nickel metacomposites

Acta Materialia 185 (2020) 412–419

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Design and analysis of negative permittivity behaviors in barium titanate/nickel metacomposites Zhongyang Wang a,b,c, Kai Sun a,∗, Peitao Xie b, Qing Hou d, Yao Liu b, Qilin Gu c,∗, Runhua Fan a,∗ a

College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China Department of Materials Science and Engineering, National University of Singapore, 117574, Singapore d Kathleen Lonsdale Materials Chemistry, Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK b c

a r t i c l e

i n f o

Article history: Received 5 August 2019 Revised 7 December 2019 Accepted 17 December 2019 Available online 19 December 2019 Keywords: Negative permittivity Cermet Dielectric Electrical property Nickel

a b s t r a c t As an important supplement to the metamaterials, negative permittivity in ’natural’ materials has attracted increasing attention, while some fundamental regulation mechanisms and common theoretical principles have not yet been systematically explored. In this paper, the permittivity transition is investigated along with insulator-conductor conversion in BaTiO3 /Ni composite. When the Ni content in BaTiO3 /Ni composites is lower than and higher than the percolation threshold, Lorentz-like and Drudetype negative permittivity behaviors is obtained, respectively. In addition, the fundamental principles of negative permittivity are discussed, especially the validity of the Kramers–Kronig relations and the relationship between the negative permittivity and the reactance characters. Further, a universal regulatory mechanism of the Drude-type negative permittivity profile is qualitatively analyzed. Negative permittivity and negative permeability are achieved simultaneously in BaTiO3 /Ni composites with 35.56 vol% of Ni loading, which show potential application in electromagnetic wave absorption and shielding. © 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction Themes in magnetic and electrical materials have some similar features that are established by Maxwell’s electromagnetic duality principle. However, there are still some interesting distinctions. For example, diamagnetic materials have been extensively studied, but the “diaelectricity” has been rarely proposed. The negative permittivity materials reported in recent years are identified as lacking “diaelectricity” [1–3]. Materials exhibiting a negative permittivity have drawn a great deal of attention due to their potential applications in antennas [4], electromagnetic cloaking [5], novel capacitors [6,7] and negative capacitance field transistors [8,9], etc. Negative permittivity behavior has been observed in metamaterials with various periodically artificial units [10,11]. In fact, negative permittivity behavior can also be obtained in “natural” materials and further tuned by their composition and microstructure. For example, negative permittivity of metals is almost commonplace in the ultraviolet or visible spectrum. However, at radio frequency, negative permittivity is not universally observed. It is mainly originated

∗

Corresponding authors. E-mail addresses: [email protected] (K. Sun), [email protected] (Q. Gu), [email protected] (R. Fan). https://doi.org/10.1016/j.actamat.2019.12.034 1359-6454/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

from the dielectric resonance of ferroelectric [12–14] or plasmalike oscillation of percolating composites [15–17]. In general, the negative permittivity in ferroelectric shows a narrow bandwidth, poor tunability, and relatively low loss [18,19]. In contrast, the negative permittivity achieved in the conductor shows broadband, easy-totailor, and high-loss [20,21]. Combining the advantages of these two kinds of negative permittivity will facilitate the multifunctional applications of negative permittivity materials, especially in high-power microwave filters [22] and coil-free resonators [23], etc. The construction of ferroelectric-conductor percolating system is an efficient way to obtain both these two kinds of negative permittivity materials. When the content of conductive fillers is below the percolation threshold, the composite exhibits a dielectric resonance type negative permittivity. On the other hand, the plasmalike negative permittivity can also been achieved in percolative composites when the content of conductive fillers is beyond the percolation threshold. As is well known, for traditional percolating materials, the high permittivity is usually obtained near the percolation threshold. In this case, the percolating system contains two types of negative permittivity materials, and the behavior of the permittivity close to the threshold is rather extraordinary. Therefore, it is necessary to investigate the transformation process near percolation threshold and the internal mechanism of these two negative permittivity behaviors.

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Moreover, in percolating composites, there is still a theoretical controversy about how negative permittivity changes as the function of the conductive filler content. The scale of negative permittivity become either larger or smaller with the increasing conductive fillers content and can be found in most of the recently reported literatures [24–26], but there is no scientific explanation for this phenomenon. Therefore, a universal regulatory mechanism of negative permittivity is worth being further explored, which would be the analytical guidance to obtain a weakly negative permittivity [27]. It is well known that the real and imaginary parts of the complex constitutive parameters follow the general causality principle, in which the real and imaginary parts obey the Kramers-Kronig relations [28]. The inverse positive permittivity (1/ε ) follows the Kramers-Kronig relations. It is widely recognized that when the permittivity exhibits low frequency dispersion, the Kramers-Kronig relations can be applied in a finite frequency range [29]. However, the universality of Kramers-Kronig relations for negative permittivity with strong dispersion and high loss has never been defined. Therefore, the suitability of this relationship needs to be further clarified. In this paper, in order to describe the negative permittivity behaviors of ferroelectric and percolating composites, the barium titanate/nickel (BaTiO3 /Ni) composites were purposely prepared. Most importantly, two kinds of negative permittivity are realized as expected, which are clarified based on the Lorentz model and Drude model, respectively. Meanwhile, the transformation process of negative permittivity from Lorentz-type to Drude-type is also discussed. The universal regulatory mechanism of Drude-type negative permittivity profile is qualitatively analyzed. Moreover, the validity and rationality of negative permittivity are further explored based on the quantitative analysis of Kramers-Kronig relations. Interestingly, in the resultant composites with 35.58 vol% of Ni content, a double negative permittivity and permeability behavior is realized. 2. Experimental The BaTiO3 /Ni composites were prepared by combining the sol-gel method, hydrothermal method and subsequent sintering process. Firstly, tetrabutyl titanate (Ti(CH3 (CH2 )3 O)4 , purity>99%, Aladdin, China) and barium acetate ((CH3 COO)2 Ba, purity~99%, Aladdin, China) were dissolved in acetic acid and ethanol, respectively. After stirring at room temperature for 4 h, the homogeneously mixed solutions were kept stirring for additional 30 min to form the sol, which was then stood for 4 h in air to get the gel. Subsequently, the gel was calcined for 2 h at 600 °C in air to achieve BaTiO3 powders. Nickel acetate (Ni(CH3 COO)2 •4H2 O, purity ~99%, Aladdin, China) and the obtained BaTiO3 powders were mixed in ethanol and stirred for 2 h, then the slurry was gently poured into a reaction still and heated at 180 °C for 2 h. After completely cooling down to room temperature, the precipitation was filtrated and washed with deionized water for several times. Further, the powders were pressed at 30 MPa to form green bodies with 15 mm in diameter and about 2 mm in thickness. Finally, BaTiO3 /Ni composites were obtained after sintering at 1200 °C for 2 h in H2 atmosphere. Phase composition of the as-synthesized samples were examined by X-ray diffraction (XRD, D/Max2550VB+/PC, Japan) with ˚ Cu-Kα radiation (λ=1.5406 A). Morphology of sintered samples was analyzed using a field-emission scanning electron microscopy (FE-SEM, SU-70, Japan). The electrical properties including AC conductivity, reactance, permittivity and permeability of the BaTiO3 /Ni composites were measured by impedance analyzer (Agilent E4991A RF Impedance, USA) equipped with 16453A dielectric test fixture and 16454A permeability test fixture in the frequency

413

range from 1 MHz to 1 GHz. Temperature dispersions of the permittivity and ferroelectric hysteresis loop were tested by precision LCR Meter (Agilent E4980, USA)) equipped with temperature control box and ferroelectric analyzer (aixACCT TF20 0 0E, Germany), respectively. 3. Results and discussion 3.1. Negative permittivity behaviors The phases and morphologies of BaTiO3 /Ni composites are shown in Fig. 1. The XRD patterns in Fig. 1a show the typical spectra of Ni and BaTiO3 , and no other phases can be found. All the diffraction peaks of BaTiO3 are in good agreement with the tetragonal BaTiO3 phase (JCPDS No. 05–0626). In addition, the diffraction peaks of BaTiO3 do not show obvious changes in position or intensity, indicating that Ni particles were well preserved in the samples and no unexpected reactions occurred during the synthesis. The permittivity as function of temperature in Fig. S1 shows that there is no shift of Curie temperature, further confirming that Ni ions have not dissolved in the crystal lattice of BaTiO3 . The morphology of the BaTiO3 /Ni composites is shown in Fig. 1b-f. Sphere-like Ni particles are distributed around the BaTiO3 grains. When the Ni content is increased to 35.58 vol%, Ni particles are stacked together and formed the conductive pathways, which are also verified by energy dispersive spectroscopy (EDS) of the Ni element (Fig. 1g). The dielectric behaviors of BaTiO3 /Ni composites from 1 MHz to 1 GHz are shown in Fig. 2. In the composites with various Ni loadings, their permittivity spectra are clearly different. When the Ni content is low, the frequency response from BaTiO3 is predominant and exhibits a typical ferroelectric characteristic. Thus, the hysteresis loops can be observed in BaTiO3 /Ni composites with lower Ni content. On the contrary, when the Ni content is increased to a higher level, it transformed into a conductor, and the hysteresis loop cannot be tested (Fig. S2). The negative permittivity is observed along with a dielectric resonance in Fig. 2a, due to the fact that the Ti4+ moves from the center to the equilibrium position in Ti-O octahedral sites of BaTiO3 and leads to a collective resonance of charge under an external alternating electric field [30,31]. The dipoles charges resonance can be considered as mechanical linear oscillators, and their restoring force would balance the force induced by the applied electric field. A resonance usually occurs at a certain frequency, and the permittivity can be described as Lorentz model [31], as follows,

εr = 1 +

ω02 − ω2 N q2 meff ε0 (ω2 − ω2 )2 + ω2 ω2 τ 0

(1)

where ω is angular frequency, ωτ is the collision frequency (inverse of the mean free collision time), ω0 =2π f0 is the characteristic frequency, q is the charge of dipole, meff is the effective mass of the dipoles and N is charge numbers per unit volume. The experimental results are fitted well with the Lorentz model (solid lines in Fig. 2a). Meanwhile, it can be observed that the permittivity at low frequency gets enhanced with the increasing of Ni content due to the interfacial polarization, also known as the Maxwell-WagnerSillars effect [32]. In addition, when the Ni content is further increased, the negative permittivity derived from plasma oscillation of delocalized electrons is observed in Fig. 2c and d. Nickel particles embedded in BaTiO3 matrix lead to a dilution of the effective electron concentration, so low-frequency plasma is obtained in contrast to that of metals. The similar phenomenon has been also reported in other cermets [33,34]. Such a negative permittivity behavior can be described by the Drude model [16], as follows,

εr (ω ) = 1 −

ωp 2 ω2 + ωτ2

(2)

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Fig. 1. (a) XRD patterns of BaTiO3 /Ni composites, and the inset is the partial enlarged view. SEM images of BaTiO3 /Ni composites with different volume fractions of Ni: (b) 6.98 vol%, (c) 10.64 vol%, (d) 14.44 vol%, (e) 22.44 vol%, (f) 35.58 vol%. (g) the EDS of f.

Fig. 2. The permittivity spectra of BaTiO3 /Ni composites with different nickel content. (a)–(d) the permittivity spectra of resultant composites below (a), near (b) and above (c,d) the percolation threshold. The solid lines are fitted by Lorentz model (a), combining Lorentz and Drude model (b) and Drude model (c,d). The inset in (a) is the partial enlarged view of permittivity spectra in lower frequency region. The inset in (c,d) show the details of negative permittivity near the zero-cross points.

Z. Wang, K. Sun and P. Xie et al. / Acta Materialia 185 (2020) 412–419

 ωp = 2π f p =

neff e2 meff ε0

(3)

where ωp is the plasma frequency, neff is effective concentration of the conduction electrons and meff is the effective mass of the electron. Based on the aforementioned equations, the mean free path and the concentration of carriers play a primary role in the bandwidth and dispersion of negative permittivity. It shows that the Drude model satisfies well with the experimental data (red lines in Fig. 2c and d). With the increase of the nickel content, zerocross point corresponding to the ωp moves to higher frequency. Additionally, the fitted results in Fig. 2c and d shows that the ωτ of the resultant composites with different nickel content (26.66, 31.03 and 35.58 vol%) are 7.22 MHz, 11.72 MHz and 220.5 MHz, respectively, indicating that ωτ is positive correlation with the Ni content. When the conductive network is formed, the increasing of Ni content will cause a shortened mean free path of electrons, so the electron collision frequency ωτ is enhanced. Moreover, the absolute value of negative permittivity at low frequency (1 MHz) is reduced with the increase of Ni content. In detail, the negative permittivity changes from −106 to −103 , when the volume fraction of Ni increases from 26.66 vol% to 35.58 vol%. It is worth noting that the unique permittivity behavior of transition component composite is observed in Fig. 2b. Negative permittivity is achieved in a wide frequency range when the volume fraction of Ni reaches to 22.44 vol%. A giant permittivity (about 32,081 at 2 MHz) is also observed, which is three orders of magnitude larger than that of pure BaTiO3 . A similar behavior with the εr ’ of about 70,0 0 0 at 10 kHz has been reported in Moya’s work [35]. The significant enhancement of permittivity is attributed to interfacial polarization. However, the interfacial polarization can hardly keep up with the large change of external electric field, so the permittivity abruptly decreased at 20.6 MHz in Fig. 2b. In addition, due to the content of Ni in the BaTiO3 /Ni composites is 22.44 vol%, which is near the percolation threshold. Therefore, the permittivity is not only related to the Lorentz-type resonance of BaTiO3 , but also affected by the plasma oscillation of electrons in Ni (Drude-type permittivity). It is worth noting that the Lorentz model of materials already contains the short-range movement of the charges, and in case of the high damping, it represents polarization. Thus, we use the linear combination of Lorentz and Drude mode to fit the experimental data (red line in Fig. 2b). The modified model is expressed in Eq. (4), which is in good accordance with experimental results.

εr = 1 +

ω02 − ω2 ωp 2 N q2 − meff ε0 (ω2 − ω2 )2 + ω2 ω2 ω2 + ωτ2 τ 0

(4)

The imaginary parts of permittivity are shown in Fig. S3. For the BaTiO3 /Ni composites with Lorentz-type negative permittivity, the corresponding imaginary permittivity shows a loss peak around the dielectric resonance (Fig. S3a). Meanwhile, the giant permittivity induced by the interfacial polarization also shows a giant imaginary permittivity in the low frequency region (Fig. S3b). For the BaTiO3 /Ni composites with plasma-like negative permittivity, a high imaginary permittivity is observed at the lower frequency (Fig. S3c and d), which is attributed to the Drude peak [36]. 3.2. Generally tunable mechanism for negative permittivity Since negative permittivity induced by the dielectric resonance has always been ignored, it is worth studying the internal mechanism for this dispersion. The approximate circular Cole-Cole plots of permittivity near resonant frequency are shown in the Fig. 3a. The circle with small radius commonly means the higher damping coefficient. When the damping coefficient increases to infinity, the dielectric response gradually transforms to an ideal Debye model

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[37]. That means the ωτ of the composites is increased with the increasing Ni content. The loss peak also becomes wider with the increase of damping (Fig. S3a). It is worth pointing out that extremely high ωτ makes the negative permittivity disappear. Fig. 3b shows the relationship between the permittivity and the volume fraction of Ni, which obeys the percolation theory [38]:

εr =

ε0 for f < fc | fc − f |q

(5)

where f is the volume fraction of Ni, fc is the percolation threshold, and q is the critical exponent. The permittivity increases dramatically near the percolation threshold. According to Eq. (5), the fitted percolation threshold fc is 22.6 vol%. Hence, the peculiar permittivity spectrum was observed in BaTiO3 /Ni composites with a Ni content of 22.44 vol% (Fig. 2b). The inset in Fig. 3b is ac conductivity (σ ac ) at 2 MHz. The σ ac of the composites is gradually increased at higher Ni content. It is demonstrated that the abrupt enhancement of σ ac is attributed to the conductive networks, which are formed near the percolation threshold. The frequency dependence of σ ac in the BaTiO3 /Ni composites is shown in Fig. S4, which changes distinctly at different Ni content. When the Ni content is below the percolation threshold, the frequency dependence of σ ac shows typical dielectric characteristics, manifesting the hopping conduction of located electrons [39]. The relationship between ac conductivity and imaginary permittivity follows: σ ac =ε "ω/4π [36]. Therefore, the peaks of conductivity (inset in Fig. S4) are dependent on the loss peak resulting from dielectric resonance. Furthermore, when the Ni content exceeds the percolation threshold, σ ac is decreased with the increase of the frequency due to the skin effect [40], which shows a metal-like conductive behavior. For the other type of negative permittivity induced by plasma oscillation, the negative permittivity as function of conductive fillers’ content has not been defined. Negative permittivity described by Drude model is bound up with the ωp and ωτ , which can be expressed as the equation: ε r ’=1-ωp 2 /(ω2 +ωτ 2 ). As discussed above, both ωp and ωτ are increased with the increase of Ni content, so it is hard to predict their permittivity. The qualitative analysis (verified by Matlab R2009b) is shown in the Fig. 3c and d, where the parameters including two negative permittivity materials (ε 1 and ε 2 ), along with the same lower-right markers ωp1 , ωτ 1 and ωp2 , ωτ 2, are set, separately. The material with negative permittivity ε 2 has a higher concentration of effective free electron compared with that with the permittivity ε1 , so ωp2> ωp1, and ωτ 2> ωτ 1. For ωτ 2 /ωτ 1 >ωp2 /ωp1 , the calculation results are  shown in the Fig. 3c. The frequency of cross-point is named as

2 ω 2 −ω 2 ω 2 ωp1 τ2 p2 τ 1 = 2 −ω 2 ωp2 p1

ωc . When the frequency is in the

range of ωc <ω<ωp1 , the negative permittivity ε 1 >ε 2 ; when the frequency follows ω<ωc , the negative permittivity ε 1 <ε 2 . While for ωτ 2 /ωτ 1 <ωp2 /ωp1 , the negative permittivity is always obeying ε 1 >ε 2 (Fig. 3d). Therefore, the negative permittivity decreases with the increase of conductive filler content in percolating composites, corresponding to the case of ωτ 2 /ωτ 1 <ωp2 /ωp1 , or the test frequency in the range of ωc <ω<ωp1 , where ωτ 2 /ωτ 1 >ωp2 /ωp1 . While negative permittivity increases with higher conductive fillers content due to ωτ 2 /ωτ 1 >ωp2 /ωp1 , and the frequency in the range of the ω<ωc . Clearly, the curves in Fig. 3c are similar to the experimental data (inset in the Fig. 2c), demonstrating that ωτ is increased even more than ωp at higher Ni content. Thus, the negative permittivity for BaTiO3 /Ni composites with 35.58 vol% of Ni content is less than that of the composites with 26.66 vol% of Ni content at 1 MHz. Further, we conclude that ωp affects the bandwidth of the negative permittivity, and higher ωτ is helpful to obtain the weak negative permittivity. However, when ωτ is extremely high, the permittivity becomes imaginary and proportional to ω [41].

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Fig. 3. (a) The Cole-Cole plots of the complex permittivity data around the resonance peak of BaTiO3 /Ni composites with lower Ni content. (b) The permittivity as a function of Ni content in BaTiO3 /Ni cermet. The solid line is fitted by percolation theory. Inset in (b) is ac conductivity versus Ni content. (c) and (d) The scheme of the dielectric response of a free-carrier system with a collision frequency ω τ and plasma frequency ωp . (e) and (f) Frequency dependence of reactance of BaTiO3 /Ni composites. Insets in (e) and (f) are the details of reactance near the zero-cross points.

Frequency dependence of reactance of BaTiO3 /Ni composites is shown in Fig. 3e and f. The negative reactance (Z"<0) indicates a capacitive character, while the positive reactance (Z">0) represents an inductive character. The switching frequency points change from negative Z" to positive Z", corresponding to the zerocross points of the permittivity. This illustrates that the negative permittivity induced by dielectric resonance and plasma oscillation are both attributed to the inductive characteristic of composites [31,42].

3.3. Kramers–Kronig relations for negative permittivity The Kramers-Kronig relations are used to describe the dispersion functions between the action on the response linearity system and its result. As is well known, dielectric constant describes the electric displacement respond of the materials to an external electric field. Therefore, the Kramers-Kronig relations have been demonstrated valid for the inverse effective permittivity (1/ε ) [43]. The integral transformation of the Kramers-Kronig relations for

complex permittivity is shown as following:

1

ε  r (ω )

= 1+

2

π



∞ 0

ω ω 2 − ω2

1

ε  r (ω )

dω

(6)

where ε r ’ and ε r " represent the real and imaginary parts of the permittivity, respectively. This principle can reliably retrieve the positive permittivity. However, the universality of Kramers-Kronig relations for negative permittivity has never been proved. According to Eq. (6), 1/εr (1/j=-j) is negative, so 1/ε r ’ is restricted by1/ε r ’<1 [28]; equivalently, ε r ’>1 or ε r ’<0. Thus, negative permittivity does not violate the Kramers-Kronig relation in principle. The real permittivity and data calculated from the imaginary permittivity by Eq. (6) are shown in Fig. 4. It is clear that the calculated results meet quite effectively with the experimental dispersion of the negative permittivity caused by dielectric resonance (Fig. 4a). It is indicated that Kramers-Kronig relation is applicable to the Lorentz-type negative permittivity profile. Therefore, Kramers-Kronig transformation provides an effective method to verify the accuracy and reliability of experimental results.

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Fig. 4. Comparison between the experimental permittivity of BaTiO3 /Ni composites (symbols) and calculated real permittivity (lines) from the imaginary permittivity by Kramers–Kronig relation. (a) Lorentz-type negative permittivity profile is in good agreement with Kramers–Kronig relation. (b) Calculations of Kramers–Kronig relation have a similar curvilinear trend with Drude-type negative permittivity profile.

For the other kind of negative permittivity induced by plasma oscillation is also examined by Kramers-Kronig relation in Fig. 4b. The experimental data of real permittivity and calculated results based on Kramers-Kronig relation for the composites with 35.58 vol% of Ni content are plotted separately. It is obvious that the Drude-type negative permittivity does not satisfy the KramersKronig relation. However, the calculated results have a similar curvilinear trend with dispersion of negative permittivity. For the BaTiO3 /Ni composites, when the Ni content is lower than the percolation threshold, it still exhibits an insulating characteristic. When a voltage is applied, there will cause an electric displacement, and it is a linear response system. Thus, the Kramers-Kronig relationship is valid. For the composites with Drude-type negative permittivity, the content of Ni in these composites is very high, which shows a typical metal-like behavior. In this case, there will induce a current once a voltage is applied. As shown in the Fig. S4, for the composites with Drude-type negative permittivity, the ac conductivity is decreased with increase of frequency due to the skin effect [40], which is no longer a linear response system. Therefore, the calculated results by Kramers-Kronig relation shows the deviation from experimental data.

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Fig. 5. Frequency dependence of real permeability (a) and imaginary permeability (b) of BaTiO3 /Ni composites with different Ni content.

3.4. Negative permeability toward double negative materials The complex permeability spectra of BaTiO3 /Ni composites are shown in Fig. 5. It is obvious that the real part of permeability decreases with the increasing of frequency, exhibiting magnetic relaxation (Fig. 5a) [44]. The permeability at low frequency increased with the less addition of ferromagnetic Ni content, but it is reduced for the composites with high Ni content. Conductive networks can be gradually formed with the increasing amount of nickel particles, and the current loops are also generated in high frequency region. Therefore, diamagnetic behavior (i.e., μr ’<1) is observed, when Ni content exceeds the percolation threshold. Interestingly, the negative permeability is observed in BaTiO3 /Ni composites with 35.58 vol% of Ni content. On one hand, the magnetic resonances including domain wall resonance and gyromagnetic spin resonance derived from Ni particles play an important role in achieving negative permeability. On the other hand, the induced diamagnetic of current loops against the applied the external magnetic field also contribute to the negative permeability [45]. It is worth noting that eddies also increase the damping factors of resonances, which leads to the disappear of negative permeability [46]. Thus, when the content of Ni is further increased to a higher level, the negative permeability is disappeared (Fig. S5). As a whole, when the combined effects of magnetic resonances and induced diamagnetic are strong enough

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to overcome the damping contribution, the negative permeability can be produced. A similar phenomenon has been reported in previous work [15,16]. The imaginary parts of permeability are also studied in Fig. 5b. Magnetic loss mainly originates from the hysteresis loss, eddy current loss and resonance loss. In the composites with 10.64 vol% of Ni content, imaginary permeability goes up with the increasing of frequency, which is mainly attributed to hysteresis loss. When the nickel content further is increased, the eddy current loss dominates. As a result, the imaginary permeability decreases with the increase of frequency [40]. Besides, negative permittivity and permeability are successfully obtained in the composites with 35.58 vol% of Ni content in the frequency range of 121 MHz-486 MHz, which show great potential application in antennas, microwave cloaking and shielding, due to its isotropic and easier-to-manufacture feature. 4. Conclusions In summary, two kinds of negative permittivity behaviors are observed in BaTiO3 /Ni percolative composites. When Ni content is below the percolation threshold, the negative permittivity is induced by dielectric resonance of BaTiO3, which can be described by Lorentz model. Moreover, high damping of dipole resonance is detrimental to realize negative permittivity in BaTiO3 . When the Ni content exceeds the percolation threshold, negative permittivity derived from plasma oscillation is explained by Drude model. The variation of Drude-type negative permittivity with the increasing Ni loadings are qualitatively analyzed. In addition, the dielectric permittivity near the percolation threshold is further studied by combining the Lorentz and Drude models. The negative permittivity behaviors induced by dielectric resonance and plasma oscillation both exhibit an inductive characteristic. More significantly, the Lorentz-type negative permittivity obeys the Kramers-Kronig relations, while the Drude-type negative permittivity veers off the Kramers-Kronig relations due to the skin effect. Interestingly, negative permittivity and negative permeability are simultaneously achieved in the composites with 35.58 vol% of Ni content, which show great potential application in electromagnetic wave absorption or shielding. In brief, the intensively explore of the fundamental principles for the two types of negative permittivity would contribute to the development of novel metamaterials and their extensible applications. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 51601105, 51803119, 51871146), the Innovation Program of Shanghai Municipal Education Commission (Grant No. 2019-01-07-0 0-10-E0 0 053) and Chenguang Program supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (Grant No. 18CG56). Zhongyang Wang and Qin Hou acknowledge the support from the China Scholarship Council. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.actamat.2019.12.034.

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