Causality study and numerical response of the magnetic permeability as a function of the frequency of ferrites using Kramers-Kronig relations

In this paper, the numerical treatment of magnetic loss of NiZn, MnZn, Ni₂Y, and NiZnCu ferrite and their composites, by using Krameres-Kronig relations, is investigated. The complex magnetic permeability spectra for ferromagnetic materials have been studied. Due to the principle of causality and time independence in the relation between magnetic induction B and magnetic field H, the real and the imaginary part of the complex magnetic permeability are mutually dependent, and the correlation is given by the Krameres-Kronig equations. Through them, it is possible to measure the real component of the complex magnetic permeability, assuming the real component is given, and by the Hilbert transform, the imaginary part of the magnetic permeability can be calculated. Magnetic circuit model has been studied theoretically, focusing on the model's poles in the complex plane to verify the principle of causality and the temporary independence.     

Permeability enhancement by induced displacement current in magnetic material with high permittivity

Based on a analytical model, this paper reveals that instead of demagnetization, the induced displacement current in a Mn–Zn ferrite core due to its high permittivity can produce a magnetic field that effectively adds to the incident magnetic field in the low-loss frequency region. This leads to a resultant magnetic field being larger than incident field in magnitude, and results in measured permeability being higher than its intrinsic value in the low-loss frequency region. It is also found that such effect is more pronounced in large core than in small core. With increasing frequency and consequently the core being more lossy, the induced magnetic field due to both conductivity and imaginary part of complex permittivity demagnetize the magnetic material and counteracts the incident magnetic field. In consequence, the measured real part of complex permeability becomes smaller than its intrinsic value. The larger the core dimension, the smaller the real part of complex permeability is. These conclusions based on the numerical analysis are in good agreement with the experimental observation in the aspect of change tendency of permeability versus frequency.     

Modeling of ferrite-based materials for shielding enclosures

An analytical model for a magneto-dielectric composite material is presented based on the Maxwell Garnett rule for a dielectric mixture, and on Bruggeman's effective medium theory for permeability of a ferrite powder embedded in a dielectric. In order to simultaneously treat frequency-dispersive permittivity and permeability of a composite in a full-wave FDTD code, a new algorithm based on discretized auxiliary differential equations has been implemented. In this paper, numerical examples of modeling structures containing different magneto-dielectric mixtures are presented.     

Preparation and characterization of flaky FeSiAl composite magnetic powder core coated with MnZn ferrite

The flattening of FeSiAl soft magnetic powder was achieved by ball milling process, and MnZn/FeSiAl composite magnetic powder core was prepared by press molding. The effect of different coating amount of MnZn ferrite on the soft magnetic properties of FeSiAl was studied. At the same time, the optimal stress-relieving annealing temperature of the composite magnetic powder core is revealed. The results showed that the addition of MnZn ferrite affected the magnetic properties such as saturation magnetization (Ms), initial permeability (μi) and power loss (Pcm) of FeSiAl soft magnetic. With the increase of MnZn ferrite addition content, the saturation magnetization of composites decreased gradually, and the magnetic permeability increased first and then decreased, and the loss decreased first and then increased. When the addition content of MnZn ferrite was 5%, the permeability reached the maximum, which was 28.1% higher than that of the pure FeSiAl magnetic powder core under the same conditions. At the same time, the loss was the lowest, which was 13.3% lower than the pure FeSiAl powder core under the same conditions. When the annealing temperature is around 650 °C, the magnetic powder core has the largest magnetic permeability and the lowest loss.     

Giant uniaxial stress-permeability effect on electrical parameters of heterotypic MnZn ferrite devices and electromagnetic effect

The effects of uniaxial stress on permeability and electrical parameters of heterotypic manganite zinc (MnZn) ferrite devices have been investigated. Giant stress-permeability, stress-capacitance and stress-impedance that are independent of skin effects have been simultaneously observed to exist in a wide range of frequency at room temperature. All the uniaxial stress effects enhance with increasing the permeability of the ferrite. The stress-inductance is same as the stress-impedance and reverse to the stress-capacitance in phase. The stress effects under uniaxial pulling force are analogical with those under uniaxial pressing force. A composite of electrostrain/stress-permeability has been fabricated. Its electromagnetic effects have been observed to be homologous with the stress effects and can also exist in wide range of frequency but display some maximums. Analysis shows that both stress and electromagnetic effects originate from the variation of the magnetic domain structure in the ferrites caused by applied mechanical stress.     

Study of DC conductivity and relative magnetic permeability of nanoparticle NiZnFe2O4/PPy composites

The DC conductivity and the relative magnetic permeability have been measured as functions of temperature for five powder samples of nanoparticle ferrites (Ni_xZn_1−xFe₂O₄; x=0, 0.25, 0.5, 0.75 and 1), a pure polypyrrole (PPy) powder sample and many composite samples prepared by mixing different ratios of the ferrites to PPy. By comparing the results it is found that there is an obvious increase in DC conductivity of the ferrite/PPy composite samples compared to the corresponding pure ferrite samples, whereas compared to the pure PPy sample there is a decrease in DC conductivity. On the contrary, the magnetic permeability of the composites is higher than that of the pure PPy sample and lower than that of the pure ferrite samples as was expected.     

Complex impedance spectra of chip inductor using Li–Zn–Cu–Mn ferrite

A multi-layer chip inductor (MCI) was fabricated using polycrystalline Li–Zn–Cu–Mn ferrite and the green-sheet technique, and its complex impedance spectrum was evaluated with the help of numerical calculations. The complex impedance spectra of the MCI component using Ni–Zn–Cu ferrite, which have been widely used for this application, were very sensitive to the residual stress and deviated much from the calculated values; however, it was found that the complex impedance spectrum of the MCI component using Li–Zn–Cu–Mn ferrite is quite well reproduced by calculation, where the complex permittivity and permeability of the polycrystalline ferrite as well as the MCI dimensions, were used. It implied that the magneto-striction effect was negligible in case of MCI using Li–Zn–Cu–Mn ferrite, and that the difference was related to magneto-strictive coefficient of the polycrystalline ferrite. Consequently, utilization of Li–Zn–Cu–Mn ferrite enabled us to easily design the complex impedance of MCI component.     

Influence of V2O5 on the magnetic properties of nickel–zinc–copper ferrites

Additions of V₂O₅ were used to decrease the sintering temperature and to enhance the densification of NiZnCu ferrite. With a small amount of V₂O₅ (0.6–1.2 wt%) as a sintering aid, densification at low sintering temperature was observed. EDS analyses showed the presence of vanadium inside the ferrite grains. Microstructure investigation revealed heterogeneous grain size. Magnetic properties were deteriorated when increasing the V₂O₅ content. As a consequence, the permeability decreased and the core losses increased, which can be explained by the pinning of the domain walls to the grain defects.     

Synthesis, characterization and microwave absorption properties of titania-coated barium ferrite composites

Anatase titania-coated barium ferrite composites were prepared by a heterogeneous precipitation method in the presence of barium ferrite particles. The obtained samples were characterized by ξ-pH, TEM, EDX and XRD. The complex permittivity and permeability were studied in the frequency range of 2-12 GHz. The structure and microwave response properties are investigated. The results show that the coverage of titania has a great influence on microwave response of barium ferrite. The formation of an anatase titania nano-layer on the surface of a barium ferrite particle changes the character of the frequency dispersion of the complex permittivity. Comparing the anatase titania-coated barium ferrite composites with the uncoated barium ferrite, the complex permittivity of the anatase titania-coated barium ferrite composites is higher than that of uncoated barium ferrite. The complex permeability of composites was found to decrease with an increase in frequency as well as with the molar ratio of Ti:Ba. The enhancement of the complex permittivity may be due to dipolar polarization and interfacial polarization. The maximum reflection loss was obtained at the Ti:Ba ratio of 1:10, and the peak of the maximum reflection loss shifts to a lower frequency value with increasing titania fraction. By changing the thickness of titania coverage, the frequency dependence of the complex permittivity could be adjusted, which provides us an opportunity for the synthesis of tailored particles.     

Low temperature synthesis of Mn0.4Zn0.6In0.5Fe1.5O4 nanoferrite for high-frequency applications

In the present study, nanoferrite of composition Mn_0.4Zn_0.6In_0.5Fe_1.5O₄ has been synthesized by co-precipitation method. Decomposition of residue at a temperature as low as 200 °C gives the ferrite powder. The ferrite has been, finally, sintered at 500 °C. The structural studies have been made by using X-ray diffraction (XRD) technique and scanning electron microscopy (SEM), which confirm the formation of single spinel phase and nanostructure. The dc resistivity is studied as a function of temperature and values found are more than twice those for the samples prepared by the other chemical methods. It is found that the resistivity decreases with increase in temperature. The initial permeability value is found to be higher as compared to the other chemical routes. The initial permeability value is found to increase with increase in temperature. At a certain temperature called Curie temperature, it attains a maximum value, after which the initial permeability decreases sharply. Even at nanolevel, appreciable value of initial permeability is obtained and low magnetic losses make these ferrites especially suitable for high-frequency applications. The particle size is calculated using Scherrer's equation for Lorentzian peak, which comes out between 35 and 49 nm. Possible mechanisms contributing to these processes have been discussed.     

Electromagnetic wave absorption properties of carbonyl iron-ferrite/PMMA composites fabricated by hybridization method

The surface of carbonyl iron powder or a mixture of carbonyl iron and ferrite was coated with polymethylmethacrylate (PMMA) microspheres by a hybridization method to make hybrid powders, and then electromagnetic wave absorption properties of the hybrid composites prepared with these hybrid powders have been investigated. As for the carbonyl iron/PMMA hybrid composite, the reflection loss less than −20 dB could be achieved in a frequency range of 1.7–5.0 GHz when the composite thickness was below 5.00 mm. In the case of the carbonyl iron-ferrite/PMMA hybrid composite, a similar reflection loss was observed in a frequency range of 4.3–13.0 GHz. Thus, the addition of ferrite was found to be useful for achieving a large absorption in a wide frequency range, especially for higher frequency values. Simulated values for the minimum reflection loss are well agreed with actually measured ones, because of homogeneous distribution of carbonyl iron and/or ferrite in these hybrid composites.     

Effect of viscosity on the magnetic permeability of Sendust-filled polymer composites

A flake-shaped Sendust/acryl suspension is tape cast and the effect of the viscosity of the suspension on the magnetic permeability of the resulting composite is investigated. The real part of the permeability of the composite is inversely proportional to the viscosity of the suspension, indicating that the lower the viscosity of the suspension, the higher the permeability of the composite. The viscosity of the suspension is controlled by adding a small amount of surfactant; an anionic surfactant is most effective for lowering the viscosity at a given concentration range. It is thought that using a suspension with a relatively low viscosity improves the permeability of the resulting composite due to the easy alignment of the flake-shaped filler with the plain direction of the sheet.     

The grain size effect on the magnetic properties in NiZn ferrite and the quality factor of the inductor

Polycrystalline ferrite materials with the chemical composition of Ni_0.49Zn_0.49Co_0.02Fe_1.90O_x have been fabricated using the conventional ceramic sintering method. Grain sizes have been adjusted from ∼2.2 to ∼13.5 μm with changing sintering conditions. From the measurements of the complex permeability, it is suggested that the permeability is dominated only by the spin rotation at mono-domain state and both domain wall and spin rotation contribute at multi-domain state. At mono-domain state, the core loss has been drastically decreased similar to the other work. The measurement result for the loss angle indicates that the low loss state can be maintained up to the higher magnetic field with smaller grain size in spite of the mono-domain state. The simplified wire-wounded type inductors have been also fabricated and characterized. The results have shown that the inductor fabricated with the smaller grain size has a better performance in the quality value under relatively higher current.     

Dependence of microwave absorption properties on ferrite volume fraction in MnZn ferrite/rubber radar absorbing materials

We report the analysis of measurements of the complex magnetic permeability (μ_r) and dielectric permittivity (ε_r) spectra of a rubber radar absorbing material (RAM) with various MnZn ferrite volume fractions. The transmission/reflection measurements were carried out in a vector network analyzer. Optimum conditions for the maximum microwave absorption were determined by substituting the complex permeability and permittivity in the impedance matching equation. Both the MnZn ferrite content and the RAM thickness effects on the microwave absorption properties, in the frequency range of 2-18 GHz, were evaluated. The results show that the complex permeability and permittivity spectra of the RAM increase directly with the ferrite volume fraction. Reflection loss calculations by the impedance matching degree (reflection coefficient) show the dependence of this parameter on both thickness and composition of RAM.     

Localized defect modes in finite magnetic two-dimensional photonic crystals

We present a detailed study of localized defect modes in finite two-dimensional magnetic photonic crystal consisting of cylindrical ferrite material in air background by using the scattering matrix method. It is shown that due to having positive and negative value of the effective magnetic permeability in interested photonic band gap, the defect modes present different behavior. Our results show that the modes appeared in positive permeability region have features similar to the modes supported by the dielectric photonic crystal while those created in the negative permeability region are strongly localized at the interface of defect ferrite rod with air background. Moreover, results indicate that defect modes occurred in the negative region are sharper than those appeared in the positive one which means the quality factor of former case is extremely high.     

Development of low loss Mn–Zn ferrite working at frequency higher than 3 MHz

With the advance of modern electronic technology, there has been a critical need for Mn–Zn ferrites with even higher permeability and even lower power loss at higher frequencies. In this study, ferrite with extremely low losses than conventional ferrite materials at high frequency was developed employing a conventional ceramic powder processing technique. As a result, the core loss at 3 MHz, 10 mT and 100 °C is around 300 kW/m³, and its cutoff frequency is 4 MHz. Furthermore, the electromagnetic characteristics and the microstructure of this new DMR50 material are also discussed.     

On the thermal stability of Co2Z hexagonal ferrites for low-temperature ceramic cofiring technologies

Co₂Z hexaferrite Ba₃Co₂Fe₂₄O₄₁ was prepared by a mixed oxalate co-precipitation route and the standard ceramic technology. XRD studies show that at T<1300 °C different ferrite phases coexist with the M-type hexaferrite as majority phase between 1000 and 1100 °C and the Y-type ferrite at 1230 °C. The Z-type material has its stability interval between 1300 and 1350 °C. Both synthesis routes result in almost single-phase Z-type ferrites after calcination at 1330 °C, intermediate grinding and sintering at 1330 °C. The permeability of Co₂Z-type ferrite of about μ=20 is stable up to several 100 MHz, with maximum losses μ′′ around 700 MHz. Addition of 3 wt% Bi₂O₃ as sintering aid shifts the temperature of maximum shrinkage down to 950 °C and enables sintering of Z-type ferrite powders at 950 °C. However, the permeability is reduced to μ=3. It is shown here for the first time that Co₂Z ferrite is not stable under these conditions; partial thermal decomposition into other hexagonal ferrites is found by XRD studies. This is accompanied by a significant decrease of permeability. This shows that Co₂Z hexagonal ferrite is not suitable for the fabrication of multilayer inductors for high-frequency applications via the low-temperature ceramic cofiring technology since the material is not compatible with the typical process cofiring temperature of 950 °C.     

Nonlinear magnetoelectric response of a bulk magnetostrictive-piezoelectric composite

Magnetoelectric effect in a bulk composite of nickel ferrite and lead zirconate titanate has been investigated by applying an ac magnetic field with no bias field. The measurements were carried out in the low-frequency region for harmonic magnetic field modulation with amplitude up to 3 kOe. The electric field induced by out-of-plane magnetic field exceeds that induced by in-plane magnetic field by approximately 4 times. Nonlinearity of ferrite magnetostriction of the sample results in a doubling in the frequency and a strong distortion of the ME signals. The magnetically induced voltage can be found by integrating the ordinary ME voltage coefficient over magnetic field.     

Stress insensitive NiCuZn ferrite compositions for microinductor applications

Two series of stoichiometric and iron deficient NiCuZn ferrites were prepared by the conventional ceramic method. The formation of single phase was confirmed by X-ray diffraction in pure ferrites and a second phase was noticed in SiO₂ added ferrite samples. Initial permeability measurements on these samples were carried out in the temperature range of 30–300 °C. The effect of external applied stress on the open magnetic circuit type coil with these ferrite cores was studied by applying uniaxial compressive stress parallel to the magnetizing direction and the change in the inductance was measured. These studies show that stress sensitivity is more in stoichiometric ferrite samples than in iron deficient ferrite samples. In order to make them stress insensitive various amounts of SiO₂ were added and the stress insensitivity was examined. SiO₂ addition was found to be effective in reducing the stress sensitivity. This was confirmed by elastic behaviour studies at room temperature on these ferrite samples by employing composite oscillator technique. These ferrite compositions have been developed for their use as core materials for microinductor applications.     

Magnetic properties of Cr substituted Li–Sb ferrites

The magnetic properties, such as initial permeability and hysteresis loop properties of the chromium substituted Li–Sb ferrite system have been investigated. The SEM micrographs reveal the microstructure of the samples. The initial permeability is observed to decrease with the increase of chromium concentration. Frequency variation of permeability indicates that for all samples the resonance peak due to domain wall oscillations is at a frequency above 15 MHz. The hysteresis loop parameters have been calculated from the hysteresis loop studies. The magnetic parameters are observed to decrease with higher level of substitution.