approaches to adjusting the location of magnetic loss peak in magnetic metamaterials. High-frequency permeability of the metamaterial samples has been measured in a rectangular waveguide. It is shown that by varying the geometry, structure, and composition of the measured metamaterial samples, the magnetic spectra can be radically changed. Excitation of electromagnetic resonance in the ferromagnetic core with the resonant wire is discussed within the frame of the quasi-static approximation.

Surfactant-assisted ball milling is employed for preparation of metal powders for magnetodielectric composites. The iron powder is mechanically milled in various organic media (paraffin, polystyrene, polyethylene) with and without surfactant additives (perfluorononanoic acid and stearic acid). The structural characterization of the body and surface of the particles of the produced powders is performed and the magnetostatic and microwave properties of the powders are measured. It is shown that ball milling of Fe powder in organic media results in the formation of polyaromatic structures due to catalytic dehydrogenation on bare surface of Fe particles. Then, the polyaromatic carbon structures transform into carbides. The surfactant-assisted ball milling allows platelet powder particles to be fabricated with a decreased amount of carbides in the composition. The magnetic permeability of the composites filled with as-obtained particles is governed mainly by the shape of the filler particles. For the composites filled with the platelet particles, an organic surface layer formed during the surfactant-assisted ball milling is an important parameter determining the dielectric permittivity of the composites.

Structural and phase composition and magnetostatic and microwave properties of Fe70Co30–SiO2 systems obtained by high-energy milling in acetone for different times (from 6 to 48 h) are studied. It is found that, after the longest milling time, the obtained particles have sizes from 0.5 to 5 μm, are covered with a thin layer of SiO2, and contain 10 wt % iron carbides. Milling-induced change in the phase composition of the particles influences their specific magnetization of saturation and coercive force, but has a small effect on the microwave permittivity of composite materials containing these particles in the frequency range of 0.1–6 GHz. As the milling time grows, the imaginary part of the microwave permeability decreases at frequencies below 1 GHz.

Iron powder particles were coated with a thin SiO 2 shell for protection of corrosion. Dynamic magnetic behavior of the as-synthesized material was studied in comparison with uncoated metal in terms of frequency dispersion of the microwave permeability and permittivity. A uniform 100-nm SiO 2 shell provides durable corrosion resistance to a 4.5-μm carbonyl iron powder. The shell was deposited through tetraethyl orthosilicate hydrolysis of technical grade chemicals. It was shown that the shell did not influence the magnetic properties of the iron powder. Electron microscopy, particle size analysis, and γ-resonance spectroscopy were applied in the study. The deposited SiO 2 decreased the microwave permeability value and prevented percolation conductivity in a composite with a paraffin wax dielectric matrix.

The magnetoresonance properties of a composite film system based on alsifer nanoparticles in a polymer matrix are studied. It is shown that the system has uniaxial anisotropy of magnetic properties in a sample’s plane. The magnitude and orientation of the field of anisotropy upon varying the alsifer concentration do not change appreciably.

Znx-1NixFe2O4 samples have been synthesized by solid-state reactions. Data on the chemical composition and the surface morphology of the samples have been obtained using a scanning electron microscope. X-ray powder diffractometer has been used to establish the phase purity and to determine the unit cell parameters. It has been found that the obtained samples had the spinel structure with Fd-3m (No. 227) space group. The unit cell parameters decrease with increasing nickel concentration. The magnetic characteristics of the obtained samples are determined and discussed. The Curie point of obtained samples varies in the range of 803.5–572.7 K. The maximum spontaneous magnetization of ~74.6 emu/g at room temperature was fixed for the solid solution with x = 0.6. The maximum value of the μ/real part of ~12 and μ//imaginary part of 6 of the permeability in the frequency range of 50 MHz–10 GHz is observed for the composition with x = 0.3. The composite samples for microwave study were prepared by mixing the ferrite powders with molten paraffin wax. The largest value of the μ/ real part of ~3 and μ// imaginary part of 0.63 of permeability is found for the x = 0.4 composite. The formation of the composite significantly reduces permeability.

The results of investigation of the morphology, structure–phase composition, surface structure, and properties of iron particles, which were prepared by mechanoactivation in planetary ball mill in cis- and trans-polyisoprenes and cis-polybutadiene in the presence of perfluorononanoic acid acting as a surfactant, are given. It is determined that there are high-disperse carbides in bulk particles, whose major part is formed during the grinding with polybutadiene. The difference in phase composition of particles does not affect the UHF characteristics of composites. The organic layer is formed on a surface of particles that contains modified molecules of polymers and perfluorononanoic acid and is thinnest after grinding with cis-polyisoprene. The thickness of the organic layer does not influence either the UHF values of the dielectric and magnetic permittivities of composites or the corrosion properties of particles in acidic media. Material parameters of UHF composite materials filled by the powders under study are mainly determined by the shape of powder particles.

The paper considers the application of mixing rules to the analysis of the microwave effective material parameters, the permittivity and permeability, of composites. It is suggested to perform the analysis in terms of the normalized inverse susceptibility defined as the volume fraction of inclusions divided by the effective dielectric or magnetic susceptibility of the composite. This allows the volume fraction dependence of the effective material parameters to be represented in a form that is convenient for the analysis, so that distinguishing features of the dependence become more pronounced and helpful for understanding the factors that affect the effective properties of the composite. The proposed approach is illustrated by the analysis of the measured data on the microwave material parameters of composites comprising Sendust powder with either spherical or platelet powder particles, and Permalloy powders with particles of the stone-like shape. The microwave material parameters are measured with paraffin-based composite samples in the 7/3-mm coaxial air-filled waveguide by the Nicolson‒Ross‒Weir technique. It is shown that for Sendust particles, the interaction between inclusions is low. For the composites comprising spherical particles, the Maxwell Garnet mixing rule is a good approximation of the volume fraction dependence of microwave permeability. For the platelet powder particles, the magnetic performance is governed by the Wiener mixing rule. For composites filled with Permalloy powder, the contribution of the interaction between inclusions to the effective permeability is essential. Therefore, the suggested approach allows the type of mixing rule suitable for description of material parameters of a given composite to be determined.

The paper discusses available analytical approaches for analyzing radar absorbing performance of composite materials. Most published reports on the microwave properties of magnetic composites refer to radar absorbers as possible applications. The conventional approach is based on measurements of the effective permittivity and permeability of a composite with certain concentrations of inclusions; calculations of reflection coefficient of the composite layer backed by a metal substrate for the normal incidence of electromagnetic wave; and selection of the layer thickness that produces deep minimum of the frequency dependence of the reflectivity. The obtained reflectivity minimum, typically of −30, −40 dB, or even −60 dB deep is conventionally considered as a proof for “a good absorbing ability” of the inclusions comprising the composite. In the paper, simple analytical approximations based on the series expansions of the reflection coefficient are suggested for the reflection coefficient of radar absorbers. It is shown that the problem of radar absorbing performance is not reduced to obtaining good absorbing ability, but is a problem of matching of parameters of the absorbing material. Therefore, the depth of reflection minimum is not a suitable measure for the characterization of radar absorbers. To describe the quality of an absorber, other quality criteria are needed.

The influence of the nanocrystalline state of Fe and Fe75Si25 particles and their electrical resistance on the microwave properties of composite materials that contain these particles has been investigated experimentally. The main factors that determine changes in the frequency dispersion of the permeability are the skin effect and the decrease in the internal field of anisotropy of the particles. In the case of Fe particles, the role of skin effect of prevails.

Reactive sputtering of permalloy typically reduces crystallite size in films, if the concentration of reactive gas is low. This advances magnetic properties: decreases coercivity and increases good in-plane magnetic anisotropy. But oxygen is rarely applied for this purpose. Here, peculiar deposition conditions, including the geometry of the vacuum deposition system and large polymer substrate, allowed for the deposition of supermalloy with unusually high admixture of oxygen. Evolution of both static and dynamic magnetic properties with an increase in oxygen concentration proved to be dealt with the balance between grain size, surface structure, disordering of atomic structure and internal stresses. The critical concentration when supermalloy shows indications of oxidation is 5% of O2. Coercivity, resistivity, roughness and ferromagnetic resonance frequency are the parameters that are most sensitive to oxidation.

The effect of Ti substitution on the microwave and magnetostatic properties of nanostructured hexagonal BaFe12&minus, xTixO19 ferrite composites is studied. The microwave permeability is measured in the frequency range of 0.1&ndash, 22 GHz by a coaxial technique. An analysis of the magnetostatic data is made by the law of approach to saturation. The ferrimagnetic resonance frequencies calculated from the magnetostatic data are consistent with those obtained from the microwave measurements. The natural ferrimagnetic resonance frequencies are located in the frequency range of 15 to 22 GHz, depending on the substitution level x. An increase in the amount of substitution elements results in a low-frequency shift of the ferrimagnetic resonance frequency for samples with x &lt, 1. With x rising from 1 to 2.5, the resonance frequency increases. The results of the study demonstrate that the tailored optimization of the nano-structure of a functional material is a robust tool to fine-tune its microwave magnetic properties. The ferrites under study are promising materials to be applied as functional coatings intended to control electromagnetic interference in microwave devices.

The Fe-Ti-B films were obtained by dc magnetron sputtering of the Fe + 15% TiB2 and Fe + 30% TiB2 targets. The chemical composition and structure were studied in the as-sputtered state and after vacuum annealing at 500°C. The static (saturation magnetization Ms and coercive field Hc ) and rf magnetic properties (magnetic permeability µ’, frequency of natural ferromagnetic resonance fr and the frequency range in which µ’ is kept) were determined.

The use of a coaxial air-filled line as a test fixture for measuring complex permittivity and permeability often shows odd resonance-like behavior of material parameters as functions of frequency. This effect is typically either ascribed to the half-wavelength resonance at the sample length, or erroneously misinterpreted as intrinsic resonance behavior of the material. However, as is shown in this paper, such behavior can be attributed to excitation of the higher-order modes on the surface of the sample resulting in resonance absorption of electromagnetic energy in the test fixture. Herein, analytical, numerical, and experimental results show that there can actually be a significant impact of higher-order modes in a coaxial line on the extracted constitutive material parameters of samples.

The microwave permeability of nickel (Ni) is reconstructed from constitutive parameter measurements of paraffin-binded composites filled with flakes or spheres of carbonyl nickel. The metal permeability is assumed to be equal to the intrinsic permeability of inclusions. The mean diameter of spheres is about 12μm, the mean diameter of flakes obtained from spheres by ball milling is about 50μm, the thickness is about 2μm. The shape and size are determined by microscopy and by laser particle sizer Analysette 22. The measurements of composite permittivity $\varepsilon _{mix}$ and permeability $\mu _{mix}$ are performed with MS2028 VNA applying the reflection-transmission coaxial-line technique within 0.05–20GHz frequency band. The calculations are performed for isotropic mixtures filled with spheres and for plane-isotropic mixtures filled with flakes. The assumption of plane isotropy for flakefilled samples is reasonable as for the pressed washer sample the thickness (~0.8mm) is much smaller than the diameter (7mm). The effects of filling factor, particle shape and size on permittivity and permeability are analyzed. The reconstruction of inclusion permeability $\mu _{incl}$ is based on treatment of the measured dependence of $\varepsilon _{mix}$ and $\mu _{mix}$ on frequency f and volume fraction of inclusions p.The procedure is based on generalized Sihvola mixing model [1] simplified for a plane-isotropic composite. The model is valid for wide range of susceptibility contrast and accounts for inclusion shape and geometric spectral linewidth [2] described by parameter a in equation (Eq.1). The dependence of composite susceptibility $\chi_{32}$ on frequency is defined by the corresponding dependence of inclusion susceptibility $\chi_{12}$. The susceptibilities $\chi_{12}$ and $\chi_{32}$ are normalized by the corresponding constitutive parameter of a binder: permittivity $\varepsilon _{2}$ or permeability $\mu _{2}$ of polymer. Equation (Eq.1) relates susceptibility of a composite $\chi_{32}$ to the filling factor p, inclusion susceptibility $\chi_{12}$, inclusion depolarization factor N and mixture structure characterized by parameter a. $\chi_{m32}/\chi_{m12}= {p(1}+a\chi_{m32} {)/[1}+ a\chi_{m32}+ N\chi_{m12} {(1-p)] }$ (1) Indexes 1, 2 and 3 relate to inclusion, binder and mixture. The inclusions are assumed to be identical spheres or identical oblate ellipsoids of rotation; their shape defines the depolarization factor N [3]. The similar equation (Eq.2) describes composite electric susceptibility $\chi_{e32}$. As metal conductivity is about 108Ohm×m,thus $\chi_{e12} > >\chi_{e32}$ at practicable fillings, and Eq.1 may be simplified as shown below. $\chi_{e32\, =} p\chi_{e12} { (1}+a\chi_{e32} {)/ [1}+ a\chi_{e32} + N\chi_{e12} { (1-p)] }\approx { p/[N (1-p)-ap]}$ (2) The difference in electric and magnetic susceptibility of metals ${{\chi }_{e12}}/{{\chi }_{m12}}>>1$ makes it possible to estimate intrinsic permeability of metals at microwaves, where the measurements with bulk metals are impossible because of skinning. Moreover the mixing model (Eq.1) makes it possible to estimate from the measured data the spectral linewidth a as well. It is easy to show that for metal inclusions $({{\chi }_{\varepsilon 12}}\to \text{ }\!\!\alpha\!\!\text{ }\infty )$ the inclusion depolarization factor N and percolation threshold $p_{c}$ are related to linewidth parameter a as Eq.3 $a= {N(1-p}_{c})/p_{c}$ (3) The parameters N and $p_{c}$ are readily determined experimentally and are used in the generalized Maxell Garnett (Odelevskiy) equation to relate a composite susceptibility to that one of inclusion [4]. The measured at 50MHz quasistatic permittivity and permeability $\varepsilon _{mix}(p)$ and $\mu _{mix}(p)$ data are shown in Fig.1 by circles and squares correspondingly. As the imaginary permeability $\mu ''_{mix}$ at 50MHz is comparable to real part $\mu '_{mix}$, the value $\mu _{mix}(p)$ is presented by the absolute value of $\mu _{mix}$. In the vicinity of percolation threshold $p_{c}$ the samples become electrically conductive and the measured permittivity has poor reprodusability and jumps from high positive to negative values. The effect of negative permittivity is known [5] but we relate it to inductive resistance of long clusters similar to that of wire sections [6]. The dashed lines in Fig.1 present the permittivity curves calculated from Eq.2 with N and $p_{c}$ as fitted parameters. The fitted values of depolarization factor $N_{sph}=0.149$ and $N_{flk}=0.04$ agree with microscopic measurements. The percolation threshold values are correspondingly $p_{c-sphere}=0.56$, and $p_{c-flake}=0.19$; thus Eq.3 gives $a_{sphere}=0.111$ and $a_{flake}=0.167$. The measured frequency dependence of microwave permeability for composites filled with flakes and spheres (the data in Fig.2 are selected for composites with approximately the same $\varepsilon _{mix}$ values) shows that the absorption peak shape and frequency strongly depend on inclusion shape and on thickness because of skinning. The absorption frequency is much lower than that of composites with carbonyl iron [1] and the permeability values measured at 50MHz are far from static ones. The reconstructed inclusion permeability at this frequency is also far from the static one as the loss tangent for spheres and flakes is close to unity, while the permeability real value is about 5 for both inclusion types; the value is about 2 times lower than the reported data [7]; the difference may be attributed to skinning and structural defects introduced in flakes while ball milling. The measured microwave constitutive parameters of composites show that Ni flakes and spheres both are promising fillers for interference suppressors and UHF-band absorbers similar to sendust powders [4].

In this letter, microwave and magnetostatic measurements of single- and multilayer Permalloy films are made to find physical reasons causing the decrease of the microwave permeability of the films with increase in film thickness. The permeability is measured in the frequency range of 0.1–10 GHz by a coaxial technique. From the measured permeability, a contribution to the effective field from the magnetoelastic effect is determined. The decrease of microwave permeability in thick films is shown to arise mainly due to the perpendicular magnetic anisotropy rather than from the effect of eddy currents, as is frequently suggested. It is also shown that both these effects are reduced in multilayer films comprising alternating magnetic and dielectric layers. Therefore, such films are promising materials for developing magnets that possess high permeability at high frequencies.

The effect of additions of surfactants (stearic and perfluorononanoic acids, stearylamine, and of their mixtures) on the morphology, structural-phase composition, structure of the surface, and magnetostatic and microwave properties of ferromagnetic powders obtained by the joint high-energy milling of Fe and polystyrene has been investigated. It has been shown that the use of a mixture of stearic and perfluorononanoic acids during milling made it possible to obtain particles of plate-like shape with minimum changes in the phase composition and to produce shells on their surface that consist of the surfactant molecules. All of these factors have positively affected the microwave properties of the composites prepared from thus obtained powders.

An analytic approach to calculate induced permeability of metamaterial filled with helix inclusions is developed. For an electrically small coil, the dynamic magnetization is determined by lumped inductance, capacitance, and resistance that are calculated from the coil design. The susceptibility of a coil is shown to be close to that of diamagnetic ellipsoid of the same elongation. Contrary to permeable particles in a composite, the coils screen each other thus decreasing the magnetic response of metamaterial compared to total response of comprised coils. The filling effect on magnetic spectrum of metamaterial is analyzed and verified by measurements for the case of identical coaxially placed coreless coils. The critical filling where magnetic response of metamaterial is maximal depends on coil shape and resistance. The coil-filled metamaterials may find applications as permeable EMI suppressors or microwave absorbers free of Snoek or Acher limitations on the high-frequency permeability, as well as of Curie limitation on the high-temperature magnetic performance.

Fe–Cu–Nb–Si–B microflakes have been prepared by ball milling. The structural, magnetostatic and microwave permeability of the flakes and flake-filled composites have been studied. Two ferromagnetic phases, nanograins and amorphous matrix, are found in the flakes. The Mossbauer study shows that the nanograins are α -Fe 3 (Si) with D0 3 superlattice structure. High resolution transmission electron microscopy shows that the nanograins are well dispersed in the matrix. The microwave permeability of composites containing the flakes has been measured. The comparison of the intrinsic permeability of the flakes obtained from the permeability measurements and from the anisotropy field distribution reveals a disagreement in the magnetic loss peak location. It is concluded that the low-frequency loss in the composites is not due to the effect of eddy currents. The low-frequency loss may be attributed to other sources, such as domain wall motion or peculiarities of the magnetic structure of the flakes in the composite.

Frequency dependencies of permittivity and permeability of composites filled with Permalloy powder with various concentrations and shapes of particles have been measured and discussed. The powder particles of various shapes were obtained by mechanical milling of industrial Permalloy powder in organic media. Paraffin wax was used as a matrix for producing the composites. A shape data of the particles was obtained with an electron microscope. The permittivity and permeability were measured in the frequency range of 0.13 to 10 GHz. The shape of the particles changes from sphere to platelet with increase of milling time. The change leads to a shift of the ferromagnetic resonance (FMR) frequency and magnetic loss peak. It is shown that for larger particles, a decrease of the Q-factor of the ferromagnetic resonance is observed, which is explained by the strong influence of the skin effect. With increase of the concentration of the Permalloy particles in composite, the magnetic loss peak shifts to low frequencies. When the spherical particles are flattened, the resonance frequency shifts to high frequencies, which indicates that the shift to high frequencies due to the decrease of the skin effect and the change in the magnetic structure is stronger than the shift to the low frequencies by changing the shape and reducing the demagnetization.

In this paper, we obtained resistive frequency-selective gratings, where a composite (Co40Fe40B20)60(SiO2)40, a chromium film and a two-layer chromium film and a composite were used as a resistive material. Their magnetostatic and magnetodynamic properties were investigated, and a parameter S21 (reflection) in an anechoic chamber was measured using two horn antennas. The samples with a resistive film of a nanocomposite (Co40Fe40B20)60(SiO2)40 exhibit significant absorption.

A theoretical and experimental study of filling effect on the microwave constitutive parameters of a metamaterial with resonant inclusions is performed. The metamaterial is a planar anisotropic layer containing a regular array of coreless split ring inclusions and is considered to be a homogeneous medium. The electric and magnetic susceptibilities of the inclusions are measured and compared with predictions of the generalized Maxwell Garnett theory that accounts for the percolation threshold. The threshold for permittivity is calculated based on the structure of the sample and the sizes of the split rings. The electric interaction of the split rings is close to the dipole interaction of the metal disks. The magnetic interaction depends on the overlapping of ring-induced magnetic fields. When the overlap is negligible, the permeability is defined by the volume of a permeable prolate ellipsoid with magnetic moment equal to the moment induced by the ring. The flatter the split ring, the longer is the prolate ellipsoid and the higher is its volume compared to the volume of the ring inclusion itself. This approach allows the metamaterial constitutive parameters to be calculated based on the dimensions and filling factor of the inclusions, the same as in a powder-filled composite.

Known mixing models are analyzed with the aim to retrieve permeability of metal inclusions from the measured constitutive parameters of a binary composite. The application-oriented models are interpreted in terms of inclusion shape-factor and percolation threshold, which are two measurement-fitted parameters. A model that accounts for the inversion of the Maxwell Garnett matrix structure is proposed. The structure inversion point is close to the percolation threshold, and the inversion takes place within a transition filling range that is a third fitting parameter. The proposed model is compared with the effective medium model in terms of the complex susceptibility calculated as the function of filling and of frequency and in terms of Bergman-Milton shape-factor distribution charts. The model validity is illustrated by treatment of the measured microwave constitutive parameters of a composite filled with carbonyl nickel.Known mixing models are analyzed with the aim to retrieve permeability of metal inclusions from the measured constitutive parameters of a binary composite. The application-oriented models are interpreted in terms of inclusion shape-factor and percolation threshold, which are two measurement-fitted parameters. A model that accounts for the inversion of the Maxwell Garnett matrix structure is proposed. The structure inversion point is close to the percolation threshold, and the inversion takes place within a transition filling range that is a third fitting parameter. The proposed model is compared with the effective medium model in terms of the complex susceptibility calculated as the function of filling and of frequency and in terms of Bergman-Milton shape-factor distribution charts. The model validity is illustrated by treatment of the measured microwave constitutive parameters of a composite filled with carbonyl nickel.

The structural and phase composition and magnetostatic and microwave properties of powders produced by simultaneous milling of carbonyl iron and paraffin taken in volume ratios ranging from 10 : 90 to 80 : 20 have been studied. It has been shown that the shape of the powder particles depends substantially on the amount of Fe in the mixture. At an Fe content of 30 vol %, the particles acquire a platelet shape; at an Fe content of more than 40 vol %, the agglomeration of the particles is observed. At an Fe content above 30 vol %, the Fe3C phase is formed in the particles, which leads to an increase in the coercive force and a decrease in the specific saturation magnetization of the powder. The frequency dependences of the microwave magnetic and dielectric permeabilities of the composite materials containing the prepared powders have been measured, and the frequency dependences of the intrinsic magnetic permeability of these powders have been determined. It has been shown that the static magnitude of the intrinsic magnetic permeability reaches a maximum in powders containing 30 vol % Fe in the initial mixture.

Fe84.94Si9.68Al5.38 flaky particles have been obtained by ball attrition method. The volume fraction dependence of microwave permeability has been measured for composites filled with these particles. Effective medium theories have been employed to extract the apparent microwave permeability. It is found that the flaky Fe-Si-Al particles have large apparent microwave permeability and large microwave magnetic loss. For example, at 0.5 GHz, the real and imaginary parts of apparent permeability are 10 and 5, respectively. The extracted microwave permeability is found to be consistent with generalized Snoek's limit. Due to high microwave magnetic loss, the flaky Fe-Si-Al particles can be useful for technical applications in the field of electromagnetic compatibility. Mossbauer spectroscopy measurements show that the hyperfine magnetic field and isomer shift have wide distribution, indicating that Fe atoms in the flaky Fe-Si-Al alloys have complicated environments.