Tunable Negative Permittivity with Fano-like Resonance and ... in pdf/JPCC_2017 Sun.pdfTunable Negative Permittivity with Fano-like Resonance and Magnetic Property in Percolative Silver/Yittrium

Tunable Negative Permittivity with Fano-like Resonance andMagnetic Property in Percolative Silver/Yittrium Iron GarnetNanocompositesKai Sun,†,‡ Runhua Fan,*,† Yansheng Yin,† Jiang Guo,‡ Xiaofeng Li,† Yanhua Lei,† Liqiong An,†

Chuanbing Cheng,‡,§ and Zhanhu Guo*,‡

†College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, P. R. China‡Integrated Composites Laboratory (ICL), Department of Chemical & Biomolecular Engineering, University of Tennessee, Knoxville,Tennessee 37996, United States§Dezhou Meta Research center of Innovative Materials, Dezhou 253000, P. R. China

ABSTRACT: Composites with negative electromagneticparameters can be promising candidates for metamaterials.In this paper, the impedance, permittivity, and permeabilitywere investigated in the silver/yrrium iron garnet (Ag/YIG)composites, which was fabricated by in situ synthesis process.In the vicinity of the percolation threshold, the dielectric loss isdominated by conduction and polarization. When thepercolative state was reached, the negative permittivity withFano-like renonance (an asymmetric resonance) was observed.Furthermore, the negative permittivity behavior was attributedto inductive character, and the LC resonance was responsible for the Fano-like transition from negative to positve permittivity. Inaddition, it was demonstrated that the permeability of Ag/YIG composites presented frequency dispersion due to the domainwall motion and the gyromagnetic spin rotation. The percolative Ag/YIG composites with tunable negative permittivity havegreat potential in the field of electromagnetic attenuation, shielding, and antenna.

1. INTRODUCTION

The percolation phenomenon, which is a classic and significantbehavior in physics, is widespread in heterogeneous multi-components of materials.1−4 When the concentration offunctional fillers approaches a critical value (i.e., percolationthreshold), the filler particles come into contact with each otherand establish a continuous network throughout the system.Along with the change of microstructure, the physicalproperties of the composites also undergo an abrupt shift andbring about attractive performances, such as high dielectricconstant or high electrical or thermal conductivity.5−8 Thepercolation behaviors especially near percolation threshold havedrawn intensive attention due to their fascinating propertiesand potential applications in the field of thermal storage,9 light-emitting diodes,10 and charge-storage capacitors,11 etc. It hasbeen proved that conductive fillers can dramatically increase thepermittivity of polymer−metal composites by taking advantageof the percolation threshold.12 Accordingly, extensive inves-tigations13−19 have been particularly focused on the compositeswith high dielectric constant and low dissipation, due largely totheir promising applications in microelectronics, electricalengineering, and even biomedical engineering.12

When the fraction of conductive filler exceeds the percolationthreshold, the negative permittivity can be achieved in thecomposites,20−26 which have great potential for electromagneticinterference shielding,23 near field amplifying,27 antenna,28 and

sensors,29−31 etc. Zhong et al.32 obtained negative permittivityat the kilohertz region in percolative polymer nanocomposites,due to the dielectric resonance of polarization. Guo et al.33,34

also achieved negative permittivity at lower frequency region inpolymer composites, when carbon nanotube or graphene wasbeyond the percolation threshold. Moreover, Wang et al.35

reported negative permittivity with a low-frequency plasmonicoscillation of delocalized electrons in metallic cobalt networksformed in the alumina matrix.As an alternative to metamaterials, which are composed of

periodic structure units and possess peculiar properties, Chui etal.36 theoretically investigated that the negative permittivity andnegative permeability can be simultaneously attained byincorporating metallic magnetic nanoparticles into insulatingmatrix. Shi et al.37,38 initially observed double negative propertyin ceramic matrix composites with nickel or iron particles in theradio-frequency region, which expanded the scope ofmetamaterials. In addition, Tsutaoka et al.39,40 obtainednegative permittivity and negative permeability at microwavefrequency regime in percolative polymer (polyphenylenesulfide) composites combined with conductive copper andmagnetic yttrium iron garnet (YIG). Consequently, the

Received: March 3, 2017Revised: March 16, 2017Published: March 20, 2017

Article

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© 2017 American Chemical Society 7564 DOI: 10.1021/acs.jpcc.7b02036J. Phys. Chem. C 2017, 121, 7564−7571

composites with tunable negative permittivity are expected tobe promising candidates for double negative materials, whichprovides a novel avenue to design metamaterials.Metal−ceramic composites are excellent candidates to

fabricate multifunctional devices owing to the combineddifferent properites of metal and ceramic, which have hugecontrast especially in electrical and magnetic properties.41−43

Compared with the reported ceramics including alumina35,44

and silicon nitride,4,45 YIG was widely used for high-frequencyelectronic devices such as resonators,46 filters,47 and phaseshifters48 owing to its unique physicochemcial proeprties.Meanwhile, compared with the reported metals includingcopper,6 iron,49 and alloy,50 silver was selected due to itsexcellent electrical conductivity and oxidative stability.51 Hence,Ag/YIG composites can be promising candidates to achievetunable electrical and magnetic property by tuning theircompositions and tailoring their microstructures. In previousresearch,52 the negative permittivity was achieved in porousAg/YIG composites; however, the porosity was detrimental totheir mechanical and electromagnetic properties, limiting theirdevelopment and applications. Additionally, it was difficult toeffectively control the content of functional phases via achemical impregnation method.Herein, an effective and versatile strategy (i.e., in situ

synthesis) was used to prepare percolative Ag/YIG composites.

The impedance, permittivity, and permeability of Ag/YIGcomposites were investigated. There was an obviouspercolation phenomenon observed with the increase of silvercontent. With the geometric transition of the silver particlesmicrostructure, the capacitive−inductive character transitionand positive−negative permittivity transition occurred in Ag/YIG composites. The nature of the negative permittivity wasstudied and attributed to the inductive character by equivalentcircuit analysis. In addition, the dielectric loss mechanism ofheterogeneous composites in the vicinity of percolationthreshold was further clarified. The dependences of perme-ability on frequency and silver content in percolative Ag/YIGcomposites were also explored.

2. EXPERIMENT2.1. Preparation Process. The yttrium iron garnet

Y3Fe5O12 (YIG) powders were prepared by a conventionalsolid state reaction.27 The raw materials, i.e., Y2O3 and Fe2O3powders, were mixed in 3:5 stoichiometric ratios and sinteredat 1573 K for 6 h. The prepared YIG powders added withdifferent mass fractions of silver oxide (5, 15, 25, 30, and 40 wt%, which were denoted as samples AY5, AY15, AY25, AY30,and AY40, respectively) were dispersed in absolute ethanol anduninterruptedly milled for 10 h. After ball-milling and sieving,the powders were pressed into green bodies at 30 MPa

Figure 1. XRD patterns and the microstructures of Ag/YIG composites: (a) the phase characterization of YIG powders and Ag/YIG composites,(b−f) the SEM images of Ag/YIG composites with 5, 15, 25, 30,and 40 wt % silver contents, respectively. The red and blue areas in (e) show thecontinuous and isolated silver particles. All the scale bars in SEM images are 10 μm.

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pressure. The compact bulks were sintered at 1323 K for 1 h ina resistance furnace. During the sintering process, the silveroxide was decomposed into metallic silver and YIG couldmaintain its chemical stability. It meant that the Ag/YIGcomposites with different silver contents were fabricated byone-step in situ synthesis process.2.2. Characterization and Measurement. The phase

identifications of the composites were investigated by X-raydiffraction (XRD; Tokyo, Japan) using the Rigaku D/max-rBX-ray with Cu Ka radiation. The fracture surface morphologiesof the composites were observed by SU-70 field emissionscanning electron microscope (FESEM; Tokyo, Japan).The electromagnetic parameters measurements were carried

out at room temperature using an impedance analyzer E4991A(Agilent Technologies Co. Ltd.) in the frequency range from10 MHz to 1 GHz. The samples were machined into disks witha dimension of 12.5 mm in diameter and approximately 2.0 mmin thickness for impedance and permittivity measurement. Thesilver paste was painted between samples and electrodes toeliminate the contact resistance. After calibration andcompensation for the analyzer, the samples were put betweenthe two planar electrodes of 16453 A dielectric test fixture forpermittivity measurement, under a 100 mV ac voltage.53 Theimpedance data (Z′ and Z″) were converted to capacitance Cand resistance R for permittivity calculation ε′r = Cd/Aε0 andεr″ = d/2πfAε0, where C is capacitance, d is the thickness ofsample, f is the test frequency, R is the resistance, A is the areaof the electrode, and ε0 is the permittivity of vacuum.The 16454A test fixture was used to measure the

permeability under 100 mA ac current. The samples wereprocessed into toroidal form (inner diameter is 6.5 mm andouter diameter is 19.0 mm). The permeability μ′r = 2π(Z −Z0)/[jωμ0d ln(c/b)] + 1, where Z and Z0 are the impedances ofthe test fixture with and without the sample mounted; d, c, andb are the thickness, outer diameter, and inner diameter of the

sample; ω is the test angular frequency; and μ0 is thepermeability of vacuum.

3. RESULTS AND DISCUSSION

Figure 1 shows the XRD patterns and SEM images of Ag/YIGcomposites. It can be seen that no impurity phase was observedin the sintered samples, except for silver (JCPDS card 04-0783)and yttrium iron garnet (JCPDS card 43-0507). In other words,the silver oxide was totally decomposed into metallic silver, andthere was no other reaction during the sintering process.Therefore, the Ag/YIG cermet composites were successfullyfabricated. In the SEM images, the silver particles wererandomly distributed in the matrix; with an increase in silvercontent, the isolated silver particles enhanced their inter-connection and aggregated together to form clusters, eventuallyestablishing a percolating network (in the red area of Figure1e). In addition, partial islandlike silver particles were stillrandomly distributed in YIG matrix (in the blue area of Figure1e). Further increasing the silver loading level, the isolatedsilver particles were hardly observed and gradually formednetworks (Figure 1f).Figure 2 shows the frequency dispersion of the complex

permittivity for Ag/YIG composites with different silvercontents. The dielectric constant of the resultant compositeswas gradually enhanced with the increase of silver particles(shown in Figure 2a). Additionally, the real permittivity spectrapresented frequency-independent behavior, which demonstra-ted that the frequency response from the matrix becamedominant when the content of silver filler was relativelylow.54,55

Further improving silver content, the spectra of the complexpermittivity exhibited relaxation behavior; the dielectricconstant markedly reached up to several hundred, because ofthe charge accumulation at the interfaces between silver andYIG particles. The interfacial polarization, also known as the

Figure 2. Complex permittivity spectra of Ag/YIG composites. (a) and (b) Complex permittivity of AY5, AY15, and AY25. (c) and (d) Real andimaginary permittivity of AY30 and AY40. The inset in (c) shows the local enlarged view of Fano-like resonance.

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Maxwell−Wagner-Sillars effect,56 is responsible for theenhancement of dielectric constant. It is worth noting thatthe spectrum of the imaginary part manifested a special shape,which can be divided into two parts (Figure 2b).In the vicinity of the percolation threshold, partial silver

particles were gradually agglomerated and brought about theleakage current.57 Hence, the dielectric loss (εr″) was ascribedto the combined contributions of conduction and polar-ization,58 which could be described as eq 159

ε σωε

ε εω τ

ωτ ε ε″ = +−

+= ′ + ′∝ ′ ′

1r0

s2 2 c p

(1)

where ω is angular frequency, σ is dc conductivity, τ isrelaxation time, ε0, εs, and ε∝ are the vacuum, static, and high-frequency dielectric constant, respectively. εc″and εp″ representthe dissipation in the form of conductivity and polarization,respectively. The former refers to electrical leakage, whichmakes a great contribution in lower frequency. The lattermeans energy loss determined by polarizing dipoles under theaction of ac electric field. When the alternative frequency ofexternal field is too slow or too fast, the dielectric loss is soweak as to be neglected; the maximal dielectric loss appears atthe critical frequency.27 Therefore, in the lower frequencyregion (part I of Figure 2b), there was an apparently linearcorrelation between εr″and frequency, which suggestedconductive carriers played a primary role in dielectric loss.6

With the increase of frequency, the energy loss in thecomposites was gradually dominated by polarization ratherthan conduction, so the permittivity exhibited relaxationcharacteristic and the εr″ spectrum showed a loss peak at thecritical frequency (part II of Figure 2b). For heterogeneouscomposites with conductive fillers, the conductive carriers andpolarizing dipoles make a combined effect on the energy lossespecially near the percolation threshold.58 Further improvingthe conductive silver content (sample AY40), there also existsleakage current due to the conductive silver clusters. Hence, theconduction electrons made a primary contribution to thedielectric loss at lower frequency, resulting in the rapid decreaseof initial imaginary permittivity with increasing of thefrequency.When silver fraction exceeded the percolation threshold, the

negative permittivity behavior was observed, which indicatedthat there existed a percolation phenomenon between samplesAY25 and AY30. Compared with the negative permittivitybehavior in previous investigations,60−62 interestingly, the realpart of permittivity with a Fano-like resonance went across thezero point (Figure 2c), where the dielectric constants ofsamples AY30 and AY40 switched from negative to positive atnearly 309 and 40.3 MHz, respectively. Meanwhile, there was ahuge loss peak obtained at the zero crossing point in Figure 2d.Similarly, the dielectric resonance with negative permittivitywas also reported in Fe/Al2O3 composites.38,63 Further,investigations demonstrate that the external factors includingthe sample thickness, size, and sample−electrode contact areado not affect the Fano-like resonance behavior. Hence, itreveals that the resonance behavior stems from the intrinsicproperty rather than the dimensional resonance.63 In order toclarify the mechanism of negative permittivity behavior andFano-like resonance, the impedance property of Ag/YIGcomposites was further investigated in the following sections.The frequency dependence of reactance Z″ for Ag/YIG

composites is presented in Figure 3. In the samples with lowersilver content, the value of Z″ was negative throughout the test

frequency region (Figure 3a), which means the voltage phaselags behind current phase. It was demonstrated that thecomposites exhibited capacitive character.27 With increasing ofthe silver loading level, the absolute of reactance was reduced.When the resultant composites reached the percolative state,the reactance became positive and presented inductivecharacter, which meant that there was a capacitive−inductivetransition near the percolation threshold. A similar phenomen-on was also achieved in perovskite La1−xSrxMnO3 materials.

64

In addition, with the increase of frequency, the reactance ofsamples with high silver content (AY30 and AY40) changedfrom positive to negative at nearly 309 and 40.3 MHz,respectively, which corresponded to the Fano-like resonancesfrequency with a negative−positive permittivity transition(Figure 2c). Combined with the variation trend of the realpermittivity and reactance in Ag/YIG composites, it suggestedthat the reactance played an important role in the permittivity.It was indicated that the complex impedance and complexpermittivity can be expressed as the equation65

επ

* = −*

if C Z2 0 (2)

επ

′ = − ″′ + ″

⎜ ⎟⎛⎝

⎞⎠f C

ZZ Z

12r

02 2

(3)

where f is the test frequency, Z*, Z′, and Z″ are the complex,real, and imaginary impedance, and C0 is the capacitance ofvacuum. It is shown that the imaginary impedance (i.e.,reactance) determines the real permittivity. Namely, when Z″ <0, the real permittivity became positive; when Z″ < 0, the realpermittivity was negative. Therefore, the positive permittivity isattributed to capacitive character (Z″ < 0) and the negativepermittivity results from the inductive character (Z″ > 0).The equivalent circuit analysis was performed to clarify the

origin of capacitive and inductive characters in the resultant

Figure 3. Dependence of reactance on frequency for Ag/YIGcomposites. (a) and (b) are the reactance spectra of Ag/YIGcomposites with low and high silver contents, respectively. Thedashed line is the zero baseline.

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composites. The relationship between permittivity andimpedance of the composites far below the percolationthreshold has been explained in previous study.27 Herein,taking the special permittivity spectra in the vicinity ofpercolation threshold into consideration, we focus on revealingthe relationships between impedance and permittivity near andabove percolation.The real and imaginary impedance spectra near and above

the percolation threshold are shown in Figure 4a and b,

respectively. The fitted curves of impedance are in goodagreement with the experimental results. The values ofreliability factor of the fitting results for sample AY25 andAY40 are 0.95 and 0.99, respectively. In the vicinity ofpercolation threshold, the real permittivity of resultantcomposites showed positive values, and the impedance couldbe simulated by resistance R and capacitance C. The resistanceis determined by grain boundary and grain, corresponding totwo different resistances; the capacitance is derived from theinterface between isolated silver particles and YIG host.27,64

The silver clusters were partially cut off by the insulating matrix,so the capacitance and resistance were connected in parallel. Inthe percolating Ag/YIG composites, there coexisted resistanceR, inductance L, and capacitance C. The exotic inductance isproduced by the conduction electrons in the continuous silvernetworks, and the capacitance depends on polarized electrons.There were several conductive networks distributed in thecomposites and induced loop current; hence, the circuit wasequivalent to several shunt inductances, leading to the negativepermittivity.52

Under the action of an external electric field, the inductivecharacter is suppressed, while the capacitive character isenhanced with an increase in frequency.63 Accordingly, there

were inductive−capacitive transitions observed in the perco-lated samples with the increase of frequency. As discussedabove, the percolative composites could be equivalent to acircuit composed of L, C, and R. When reactance Z″ becomeszero, LC resonance will take place and lead to the emission ofelectromagnetic waves.52 When the emitted electromagneticradiations interfere with the external high-frequency electricfield, the Fano-like dielectric resonance appears at the zerocross point. Hence, the LC resonance was responsible for theFano-like dielectric resonance, in which the permittivitychanged from negative to positive.Figure 5 shows the complex permeability spectra of Ag/YIG

composites with different silver contents. The real permeability

was gradually reduced with the increase of frequency, and thecorresponding imaginary permeability peaks were observed,which exhibited relaxation-type frequency dispersion behavior.In addition, the real permeability was reduced with the increaseof silver concentration; meanwhile, the relaxation-type spectraof permeability gradually became indistinct in the compositeswith higher silver content. Generally, the frequency dispersionof permeability is attributed to the domain wall motion and thegyromagnetic spin rotation.66,67 The permeability dispersionwith relaxation character can be described as eqs 4 and 5

μω

ω ωω

ω ω′ = +

++

+x x

1 sr

d0 d2

2d2

0 s2

2s2

(4)

μω ω

ω ωω ω

ω ω″ =

++

+x x

rd0 d2

d2

s0 s2

s2

(5)

where χd0 and χs0 are the static magnetic susceptibility of thedomain wall and spin components, ωd and ωs are the resonancefrequency of each component, and ω is angular frequency. Thecalculated permeability parameters are shown in Table 1, and R

Figure 4. Real and imaginary impedance for Ag/YIG composites. (a)and (b) are near and above percolation threshold. The insets presentthe equivalent circuits, and the solid lines show the fitted results.

Figure 5. Complex permeability spectra of Ag/YIG composites. (a)and (b) Real and imaginary permittivity. The solid lines show thefitted data.

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is the reliability factor of the fitting result. It can be seen thatthe fitted curves were consistent with the experimental data.The frequency dispersion of permeability in the radio-frequency region corresponds to the domain wall motion,and the gyromagnetic spin rotation plays an important role inthe high-frequency regime.66 Hence, the real permeability ofAg/YIG composites was decreased with the increase offrequency.When the metallic silver content was increased, it meant that

the relative amount of ferrimagnetic YIG was reduced.Therefore, the initial permeability of resulting composites wasgradually decreased. On the other hand, the adjacent silverparticles gradually formed a conductive network and generatedlocal current loops.27 Under the action of an alternating electricfield, the current loops could induce a reversed magnetic fieldand restrain the external electromagnetic field,52 resulting in thedecline of permeability. In the high-frequency region, theinduced current will be significantly enhanced and cause therapid decay of permeability. Consequently, when silver contentwas beyond the percolation threshold, the permeability spectraof Ag/YIG composites were not shown as relaxation character-istic in the test frequency region.It is indicated that the negative permeability can be realized

in natural magnetic materials due to magnetic resonance.39

Tsutaoka et al.40 observed the negative permeability in YIG/polymer composites. Shi et al.68 made a theoretical calculationthat the tunable negative permeability can be obtained in Cu/YIG composites by applying different external dc magneticfields. The above discussions show that the tunable negativepermeability could be also achieved in Ag/YIG composites.

4. CONCLUSIONSThe impedance, permittivity, and permeability were inves-tigated in percolative Ag/YIG composites, which werefabricated by in situ sintering process. In the vicinity ofpercolation threshold, the conduction and polarization make acombined contribution to the dielectric loss. When reaching apercolated state, Fano-like resonance was observed and thedielectric constants switched from negative to positive. It isrevealed that the inductive character brings about the negativepermittivity, and the capacitive is responsible for positivepermittivity. LC resonance leads to the Fano-like resonance,where the permittivity changed from negative to positive.Moreover, the permeability of Ag/YIG composites presentedfrequency dispersion due to the domain wall motion and thegyromagnetic spin rotation. Hopefully, the tunable negativepermittivity and permeability can be obtained in percolativeAg/YIG composites, which have great potential applications inelectromagnetic shielding, microwave absorbing, and antenna.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: [email protected].

*E-mail: [email protected].

ORCIDZhanhu Guo: 0000-0003-0134-0210NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The authors acknowledge the support of the National BasicResearch Program of China (973 Program, No.2014CB643306), National Natural Science Foundation ofChina (Grant No. 51172131, 51402170, 51602194, and51602195), Natural Science Foundation of Shandong Province(No. ZR2016EMM09), and China Scholarship Council.

■ REFERENCES(1) Nan, C.-W. Physics of Inhomogeneous Inorganic Materials. Prog.Mater. Sci. 1993, 37, 1−116.(2) Nan, C.-W.; Shen, Y.; Ma, J. Physical Properties of Compositesnear Percolation. Annu. Rev. Mater. Res. 2010, 40, 131−151.(3) Bergman, D. J.; Stroud, D. Physical Properties of MacroscopicallyInhomogeneous Media. Solid State Phys. 1992, 46, 147−269.(4) Cheng, C.; Yan, K.; Fan, R.; Qian, L.; Zhang, Z.; Sun, K.; Chen,M. Negative Permittivity Behavior in the Carbon/Silicon NitrideComposites Prepared by Impregnation−Carbonization Approach.Carbon 2016, 96, 678−684.(5) Shi, Z.; Mao, F.; Wang, J.; Fan, R.; Wang, X. Percolative Silver/Alumina Composites with Radio Frequency Dielectric Resonance-Induced Negative Permittivity. RSC Adv. 2015, 5, 107307−107312.(6) Sun, K.; Zhang, Z.; Qian, L.; Dang, F.; Zhang, X.; Fan, R. DualPercolation Behaviors of Electrical and Thermal Conductivity inMetal−Ceramic Composites. Appl. Phys. Lett. 2016, 108, 061903.(7) Shen, Y.; Lin, Y.; Nan, C. W. Interfacial Effect on DielectricProperties of Polymer Nanocomposites Filled with Core/Shell-Structured Particles. Adv. Funct. Mater. 2007, 17, 2405−2410.(8) Gu, J.; Liang, C.; Zhao, X.; Gan, B.; Qiu, H.; Guo, Y.; Yang, X.;Zhang, Q.; Wang, D.-Y. Highly Thermally Conductive Flame-Retardant Epoxy Nanocomposites with Reduced Ignitability andExcellent Electrical Conductivities. Compos. Sci. Technol. 2017, 139,83−89.(9) Zheng, R.; Gao, J.; Wang, J.; Feng, S.-P.; Ohtani, H.; Wang, J.;Chen, G. Thermal Percolation in Stable Graphite Suspensions. NanoLett. 2011, 12, 188−192.(10) White, M. S.; Kaltenbrunner, M.; Głowacki, E. D.; Gutnichenko,K.; Kettlgruber, G.; Graz, I.; Aazou, S.; Ulbricht, C.; Egbe, D. A.;Miron, M. C.; Major, Z.; Scharber, M. C.; Sekitani, T.; Someya, T.;Bauer, S.; Sariciftci, N. S. Ultrathin, Highly Flexible, and StretchablePleds. Nat. Photonics 2013, 7, 811−816.(11) Chu, B.; Zhou, X.; Ren, K.; Neese, B.; Lin, M.; Wang, Q.; Bauer,F.; Zhang, Q. A Dielectric Polymer with High Electric Energy Densityand Fast Discharge Speed. Science 2006, 313, 334−336.(12) Dang, Z.-M.; Yuan, J.-K.; Zha, J.-W.; Zhou, T.; Li, S.-T.; Hu, G.-H. Fundamentals, Processes and Applications of High-PermittivityPolymer−Matrix Composites. Prog. Mater. Sci. 2012, 57, 660−723.(13) Yang, C.; Lin, Y.; Nan, C. Modified Carbon NanotubeComposites with High Dielectric Constant, Low Dielectric Loss, andLarge Energy Density. Carbon 2009, 47, 1096−1101.(14) Wang, J.; Shi, Z.; Mao, F.; Wang, X.; Zhang, K.; Shi, J. Ni/Al2O3/Epoxy High-K Composites with Ultralow Nickel Contenttowards High-Performance Dielectric Applications. RSC Adv. 2016, 6,43429−43435.(15) Wang, D.; Zhou, T.; Zha, J.-W.; Zhao, J.; Shi, C.-Y.; Dang, Z.-M.Functionalized Graphene−BaTiO3/Ferroelectric Polymer Nanodi-electric Composites with High Permittivity, Low Dielectric Loss, andLow Percolation Threshold. J. Mater. Chem. A 2013, 1, 6162−6168.(16) Shen, Y.; Yue, Z.; Li, M.; Nan, C. W. Enhanced InitialPermeability and Dielectric Constant in a Double-Percolating

Table 1. Calculated Permeability Dispersion Parameters(χd0, χs0, ωd, and ωs) of Ag/YIG Composites

samples

silverloading(wt %) χd0 ωd (rad/s) χs0 ωs (rad/s) R2

AY5 5 7.77 8.45 × 108 2.90 3.77 × 109 0.99AY15 15 12.26 3.83 × 108 2.89 3.78 × 109 0.99AY25 25 6.40 5.48 × 108 3.01 3.46 × 109 0.99

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