Gongwen Gn ,Dinn Zhng,* ,Jie Li ,Gng Wng ,Xin Hung ,Yn Yng ,Yiheng Ro,Xueying Wng,Huiwu Zhng,*,Ry T.Chen

a State Key Laboratory of Electronic Thin Films and Integrated Devices,University of Electronic Science and Technology of China,No.4,Section 2,North Jianshe Road,Chengdu 610054,China

bMicroelectronic Research Center,Department of Electrical and Computer Engineering,University of Texas at Austin,Austin,TX 78758,USA

Abstract The effects of Cd2+ ions on the microstructure,magnetic properties,and dielectric properties of Bi2O3-added MgFe2O4 ferrites(CdxMg1-xFe2O4, x=0.00,0.15,0.30 and 0.45) are obtained by adopting the solid-state reaction method at a low temperature (910 °C).The objective is to achieve matching impedances,low magnetic and dielectric losses (tan δμ and tan δε,respectively),and a relatively large miniaturization factor to reduce antenna size.Experimental results indicate that the cations occupying the tetrahedral (A) and octahedral (B)ion sites are redistributed,resulting in an enhanced super-exchange interaction between the two sublattices.As a result,improved magnetization,including the increase in saturation magnetization (41.74 emu/g) and decrease in coercivity (63.75Oe),is realized.The real part of permeability (μ′) also increases with increasing concentration of Cd2+ ions.When x is 0.15,matching impedances with equivalent μ′ and ε′ values are obtained over a long frequency range (1-150MHz).Moreover,the formation of a dense microstructure guarantees that losses occur at low orders of magnitude (tan δμ ≈10-2 and tan δε ≈10-3).Accordingly,these properties afford wide application perspectives for the proposed compounds in the high-frequency region,i.e.,from high-frequency to very-high-frequency bands.

Keywords: Cd-substituted Mg compounds;Magnetic properties;Dielectric properties;Matching impedance;Low loss;High frequency antenna.

1.Introduction

An enormous problem in the science of applied materials is the realization of miniaturization,integration,and excellent performance for high-frequency antennas in modern communication.In particular,such is the case with materials used as substrates [1].To satisfy these requisites,two corresponding facts should be earnestly considered.Of these,the preferential aspect pertains to the miniaturization factor (Mf) for antennas.This factor,which determines the physical dimension correlated with real permeability (μ′) and permittivity(ε′),is expressed byIn other words,the loaded substrate that exhibits magnetic and dielectric properties should be selected to obtain comparatively large μ′andε′values in magneto-dielectric materials.The natural existence of μ′can counterbalance the deterioration in radiation effi ciency and operation bandwidth.Such degradation is caused by the mutual coupling in the dielectric substrate with a largeε′.This is where the electric fiel is confine and surface wave excitation is followed by a wave trap that covers the substrate [3].To further enhance antenna efficien y based on the premise of ensuring miniaturization,a trade-off between low reflectio loss and excessive μ′orε′of electromagnetic waves is necessary.To significantl impact reflectio loss,impedance matching and loss attenuation are indispensable.Moreover,equivalent real permeability and permittivity (i.e.,μ′=ε′) should be achieved according to the transmission theory [4]:

whereZinis the normalized input impedance;fis the resonance frequency;d is the substrate thickness;Z0is the air impedance,and c is the velocity of light in the propagation medium.The equation can thus be expressed as follows.

If μ′=ε′,thenZinapproximatesZ0and matching impedances result.As one of the mainstream packaging technologies for passive integration,the low-temperature co-fire ceramic (LTCC) technology is suitable for modern antennas.These antennas can achieve high frequency,speed,reliability,and performance by adopting the multilayer interconnection technology,which improves miniaturization and integration [5].Magnesium ferrites with a special spinel structure are essential candidates for multifunctional and versatile applications,such as photochemical catalysis,sensors,medical treatment,and electromagnetic wave absorbers [6].For a microstrip antenna,Mg ferrites have a considerable potential as substrate because of their inherent advantages:high electrical resistivity,low coercivity,and low current loss.The moderate permeability and permittivity of such ferrites can achieve not only miniaturization but also relatively matching impedances with free space.Moreover,as typical soft magnetic materials,they are commonly used in high-frequency engineering applications because of their chemical,physical,and mechanical stabilities [7].The cations are indeterminately distributed at the tetrahedral (A) and octahedral (B) sites where their occupancy may differ depending on the synthesis process;accordingly,structure and performance could be tuned.Some common approaches,such as varying the synthesizing temperature and sintering environment as well as soft solution processing,have been employed [8,9].In addition to the foregoing,ion substitution is a particularly efficien approach by which the divalent and trivalent ions at the tetrahedral and octahedral sites may be redistributed [10].Accordingly,the structural,electrical,and dielectric properties of yttrium ion-substituted Mg ferrites have been investigated for high-frequency device fabrication [11].Microwave sintered Mg-Cd composites were also investigated as microstrip patch antenna substrates [3].The effects of Co and Cr-substituted Mg ferrites on the physical,structural,microstructural,dielectric,and magnetic properties have also been examined [12].It is noteworthy that this substitution technique has recently been widely employed.In our previous research,the effects of Cd2+substitution on the magnetic and dielectric properties of Mg-Co ferrites were investigated [13].Based on this previous study,it is possible to achieve a wider frequency broadening application range(1-150MHz) with lesser cation substitution (no Co3+),ensuring lesser cost and lower sintering temperature (910 °C).This means that the requisites for achieving synthesis conditions are fewer,thus making the proposed materials novel and creative.

Fig.1.Schematic of material preparation process.

The scientifi objective of this study is to explore the most suitable substitution amount of Cd2+for Mg2+to realize matching impedances,obtain an adequate miniaturization factor,and achieve a relatively wide operating frequency band.In order to reduce the sintering temperature and co-fir with Ag to achieve LTCC application,a 2.5-wt.% Bi2O3is added as sintering aid.Consequently,at a low melting temperature(820°C),Bi-Fe compounds(e.g.,Bi24Fe2O39)with high electrical resistivity and weak magnetism are produced [14].This research mainly investigates how the cation redistribution at sites A and B and the change in microstructure are induced by Cd ion substitution.Thereafter,the super-exchange interaction between sites A and B,microstructural mechanisms,and their effects on magnetic and dielectric properties are analyzed.It is predicted that the advancement in certain vital parameters,such asMfandZin,would provide an efficaciou guidance for the layout of high-frequency antennas.

2.Experimental procedures

2.1.Material preparation

The target bulk ceramic ferrites,CdxMg1-xFe2O4,withx=0.00,0.15,0.30,and 0.45 are prepared by the orthodox solid-state reaction technology.Raw oxide material powders,i.e.,MgO,Fe2O3,CdO,and Bi2O3,which are of AR grade with purity exceeding 99% and initial particle size in the range 1-5μm,are used.The synthesis route mainly includes raw material configuration firs ball milling,drying,pre-sintering,secondary ball milling,drying,hydroforming,and fina sintering,as shown in Fig.1.The precursors are stoichiometrically weighed in the same proportion as that inwhich they should appear in the processed objective compositions.This is followed by an intensive 12-h firs ball milling with deionized water and zirconium balls of different diameters in a planetary ball mill.The weight ratio of raw materials to deionized water to zirconium balls is 1:2:1.5.The total volume of raw materials in each mill jar is 0.5mol (approximately 100g);specifi quantities are listed in Table 1.All mixtures are dried off in a thermostat,and the milled powders are thereafter screened through a 120-mesh sieve for uniform mixing.The mixtures are then pre-sintered in a welding furnace at 1100 °C for 4h for the raw materials to undergo initial reaction.To obtain a uniform fina particle size of approximately 0.5μm of mixed powders,the entire amount of pre-sintered powders is further subjected to 12h of ball milling with the addition of a 2.5-wt.% Bi2O3(Table 1).The mixed powders are dried off and again screened through an 80-mesh sieve.The dried powders are then ground into granules by adding a 15-wt.% organic glue (PVA).Using a mold,the granules are thereafter pressed into rings and discs of certain sizes at a 10-MPa pressure.This step is immediately followed by calcining,in which the pressed prototypes are sintered at 910°C for 4h to implement the LTCC process.All experimental procedures are performed in an air-conditioned room at a temperature of approximately 30 °C.

Table 1 Weights of MgO,Fe2O3,CdO,and Bi2O3 in each ball jar corresponding to various x values.

2.2.Characterization

The phase and crystallinity of ferrites are characterized by X-ray diffraction (XRD;DX-2700,Haoyuan Co.) with the Cu-Kαradiation at a wavelength ofλ=1.5418 °A and a diffraction angle (2θ) configuratio of 10°-80°.With the XRD measurement data,the crystal structure is further investigated by Rietveld refinemen using the Global Sustainability Assessment System software.It is highly possible that spinel-structured ferrites are mixed with the acceptor ferrites,and Mg2+,Fe3+,and the substituted Cd2+ions occupy sites A and B.Accordingly,the initial model is assumed as

wherexis the amount of substituting Cd2+ions,0 ≤λ≤1 and 0 ≤η≤2 are parameters.This assumption is based on the cation distribution law.In the refinemen beginning,the global (2θ-zero and background) and structural (lattice constant,atomic coordinates) parameters are refined Then the cation occupations are refinedλ,ηare f rst assumed to be(1-x) and 0.That is to say,all Mg2+ions occupy at the A site and Fe3+ions occupy at the B site.Then steps of iteration are run with decreasingλand increasingη.Finally,the parameters are fi ed and the refine results,lattice constant,goodness of reliability,theoretical density and cations occupations were educed and the subscriptsλandηare determined.The magnetic and dielectric behaviors of the compounds over the frequency range 1 MHz-1GHz are recorded using an HP-42391B RF impedance analyzer.An auto density tester (GF-300D,AND Co.) is employed to calculate the bulk density using the Archimedes principle.The sintered ring samples are cut into approximate quarter rings with a height and length not exceeding 15 and 26mm,respectively;thereafter,they are ultrasonically cleaned and dried.The surface morphology of the cross-section is captured and magnifie by scanning electron microscopy (SEM;JEOL,JSM-6490);the working conditions include a 20-kV high voltage,5.5-mm distance,5-nm spot size,and 6000×magnification The grain size distribution is estimated using Image-Pro Plus software.A Quantachrome Autosorb 1 instrument is also employed to analyze the surface parameters (e.g.,surface area,pore volume,and size distribution) of various Cd2+ion-substituted Mg ferrites using the BET (Brunauer-Emmett-Teller) method in the N2atmosphere.The samples are degassed at 150 °C for 6h to remove all absorbed fragments.The magnetization measurement is performed using a vibrating sample magnetometer(MODEL,BHL-525) with a broad magnetic fiel scope of ±5000Oe.

3.Results and discussions

3.1.Phase composition and crystal structure

Fig.2 shows the wide and regional angle views of the X-ray powder diffraction patterns of various Cd2+ionsubstituted MgFe2O4ferrites.Fig.2(a) shows the patterns of ferrites with a full 2θmeasurement range 10-80°.It is detected that two different phases appear in the synthesized ferrites:main MgFe2O4spinel phase and Bi-Fe (Bi24Fe2O39,BFO) phase.The main phase is confirme by referring to the standard spinel ferrite MgFe2O4(space group Fd-3m 227,JCPDS No.22-1086) peaks,indicating that normal spinel magnesium ferrites are obtained.The second phase,i.e.,the Bi-Fe (Bi24Fe2O39,BFO) dielectric phase (JCPDS No.42-0201),is also observed;it is found that the added Bi2O3produced BFO compounds.Further,the shift in all spinel peaks to lower 2θvalues appears with increasing quantities of Cd2+ions,as revealed by the enlarged view of the region approximately 35° of 2θin Fig.2(b).This can be explained by the substitution of Cd2+ions with an ionic radius (0.095 °A)greater than that of Mg2+(0.072 °A) ions,boosting the lattice constant (Table 2).The increment in lattice constant is mainly attributed to the following relationship:

Table 2 Rietveld refinemen results of X-ray powder diffraction sample patterns with site A ions,site B ions,lattice constant (l) (with the last digit of the standard deviation of a four-digit decimal),reliability (χ2, ωRp,and Rp),and occupation of Cd (Co) ions of various Cd2+ ion (Ci)-substituted Mg ferrites.

Table 3 Average grain size (AG),theoretical density (ρT),experimental density (ρE),and relative density (ρR) of Mg1-xCdxFe2O4 ferrites with x=0.00-0.45.

whereh,k,andlare Miller indices of planes with the interplanar spacing,dhkl.On the other hand,the change in the crystallite size (D) of samples is investigated using Debye-Scherrer equation [15]:

Fig.2.X-ray powder diffraction patterns of Bi2O3-added Mg1-xCdxFe2O4 ferrites with x=0.00-0.45 compared to standard patterns of MgFe2O4 and Bi24Fe2O39.(a) Full measurement range of 2θ;(b) Expanded view of region approximately 35° of 2θ.

whereλis the X-ray wavelength;θis Bragg’s angle;βis the full width at half maximum (in radian).Based on this relationship,the crystallite sizes of ferrites are obtained and summarized in Table 2.For the samples with increasing quantities of Cd2+ions,a decreasing trend inDis observed.

To further study the effect of ion substitution on the microstructure of Mg compounds,the density is subsequently investigated.The theoretical density (ρT) is obtained using the following equation:where MWis the molecular weight,andNAis the Avogadro constant,as listed and shown in Table 3 and Fig.3,respectively.A distinct decrease in the variation tendency of relative density is observed with increasing x.The relative density (ρR) can be obtained based on experimental bulk density (ρE) using the following equation:It is found that the actual and relative densities steadily decrease with x.This indicates that the densificatio also decreases with the introduction of Cd2+ions,contributing to pore volumes and grain boundary insulation.Meanwhile,the lowestρRvalue observed (exceeding 89%)indicates that a dense structure has formed in all samples.

Fig.3.Variation in bulk and relative densities of various Gd2+ ions-substituted Mg ferrites.

The structural details of CdxMg1-xFe2O4ferrites are characterized by Rietveld refinemen based on XRD patterns and the descriptions above;results are shown in Fig.4 and summarized in Table 2.The foregoing shows that the refine patterns are consistent with the measurements that have relatively low degrees of weighted profil factor (ωRp),profil factor(Rp),and reliability factors(χ2).The cation distribution listed in Table 2 shows that the substituted Cd2+ions only occupy site A,whereas Mg2+and Fe3+ions occupy both sites A and B.The occupation of Mg/Fe randomly changes with the increase in the quantity of Cd2+ions,leading to an inconstant super-exchange interaction[16].A three-dimensional schematic of the unit cell of Cd2+ion-substituted Mg ferrites with a spinel structure is shown in Fig.5.In this structure,each divalent metal(Cd2+/Mg2+)ion combines with four O2-ions to form site A,and the remaining cations are surrounded by six O2-ions,thus forming site B [17].

3.2.Microstructure analysis

Fig.6(a-d) shows the SEM images of Mg1-xCdxFe2O4ferrites with microscopic views magnifie 6000×.Only a portion of the spinel platelet particles is observed in the images,and most of the other particles are irregularly shaped.This could be attributed to the introduction of Bi2O3in liquid form at 910 °C (experimental temperature).The Bi2O3can either fl w into the gaps between adjacent spinel particles,producing relatively large particles with a denser structure,or individual BFO particles may form.In general,based on the Image-Pro Plus software,all particles are in the size range 0.6-1.1μm.The increase in Cd2+ion concentration is observed to lead to the increase in average particle size from 0.67 to 1.03μm.This is obtained through the use of a statistical method with the following equation [18]:

whereLis the total line length;MandNare the magnificatio and total number of intercepts,respectively.

A slightly higher pore content is also observed as the quantity of Cd2+ions increases;this is attributed to the formation of bulky spatium when more grains with irregular shapes are produced.As a result,the bulk and relative densities,listed in Table 3,Table 4 and Fig.3,decrease as the quantity of Cd2+ions increases.

Table 4 Results of BET surface areaa nalysis of Cd2+ion-substituted Mg ferrites with various x compositions.

3.3.Surface analysis (BET)

To further understand the morphology,the properties related to the surface,microtopography,and porosity of all samples are characterized using the widely used Brunauer-Emmet-Teller (BET) technique.With this method,the isotherms can be obtained by N2physisorption,yielding certain key surface parameters,such as surface area,pore volume,and pore size.The pore information and physisorption curves obtained by the BJH model of Cd2+ion-substituted Mg ferrites are presented in Fig.7(a and b).The loop in Fig.7(a),named“Langmuir hysteresis curve,”indicate the mesoporous performance of all samples.It is observed that N2physisorption increases as the volume of available pores increases,thus determining the shape of an available pore in a sample [19].

The BET surface area,pore volume,and average size are summarized in Table 4.It is observed that the surface area monotonically increases from 71.075 to 123.952 m2/g as the quantity of Cd2+ions increases.As shown i n Fig.8(a),this tendency is consistent with the decrease in crystallite size calculated through XRD data because of their inversely proportional relationship.The pore size distributions are derived from the isotherms obtained using the Barrett-Joyner-Halenda (BJH) model [20].The pores in all samples have an average radius in the range 3.5-6.5nm and are observed to be completely mesoporous.The overall average pore size shows an upward trend with the increase in the quantity of Cd ions.Fig.8(b) shows the composition-dependent variance in the pore volume vs.pore radius of Cd2+-substituted samples.The pore volume increases and saturates as the pore radius increases to 25nm with close initial values and rapidly increasing growth speed.

Fig.4.Rietveld refinemen results of X-ray powder diffraction patterns of Mg1-xCdxFe2O4 ferrites with various Cd2+ ions.

Fig.5.Crystal structure of Cd2+ ion-substituted Mg ferrites.

3.4.Magnetization analysis

The change in magnetization as a function of the magnetic fiel in all samples is shown in Fig.9(a).The hysteresis loops indicate an enhanced magnetization with the increase in Cd concentration and visible soft magnetic properties of all samples.Two significan magnetic parameters,i.e.,saturation magnetization (Ms) and coercivity (Hc),are derived;their variations are shown in Fig.9(b).Evidently,Msmonotonically increases from 32.07 to 41.74 emu/g as x increases from 0.00 to 0.45 ions;this can be explained using Neel’s two-sublattice (site A and site B sublattices) model [21].Based on this model,the magnetic order behaves as ferromagnetism,and magnetization is the resultant of site A (MA)and site B (MB) magnetization moments,which follow the anti-parallel collinear relationship.The super-exchange interaction between sites A and B performs a critical function in determining the magnetization over A-A and B-B interactions:it aligns all magnetic spins in site A in one direction and those in site B in the opposite direction.Based on the Rietveld refinemen results,the substituent Cd2+ions occupy site A,taking the place of magnetic Fe3+ions and preventing their migration to site B.Consequently,the quantity of Fe3+ions increases at site B and decreases at site A.In the present ferrites,Fe3+ions with a magnetic moment of 5 μB are the only ions that determine the magnetization because Mg2+and Cd2+ions are nonmagnetic.Therefore,the net magnetic moments exhibit an increasing trend as a result of the increasing difference between site A and site B magnetization moments caused by the increase inMAand decrease inMB[22].

Fig.6.Surface SEM micrographs of Mg1-xCdxFe2O4 ferrites sintered at 910 °C.(a) x=0.00,(b) x=0.15,(c) x=0.30,and (d) x=0.45.

Fig.7.(a) BET N2 adsorption-desorption curves and (b) average pore radius distribution of Mg1-xCdxFe2O4 ferrites.

The variation in coercivity (Hc) exhibits a trend opposite to that ofMs.As shown in Fig.9(b),Hcdrastically decreases from 98.15 to 70.88Oe as x increases from 0.00 to 0.15,and then gradually declines to 63.75Oe when x increases to 0.45;this indicates that the demagnetization fiel decreases with Cd substitution.This downward trend is caused by the negative magnetic crystal anisotropy of Cd,leading to a decreased magneto-crystalline anisotropy constant (Kc),which performs a key and positive function in determiningHc.In general,Hccan be related toMsthrough Brown’s relationship [23].This relationship theoretically shows thatHcandMshave a negative correlation,which is found to be consistent with experimental results.

3.5.Complex permeability analysis

Fig.8.(a) Variation of BET surface area and average pore radius;(b) variation of pore volume as a function of pore radius for Mg1-xCdxFe2O4 ferrites.

Fig.9.Magnetic properties of processed Mg1-xCdxFe2O4 ferrites with various quantities of Cd2+ ions (x=0.00-0.45).(a) Magnetic hysteresis loops;(b)Saturation magnetization and coercivity.

Fig.10.Complex magnetic and dielectric spectra of proposed Mg1-xCdxFe2O4 ferrites with x=0.00-0.45.(a) Complex magnetic permeability;(b) complex dielectric permittivity.

The frequency-dependent complex permeability(μ=μ′+jμ’′) and permittivity (ε=ε′+jε’′) of the assynthesized Mg1-xCdxFe2O4ferrites over the frequency range 1 MHz-1GHz are presented in Fig.10(a and b,respectively).As shown in Fig.10(a),the real permeability part (μ′) monotonically increases as Cd2+ions are substituted.On the one hand,this increase can be attributed to Cd substituents that do not merely raise the magnetic moment but also lower the anisotropy constant (Kc) according to the following [24]:whereλsδrepresents the magnetic internal stress,which is insignifican because of its low order of magnitude.HigherMsand lowerKcvalues lead to increased μ′.On the other hand,μ′is positively correlated to spin rotation and domain wall motion.In particular,the enhanced domain wall motion results from the larger domain because of the increase in grain size as shown by the SEM images,leading to higher μ′values.Generally,the relationship between spin rotation and domain wall motion can be described by the following [25]:

whereμdandμspindenote the susceptibilities of domain wall and intrinsic spin,respectively;γis the domain wall energy,which is a constant derived from the substituent.Accordingly,μ′is dominated byMsandD,which are reported to have increased.On the contrary,as shown in Fig.8(a),the observed cutoff frequency (define asfr) exhibits an inverse change trend as μ′;this could be explained by the following relationship [26]:

whereμiis approximately equal to μ′;ris a constant.Through comparison,it is observed that relatively high μ′andfrvalues could be obtained when the concentration of Cd2+ions is 0.15.The imaginary part (μ’′) of permeability exhibits a non-response as a function of the frequency under consideration,and the order of magnitude ofμ’′is between 10-1and 10°.As a result,a lower order of magnitude (from 10-2to 10-1) of magnetic loss (tanδμ) define by the quotient ofμ’′over μ′is achieved [25].Herein,tanδμresults from the lag of the domain wall motion relative to the operating alternating magnetic fields It is composed of three parts:eddy current loss (tanδe),hysteresis loss (tanδa),and residual loss (tanδc) [10],The firs in the list,tanδe,results in energy and power losses,stemming from the electromagnetic induction that mainly depends onHc;tanδais primarily affected by the processing of materials,such as uniformity,particle size,and porosity;tanδc,being correlated with Fe2+ions,only results in a marginal change in the total loss.It can be concluded that the previous discussion on various properties may be beneficia to achieve a low order of magnitude of magnetic loss (tanδμ).

3.6.Dielectric property analysis

The complex permittivity shown in Fig.10(b)demonstrates that both real (ε′) and imaginary parts (ε’′) of all ferrites remain smooth as the frequency initially increases from 1 to 500MHz and then rapidly reaches the peak in the frequency range 500 MHz-1GHz.Moreover,the values ofε′for all samples are within a relatively high range (20-30F/m).This indicates that the effect of Cd2+ions on dielectric properties is not as significan as that on magnetic properties.Furthermore,the addition of Bi2O3(which produces BFO) to the dielectric phase contributes to a higher dielectric constant [27].

Fig.11.Relative impedance (RI) and miniaturization parameters (Mf) at fi e representative frequency points (1,10,50,100,and 150MHz) of Mg1-xCdxFe2O4 ferrites with x=0.00-0.45.

The small scale variation ofε′values can be attributed to the polarization mechanisms—low displacement polarization and relaxation polarization in the ferrites.It is also found that the order of magnitude of the imaginary part (ε’′) of permittivity for all samples varies from 10-2to 10-1.This leads to the dielectric loss (tanδε) in the order 10-4-10-3,which is extremely low for antenna substrates.

Generally,tanδεresults from three factors,i.e.,relaxation,conduction,and resonance losses.The relaxation loss is related to the relaxation polarization,which lags behind the applied field especially in higher-frequency regions.Conduction loss is mainly caused by the conductivity generated by structural factors,such as purity grade,non-uniform grain boundary,and oxygen vacancies.The resonance loss exists in a considerably higher frequency band;this is considerably beyond the scope of this work [28].

3.7.Parameters comparison

As shown in Fig.10,it is possible to obtain objective ferrites with a 0.15 concentration of Cd2+ion substituents that possess the most suitable magnetic-dielectric properties.Certain key parameters,including μ′,tanδμ,ε′,tanδε,relative impedance (Zin/Z0),and miniaturization parameters (Mf)at the fi e representative frequency points (1,10,50,100,and 150MHz) of such ferrites are summarized in Table 5 and shown Fig.11.The following are observed over a wide frequency range (1-150MHz).(1) Both magnetic and dielectric losses have relatively low orders of magnitude,i.e.,tanδμ≈10-2and tanδε≈10-3,respectively.(2) The relative impedance(RI=Zin/Z0)approaches 1,and the largest discrepancy occurs at approximately 100MHz where the resonance frequency of μ′is achieved.(3) The miniaturization parame-are relatively large and within a narrow range (23-26).

Table 5 Real permeability (μ′) and permittivity (ε′),magnetic and dielectric losses (tan δμ and tan δε,respectively),relative impedance (RI),and miniaturization parameters (Mf) at fi e chosen frequency points (1,10,50,100,and 150MHz) of Mg1-xCdxFe2O4 ferrites with x=0.00-0.45.

4.Conclusions

In this work,the function of Cd2+ion substituents in tuning the magnetic-dielectric properties of MgFe2O4ferrites has been comprehensively investigated.It is found that the substituted Cd2+ions occupy site A,resulting in cation (Mg2+and Fe3+) migration between sites A and B;this leads to an enhanced super-exchange interaction between the two sites.As a result,the enhanced magnetization including increased saturation magnetization(Ms=41.74 emu/g),and reduced coercivity (Hc=63.75Oe) are obtained,thus enhancing the soft magnetic properties.The monotonous increase in real permeability (μ′) caused by the increase inMswell agrees with the real permittivity (ε′) promoted by Bi2O3.This yields a considerable miniaturization factor (Mf≈24) and well-matched impedances(Zin/Z0≈1)between the material and air medium over a long frequency range (1-150MHz).Moreover,the low orders of magnitude of magnetic and dielectric losses (tanδμ≈10-2and tanδε≈10-3,respectively) ensure that low amounts of energy and power are lost on stream.These behaviors are anticipated to result in an exceptional breakthrough in the application of such Mg-Fe ferrites in the high-frequency region.

Acknowledgments

This work was supported by National Key Scientifi Instrument and Equipment Development Project No.51827802,and by Major Science and Technology projects in Sichuan Province Nos.2019ZDZX0026 and 20ZDYF2818,and by the National Natural Science Foundation of China No.51872041,and by Foundation for University Teacher of Education of China No.ZYGX2019J011.