Frequency-dependent Permeability Research Articles

Rietveld refined crystal structure, magnetic, dielectric, and electric properties of Zn substituted Ni-Mg ferrites

Sol − gel technique was used to synthesize Ni0.7-xZnxMg0.3Fe2O4 (Ni – Zn – Mg) ferrites with x = 0.1, 0.2, 0.3, 0.4, 0.5. Formation of single phase cubic spinel structure of the synthesized samples was confirmed by employing Rietveld refinement technique. Spherical and inhomogeneous distribution of grains was observed from Transmission Electron Microscopy (TEM) image. The frequency dependent initial permeability (μi), real part of initial permeability (μ′), imaginary part of initial permeability (μ″) was studied for synthesized samples. For zinc content x = 0.2 in Ni – Zn – Mg ferrites μi is observed to be high as compare to other compositions and that attributed to grain size. DC electrical resistivity (ρdc) analysis shows both conducting and semiconducting behavior for all the samples. Room temperature electrical resistivity values were observed to be lower for lower content of zinc and higher for higher content of zinc and that attributed to the hopping mechanisms at octahedral site. The decreasing trend of Curie temperature was observed with increase in zinc content in Ni – Zn – Mg ferrites. Frequency dispersive dielectric properties study of Ni – Zn – Mg ferrites revealed normal dielectric behavior.

Investigation of annealing temperature effect on structural, morphological, optical, magnetic, and dielectric properties of cobalt-doped manganese ferrites

Spinel ferrite Mn0.95Co0.05Fe2O4 was prepared via chemical co-precipitation routes and annealed at four distinct temperatures of 600 °C, 650 °C, 700 °C, and 750 °C. The XRD peak confirmed a single-phase cubic spinel structure, with an increasing crystallite size of 21.64–23.98 nm by the annealing effect. The TEM images show an increase in particle size with rising annealing temperature and indicate well-defined nanocrystalline Mn-Co ferrite. FT-IR spectra detected two vibrational modes at interstitial sub-lattice sites, identifying Co-O, Mn-O, and Fe-O bonds with the spinel structure of Mn-Co ferrite. UV–vis–NIR reflectance revealed an optimal direct band gap of 3.76–4.70 eV, indicating a scope of semiconducting behaviors in the nanocatalysts. In the magnetic hysteresis curve, saturation magnetization decreased while coercivity increased with rising annealing and crystallite size. The M-T loop reveals the Curie temperature of Mn-Co ferrite decreases from 533.84 °C to 382.74 °C. Frequency-dependent complex permeability at different annealing temperatures shows stable initial permeability over a wide frequency range (1 kHz to 100 MHz) and a quality factor several times higher due to reduced magnetic tangent loss. The real dielectric constant and losses decline in rising alternating fields (100 Hz to 1 MHz) and stabilize at higher frequencies following Maxwell-Wagner-type polarization. Eventually, structural, morphological, and magnetic properties are performed relatively well at higher annealing temperatures, and optical and dielectric properties are performed at lower annealing temperatures.

Finding the best frequency dependent performance of 3d transition metals (Co, Ni, and Mn) substituted nano magnetite for miniaturizing device applications

Ferrite samples with enhanced magneto-dielectric properties are more essential in electromagnetic applications. Therefore, a parent composition of Fe3O4 has been modified by substituting 3d transition metal elements (Co, Ni, Mn) at a single Fe atom using the co-precipitation synthesis method. The structural properties of the synthesized Fe3O4, NiFe2O4, CoFe2O4, and MnFe2O4 samples have been evaluated from the X-ray diffraction patterns. The surface morphology and microstructures of the studied samples were studied by field emission scanning electron microscopy and the average grain size of all the studied samples varied from 60.11 to 106.03 nm. The magneto-dielectric properties were analyzed by frequency dependent permeability (μ) and permittivity (ε) measurements for the range of 100 Hz to 100 MHz. The conduction process for the synthesized ferrites has been noticed from the ac conductivity (σac). The localized relaxation mechanism for the studied ferrites has been observed from the variation of imaginary portion of the electric modulus (M") and the impedance (Z"). Moreover, the mismatch (Z/ηο) between the impedance of the antenna substrates (Z) made of the studied samples and air (ηο) has been evaluated from the permeability and permittivity. Finally, NiFe2O4 has been derived as a suitable ferrite for miniaturizing devices over a frequency range of 10 kHz-6.5 MHz.

Surface plasmon induced quantum interference at meta-material interface

In this work we investigate quantum interference in a four-level atom coupled to a negative index meta-material (NIMM) anisotropic plasmonic environment that supports both TE and TM polarized surface plasmons (SP). The analysis confirms the creation of the anisotropic environment and two dipoles can interfere with each other even if they are orthogonal by sharing such SP modes. The NIMM/plasmonic environment provides more options to control SP interaction with emitters and their spontaneous emission decays and spectrum. The spectrum depends critically on structure parameters, mode frequency, frequency dependent electric permittivity and magnetic permeability, and the location of the atom etc. We observe orders of magnitudes enhancement in the plasmonic-modified decays and spectrum compared to free space case.

Voltage control of electromagnetic properties in antiferromagnetic materials

Dynamic modulation of electromagnetic responses is theoretically examined in dielectric antiferromagnets (AFMs). While both magneto-electric and magneto-elastic coupling can achieve robust electrical control of magnetic anisotropy, the latter is considered in a bilayer structure with a piezoelectric material. Numerical calculations based on the frequency-dependent permeability tensor clearly illustrate that the anisotropy profile in the typical dielectric AFMs such as NiO and Cr2O3 can be modified sufficiently to induce a shift in the resonance frequency by as much as tens of percent in the sub-mm wavelength range (thus, an electrically tunable bandwidth over 10’s of GHz). The polarization of the electromagnetic response is also affected due to the anisotropic nature of the effect, offering a possibility to encode the signal. The intrinsic delay in switching may be minimized to the ns level by using a sufficiently thin AFM. Application to specific devices such as a bandpass filter further illustrates the validity of the concept.

Improved Anti-Saturation Performance of Fe-Si-Al Soft Magnetic Powder Core via Adjusting the Alloy Composition

Ball-milled Fe-Si-Al soft magnetic powder cores with the particle compositions away from the classical Sendust point were prepared in this work. The influences of alloy composition on the metallographic structure, density, hardness, and resistivity of Fe-Si-Al alloy, as well as the frequency-dependent permeability, loss, and the anti-saturation performance of Fe-Si-Al powder cores, were investigated systematically. It was found that the hardness of Fe-Si-Al alloy increases with the Si mass ratio and the saturation magnetization (Ms) increases with the Fe mass ratio. The alloy hardness affects the particle size after the ball-milling process and, thus, influences the porosity of the powder core. Together with adjusting the demagnetization field by controlling the particle size and the core’s porosity, changing the alloy composition to drive K and λ deviating from zero can effectively improve the anti-saturation performance of Fe-Si-Al powder cores at the expense of hysteresis loss, to some extent. In this work, good comprehensive magnetic properties were obtained in the Fe85.5-Si12-Al2.5 powder core. Its effective permeability percentage at 100 Oe and Ms were 59.12% and 132.23 emu/g, respectively, which are higher than those of the classical Sendust core. This work provides a feasible idea for optimizing the overall performance of the high-power magnetic device.

Study of permeability and permittivity of [formula omitted]-Fe[formula omitted]O[formula omitted] using computer simulation method

This study proposes a computational method to directly obtain the frequency-dependent permeability and permittivity of materials from computer simulation data. The method combines first-principles calculations, Green’s function formalism, and magnetic moment dynamics simulations. Using α-Fe2O3 as an example, we demonstrate the validation process of the computational approach. By calculating the time correlation functions of electric and magnetic dipole moments and applying linear response theory, we successfully obtained the frequency-dependent permeability and permittivity of α-Fe2O3 at 300 K. The calculated results agree well with experimental values, proving the efficacy of the proposed computational method. This study provides a reliable computational pathway to predict electromagnetic parameters of materials using computer simulations.

Broadband Modelling of Power Transformers for Sweep Frequency Impedance Studies on Winding Short-Circuit Faults

To study sweep frequency impedance (SFI) features of short-circuit (SC) faults easily, this paper proposes a broadband electric circuit model of a transformer winding and solves its three key problems. The first problem is the calculation of lumped-circuit parameters considering frequency-dependent complex anisotropic permeabilities (FDCAPs), which are caused by the physical characteristics, such as skin, proximity, and geometrical effects and anisotropic properties, of the transformer core and winding materials. The other issue is the establishment of the electric circuit model based on the SFI measurement connection mode, the transformer winding parameters, and a double-ladder network (DLN). Another issue is the construction of the state-space model of the electric circuit toward different SFI values to obtain all network branch voltages and currents. The accuracy of the proposed model is assessed by comparing its SFI signatures with those of the simulation model, without considering FDCAPs under healthy winding, and the corresponding physical transformer model during healthy winding and SC faults. It is observed that the SFI results of the proposed model are closer to the experimental measurements, and the model can be effectively used to study the SFI features of SC faults. Moreover, the impacts of different types of SC faults on the SFI data are concluded in this paper.

Convergence analysis of time-domain PMLS for 2D electromagnetic wave propagation in dispersive waveguides

This work is dedicated to the analysis of generalized perfectly matched layers (PMLs) for 2D electromagnetic wave propagation in dispersive waveguides. Under quite general assumptions on frequency-dependent dielectric permittivity and magnetic permeability we prove convergence estimates in homogeneous waveguides and show that the PML error decreases exponentially with respect to the absorption parameter and the length of the absorbing layer. The optimality of this error estimate is studied both numerically and analytically. Finally, we demonstrate that in the case when the waveguide contains a heterogeneity supported away from the absorbing layer, instabilities may occur, even in the case of the non-dispersive media. Our findings are illustrated by numerical experiments.

Dynamic Relative Permeabilities for Partially Saturated Porous Media Accounting for Viscous Coupling Effects: An Analytical Solution

We present an analytical model to compute frequency-dependent relative permeability functions for partially saturated porous media accounting for viscous coupling effects. For this, we consider the oscillatory motion of two immiscible fluid phases and solve the Navier–Stokes equations at the pore scale using suitable interface conditions between fluids. These calculations are combined with the generalized two-phase flow Darcy equations to obtain the corresponding upscaled macroscopic fluxes. By means of an analog pore model consisting of a bundle of cylindrical capillaries in which pore fluids are distributed in a concentric manner, we find closed analytical expressions for the complex-valued and frequency- and saturation-dependent relative permeability functions. These expressions allow for a direct assessment of viscous coupling effects on oscillatory flow for all frequencies and saturations. Our results show that viscous coupling effects significantly affect flow characteristics in the viscous and inertial regimes. Dynamic relative permeabilities are affected by the pore fluid densities and viscosities. Moreover, viscous coupling effects may induce two critical frequencies in the dynamic relative permeability curves, a characteristic that cannot be addressed by extending the classic dynamic permeability definition to partially saturated scenarios using effective fluids. The theoretical derivations and results presented in this work have implications for the estimation and interpretation of seismic and seismoelectric responses of partially saturated porous media.

Enhancement of magnetic and dielectric properties in (1-x).BEFO+ x.NZF nano composites

Nanostructured Bi0.9Eu0.1FeO3 (BEFO), Ni0.6Zn0.4Fe2O4 (NZF), and (1-x).BEFO + x.NZF composites have been synthesized by traditional solid state reaction process with several dispersion techniques, where x = 0.0, 0.1, 0.3, 0.5, 0.7 and 1.0. X-ray diffraction confirms the perovskite, cubic, and mixed perovskite-spinel phase formation of BEFO, NZF, and (1-x).BEFO + x.NZF composites respectively. FESEM and EDX analysis confirm the nano grain size and compositional purity of the samples. The effect of sintering temperature (TS) on grain growth was studied at 600 °C and 850 °C, where the range of the average grain size is between (90–131) nm and (157–272) nm. The magnetic hysteresis loop properties of all the samples were measured by VSM, where the saturation magnetization (MS) of BEFO increased from 10.31 emu/g to 50.54 emu/g with increasing NZF content. The increment of NZF content also modified other magnetic properties of (1-x).BEFO + x.NZF composites such as coercive force (HC), retentivity (Mr), magnetic moment (nB), and anisotropy constant (K). The frequency dependent permeability measurements show that the initial permeability (μ') was stable in a long frequency range up to 108 Hz and that the magnetic loss tangent (tanδM) decreased with increasing NZF content. The dielectric characteristics and AC resistivity of the composites were measured by an impedance analyzer over a wide frequency range (1 Hz–100 MHz). All the dielectric properties of the synthesized samples show excellent stability up to a long frequency region and vary sharply with increasing NZF content. From the optimization, 0.9 BEFO + 0.1 NZF composite has the highest permeability and dielectric values with the least amount of dielectric and magnetic losses. All the investigated composites might be strong candidates as multiferroic materials with strong magnetic and electric characteristics.

Structural and magnetic properties of Co0·85Zn0.15YxFe2-xO4 ferrites

Rare earth Yttrium doped Co0·85Zn0.15YxFe2-xO4 ferrites were synthesized by the standard double sintering method. The basic structure and phase formation of the samples were studied by the technique of XRD, reporting the formation of spinel cubic structure. Structural X-ray density was always greater than the bulk density. The microstructural grain size was obtained by SEM and confirmed that the microstructural grain size decreased at initial doping of Y3+ ion. The VSM shows the saturation magnetization decreases with increasing Y content but we get comparatively large retentivity and coercivity of the doped samples. Frequency dependent permeability measurements show that the initial permeability was stable in a long frequency range up to 108 Hz and the magnetic loss tangent was decreased with increasing Y content. All the structural and magnetic properties make these Co–Zn–Y ferrites more suitable for magnetic recording materials.

Universal Frequency-Dependent Permeability of Heterogeneous Porous Media: Effective–Medium Approximation and Critical-Path Analysis

Universal Frequency-Dependent Permeability of Heterogeneous Porous Media: Effective–Medium Approximation and Critical-Path Analysis

Modal FEM Analysis of Ferrite Resonant Structures

The finite-element method (FEM) is applied for modal analysis of ferrite-loaded spherical resonators. To improve the efficiency of the numerical calculations, the body-of-revolution (BOR) technique is utilized. Due to the frequency-dependent ferrite permeability, FEM leads to a nonlinear eigenvalue problem that is challenging to solve. To this end, Beyn’s method is proposed. The effectiveness of the proposed approach is confirmed by comparing with the results obtained analytically and with the measured data.

Зондирование частотной дисперсии магнитной проницаемости образца при динамическом взаимодействии с намагниченным зондом

The forces acting on a magnetic particle during nonrelativistic motion parallel to the surface of a homogeneous medium with a frequency dispersion of magnetic permeability are considered. General expressions are obtained for the normal (attractive) and lateral (braking) forces acting on a small dipole particle and an extended probe. It is shown that for an arbitrary orientation of the vector of the dipole magnetic moment of the particle, along with the force of attraction and the stopping force, there also appears a velocity-dependent lateral force perpendicular to the velocity vector. The possibility of using the results to study the frequency-dependent magnetic permeability of nanostructured materials and films in the dynamic scanning mode of magnetic force microscopy (MCM) with magnetic probes is discussed. Numerical estimates are given for the magnitude of the expected forces, friction coefficients, and changes in the quality factor of the MFM oscillators in the case of frequency dispersion of relaxation-type magnetic permeability.

Probing the Frequency Dispersion of the Magnetic Permeability of a Sample During Dynamic Interaction with a Magnetized Probe

The forces acting on a magnetic particle during nonrelativistic motion parallel to the surface of a homogeneous medium with a frequency dispersion of magnetic permeability are considered. General expressions are obtained for the normal (attractive) and lateral (braking) forces acting on a small dipole particle and an extended probe. It is shown that for an arbitrary orientation of the vector of the dipole magnetic moment of the particle, along with the force of attraction and the stopping force, there also appears a velocity-dependent lateral force perpendicular to the velocity vector. The possibility of using the results to study the frequency-dependent magnetic permeability of nanostructured materials and films in the dynamic scanning mode of magnetic force microscopy with magnetic probes is discussed. Numerical estimates are given for the magnitude of the expected forces, friction coefficients, and changes in the quality factor of the MFM oscillators in the case of frequency dispersion of relaxation-type magnetic permeability. Keywords: nanostructured magnetic materials, frequency dispersion of magnetic permeability, magnetic force microscopy.

Seismic waves in medium with poroelastic/elastic interfaces: a two-dimensionalP-SVfinite-difference modelling

SUMMARYWe present a new methodology of the finite-difference (FD) modelling of seismic wave propagation in a strongly heterogeneous medium composed of poroelastic (P) and (strictly) elastic (E) parts. The medium can include P/P, P/E and E/E material interfaces of arbitrary shapes. The poroelastic part can be with (i) zero resistive friction, (ii) non-zero constant resistive friction or (iii) JKD model of the frequency-dependent permeability and resistive friction. Our FD scheme is capable of subcell resolution: a material interface can have an arbitrary position in the spatial grid. The scheme keeps computational efficiency of the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces). Numerical tests against independent analytical, semi-analytical and spectral-element methods prove the efficiency and accuracy of our FD modelling. In numerical examples, we indicate effect of the P/E interfaces for the poroelastic medium with a constant resistive friction and medium with the JKD model of the frequency-dependent permeability and resistive friction. We address the 2-D P-SV problem. The approach can be readily extended to the 3-D problem.

Hybrid ECM Blended Whale Optimization Derived Frequency-Selective Conformal EMI Shielding Structure Using Ferrite Substrate

In this work, both planar and conformal novel electromagnetic interference (EMI) shielding structures with customized properties are developed using a unique coupling of frequency-selective surface (FSS) and magnetic substrate. A hybrid equivalent circuit model (ECM) blended whale optimization (WO) technique is offered in the quest of customized shielding of L-, S-, C-, X-, and Ku-bands using a simple FSS geometry. The proposed structure is designed to shield L-, S-, C-, X-, and Ku-bands with a fractional bandwidth of 66.67%, 66.67%, 66.67%, 50.2%, and 40.50%, respectively. The frequency-dependent complex dielectric permittivity ( ε'- jε") and complex magnetic permeability ( μ'- jμ") of ferrite are measured using a waveguide measurement setup at X-band. The measured electromagnetic parameters are utilized in the modeling of planar and conformal ferrite-based frequency-selective shielding structures. An optimal ferrite coupled FSS shielding structure is fabricated, and its performance is evaluated using a non-destructive free-space microwave measurement setup. The measured results are found in congruence with the full-wave simulation and WO results. Besides, the conformal configuration of the proposed shielding structure is peculiarly investigated for inward and outward curved shielding structures for different values of radius of curvature. The proposed technique is intended to achieve a customized, simple, wideband, polarization-insensitive, and angular stable structure in the desired frequency regime, thus verifying the potential of the aforementioned technique for shielding applications.

Structure-sensitive magnetic properties of nanocrystalline Co2+-substituted Ni–Zn ferrite aluminates

We report on the preparation of cobalt-substituted nickel–zinc (Ni–Zn) ferrite aluminate nanoparticles (Ni0·3Zn0.7−xCoxFeAlO4) with x = 0.0–0.5 using sol–gel chemical synthesis method. The combination of metal ions forms the structure of a spinel cubic lattice for which the lattice parameter decreases and the crystallite size increases with increasing Co2+ substitution. We have determined the cation distribution of the ferrite aluminate with the help of X-ray diffraction analysis. Analysis of Fourier-transform infrared spectra demonstrates the formation of the spinel cubic structure. The nanocrystalline nature of the product with 28−34 nm sizes is determined from the transmission scanning-electron-microscope images. The saturation magnetization of the ferrite aluminates increases with increasing Co2+ ion substitution. The magnetocrystalline anisotropy also increases with increasing Co2+ substitution, influencing the coercivity of the ferrite aluminates. Analysis shows that the frequency-dependent complex permeability of the ferrite aluminates is controlled by domain-wall motion at lower frequencies and by spin rotations at higher frequencies.

Structural effect on Magneto-electric properties in (1-x) BiFe0.9La0.1O3 + xNi0.6Zn0.4Fe1.94V0.06O4 composites

Enhancement of magnetic as well as electric properties in BiFe0.9La0.1O3 (BLFO) with the addition of Ni-Zn ferrite have been studied on the compositions (1-x)BiFe0.9La0.1O3 + xNi0.6Zn0.4Fe1.94V0.06O4 (where, x = 0, 0.1, 0.2, 0.3, 0.5, 0.7 and 1.0). The samples were synthesized by the conventional ceramic methods sintered at 850 °C for 2 h. XRD studies revealed a normal distorted rhombohedral phase (R3c space group), cubic phase (Fd-3 m space group) and some impurity phases like Bi2Fe4O9 and Bi25FeO39 in the synthesized composites. The addition of Ni0.6Zn0.4Fe1.94V0.06O4 (NZVFO) successfully eliminated Bi25FeO39 phase from the derived composites. The average grain sizes (Dg) were estimated from FESEM images and found to decrease with the increase of NZVFO content in the samples. There is a large increment in saturation magnetization (MS) from 0.1 emu/g to 50.5 emu/g for adding NZVFO in BLFO. The frequency-dependent magnetic permeability μ and dielectric constant ε and dielectric loss tanδε have been measured with an impedance analyzer. The addition of NZVFO results in decreasing the permittivity ε' and dielectric loss (tanδε). The composites with 0.7 NZVFO addition shows a stable matching impedance Z/η0≈0.5 over a wide frequency range (5–70 MHz), demonstrating its possible applications in miniaturizing devices such as microwave antenna.