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Colossal Permittivity and Variable-Range-Hopping Conduction of Polarons in Ni0.5Zn0.5Fe2O4 Ceramic Hui Zheng, Wenjian Weng, Gaorong Han, and Piyi Du* State Key Lab of Silicon Materials, Department of Materials Science and Engineering, Zhejiang University, 310027, Hangzhou, P. R. China ABSTRACT: The electrical properties of ferrites are important to their applications at high frequencies. In this paper, we investigate the colossal permittivity behavior of Ni0.5Zn0.5Fe2O4 ceramic prepared from powders synthesized by the citric acid combustion method. Its bulk conductivity is attributed to the variable-range hopping of localized polarons. These polarons exhibit universal dielectric response with frequency. They are frozen at low temperature and activated at high temperature. As temperature decreases from 235 to 130 K, their hopping energy decreases from 223 to 113 meV, while the estimated hopping range increases from 3.5 to 4.1 nm. The direct correlation of polaron conduction and colossal permittivity of NZFO is definitely established by a modified Koops’ equivalent circuit based on the internal barrier layer model, which is well confirmed by the experimental data.

I. INTRODUCTION Ferrites are important magnetic materials that are suitable for high-frequency applications.1,2 Other than high magnetic properties, they are usually required to have high resistivity and low eddy current in order to widen the applicable range to microwave frequencies. However, it has been observed for a long time that ferrite ceramics often exhibit high permittivity on the order of megahertz.2−4 Such high permittivity is comparable with or even much higher than those of ferroelectric perovskites. Thus, large displacement eddy current would be induced under high-frequency magnetic field, according to Maxwell equations. Moreover, in recent years, ferromagnetic (ferrimagnetic) ferrites are widely used to prepare multiferroic composites owing to rare single-phase multiferroics in nature.5 The multiferroic composites have potential application in new devices like capacitance−inductance integrated filters and magnetoelectric memories.4,6,7 In these applications, the high nonferroelectric permittivity of ferrites can render the ferroelectric polarization in perovskites no longer predominant in the apparent response.4 Thus, the ferroelectricity and magnetoelectricity of the composites will be weakened. However, when ferrites are used as electromagnetic wave absorbers,8 the high polarization can lead to additional loss of electromagnetic energy as well as a dimensional resonance resulting from the interaction between polarization and magnetization at lower frequencies than the natural resonance frequency.9 It has been widely accepted that the high permittivity of ferrites is attributed to the conductivity inhomogeneity between grains and grain boundaries, which was first proposed by Koops.3,10,11 In fact, close activation energies of dielectric relaxation and conductivity were reported for several ferrites,11,12 which implies inherent correlation between polarization and conduction in ferrites. Jonker et al. has © 2013 American Chemical Society

interpreted the conduction mechanism in several ferrites by charge jumping between equivalent lattice sites such as an electron transition between Fe2+ and Fe3+, which locate randomly at the interstices of oxygen octahedra (B sites).13−15 Recently, Bharathi et al. pointed out that the conductivity of nickel ferrite may originate from a variablerange-hopping mechanism in the temperature region of 160− 220 K.16 However, more investigations should be made to reveal the real conduction mechanism in ferrites as well as the definite correlation between the conduction and polarization. In this paper, we investigate the dielectric property of Ni0.5Zn0.5Fe2O4 ceramic, which is a widely used high-frequency ferrite. It is usually sintered at high temperatures and contains defects like oxygen vacancy and Fe2+.2,17 Colossal permittivity was previously observed for NZFO ceramic prepared from powders synthesized by citric acid combustion process.4 It is essentially dissipative and may be used as a wave-absorbing material with both high permeability and colossal permittivity. The intrinsic defects, which act like hopping polarons,4 may be the common origin of both the electrical and dielectric properties. The inherent correlation between the conduction and colossal polarization in NZFO ceramic will be revealed in the main text with focus on the detailed analysis on the conduction mechanism.

II. EXPERIMENTAL DETAILS Ni0.5Zn0.5Fe2O4 ceramic was prepared by a traditional ceramic method from NZFO powders that were synthesized by the Received: March 6, 2013 Revised: May 11, 2013 Published: June 10, 2013 12966

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Figure 1. Frequency dependence of (a) permittivity, ε′; (b) tangent loss, tan δ; (c) conductivity, σ′, of NZFO ceramic with a thickness of 1.32 mm sintered at 1220 °C measured at different temperatures; and (d) tan δ of NZFO sintered at 1260 °C with thickness varying from 1.03 to 0.33 mm measured at room temperature (RT). The lines in part c are fitting curves according to eq 1.

electrode/ceramic interface or inside the ceramic body.18,19 It is considered the former only if it becomes large enough for clear observation at sufficiently small thickness. Also it usually manifests at relatively low frequencies due to the larger relaxation time than that of an internal polarization.18 Figure 1d shows a comparison of tan δ of NZFO ceramics with different thicknesses sintered at 1260 °C. It shows that the lowfrequency loss has a long-term trend to decrease with decreasing thickness, although some deviation is also observed which is ascribed probably to the inhomogeneity in different patches from the same ceramic body. An additional peak at several hundreds of hertz appears only for the sample with thickness of 0.33 mm, while the peak at relative high frequencies appears for all samples with only a small shift in its position. It implies that Ag/NZFO interfacial polarization only becomes important when the sample is thin enough and that the colossal permittivity and its dispersion observed in Figure 1a−c (the sample thickness is 1.32 mm in this case) are related to the polarization inside NZFO ceramic. The origin of such huge internal polarization will be investigated in detail, and the typical properties of the sample with thickness of 1.32 mm sintered at 1220 °C will be analyzed. In fact, according to Koops, the dispersion of permittivity in NZFO was ascribed to the relaxation of interfacial polarization at grain boundaries.3 Consequently, the steplike increase in conductivity is owing to successive bridging of resistance of grain boundaries by their huge capacitance as frequency increases.18,19 The variation of the conductivity at high frequency thus is ascribed to bulk conductivity relaxation,18−20 which will be investigated in detail to reveal the nature of the conduction in NZFO. According to Jonscher, the bulk conductivity can be described by the universal dielectric response (UDR)21

citric acid combustion process. Ferric nitrate [Fe(NO3)3·9H2O], nickel nitrate [Ni(NO3)2·6H2O], and zinc nitrate [Zn(NO3)2·6H2O] were used as raw chemicals, and citric acid (C6H8O7·H2O) was stabilizer and fuel. The nominal molar ratio of these chemicals was 4:1:1:18. Initially, they were dissolved in deionized water by stirring. The obtained solution was heated until it was dried and combusted, leaving only loose brown ashes eventually. These ashes were then heat treated at 400 °C to remove the remnant organics possibly remaining. The spinel structure of the powders was confirmed. For preparing ceramics, the powders were granulated to obtain plastic precursors. They were then uniaxially pressed to form green bodies. These green bodies were calcined at 1220 or 1260 °C for 3 h to form ceramics with thicknesses between 1 and 2 mm. The spinel structure of the ceramics was confirmed by X-ray diffraction (XRD). The sample sintered at 1260 °C was divided into several pieces that were then ground to different thicknesses. The surfaces of all samples were polished, applied with Ag paint, and cured at 550 °C to obtain wellconductive electrodes. Permittivity, tangent loss, and conductivity were recorded by a precise impedance analyzer (Agilent 4294A) over a frequency range from 40 Hz to several megahertz. The temperature dependence of the electrical properties of the sample sintered at 1220 °C was measured at temperatures between 130 and 473 K.

III. RESULTS AND DISCUSSION Figure 1 shows the frequency dependence of permittivity (ε′), tangent loss (tan δ), and conductivity (σ′) of Ni0.5Zn0.5Fe2O4 ceramic. Obviously, a colossal permittivity on the order of 104− 106 appears at low frequencies for NZFO ceramic over 130− 473 K. It experiences a Debye-like dispersion as frequency increases, which is accompanied by a large peak and steplike transition in frequency spectra of tangent loss and conductivity, respectively. As known, a high permittivity at low frequencies may be attributed to interfacial polarization either at an

σ ′ = σdc + σ0f s

(1)

where σdc is the dc bulk conductivity, σ0 is a prepower factor, and s is the power of the applied frequency, which should be 12967

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between 0 and 1. As examples, typical fitting curves according to eq 1 are shown in Figure 1c for data measured at 134 and 170 K. As seen, the conductivity of NZFO is agreeable with eq 1 at high frequencies above the transition range. The obtained s is around 0.64 at temperatures below 243 K, which implies that the conduction mechanism may be not changed in this temperature range. As a matter of fact, s should equal to 0 if involved carriers are free to migrate through the ceramic body. Herein, the value of 0.64 indicates that the motion of these charges leads to not only conduction but also considerable polarization.21 It is a typical behavior of localized polarons in disordered systems.21,22 These polarons, which may form from majorities in NZFO lattice, move with the polarization induced in the circumstance with a hysteresis of the latter. Meanwhile, Figure 2 shows that the obtained σdc increases with temperature, implying that the bulk conduction is thermal-assisted.

line in the whole investigated temperature range. In fact according to the theory of nearest-neighbor-hopping (NNH) conduction, the concentration of carriers is not temperature independent but approximately proportional to kT.23 Thus, the temperature dependence of conductivity can be represented as23 σdc = σ2e−E2 / kT

where σ2 is a constant and E2 the activation energy. Consequently, a linear relationship between log10(σdc) and 1/ T is expected for NNH conduction. However, the fitting curve according to eq 3 again deviates from the experimental results to some extent, as shown in Figure 2. It is worth noting that E2 obtained (178.6 meV) is close to E1, which may be ascribed to the fact that in both mechanisms it is assumed that charge hopping only occurs between the neighboring sites and thus the hopping range and activation energy is invariable. In order to avoid the influence of a particular conduction model on the evaluation of the activation energy of the bulk conductivity (Ea), Ea is calculated with the defining equation Ea = −d[ln(σdc)]/d(1/kT).24 The result is shown in the inset of Figure 2 as a function of temperature. Clearly Ea decreases with decreasing temperature, rather than be invariable as supposed in the above two NNH models. In fact, Mott has pointed out that at low temperatures the hopping range can be much larger than the distance between the neighboring equivalent sites due to the lower activation energy involved. Such variable-rangehopping (VRH) conduction can be described by23

Figure 2. Temperature dependence of dc bulk conductivity (σdc) and σdcT of NZFO ceramic sintered at 1220 °C for 3 h. The lines represent the linear fits of the data measured below 235 K with reciprocal temperature.

σdc = σ1e−(T0/ T )

ed 2ve−E1/ kT kT

p

(4)

where σ1 is usually treated as a constant, T0 is also a constant that is given by 3α321/4/[2πkN(EF)] [in which N(EF) is the density of localized states at the Fermi level and α is the decay factor of the localized wave function], and the exponent p may be 1/4,23 1/3,23 and 1/2,25 according to different authors. By comparing eq 4 with the equation defining Ea, it is easily known that 1 − p should equal to the slope of log10(Ea) versus log10(T). From the linear fit shown in the inset of Figure 2, the slope of ∼0.798 is obtained, which is close to 0.75. Consequently, the value of p is most probably 1/4 in this case and the Mott’s 1/4 law may be applicable. Figure 3 shows the linear fit of log10(σdc) with 1/T1/4. As seen, the theoretical curve is well-consistent with the experimental data in the whole temperature range from 130 to 235 K. Furthermore, the

For spinel ferrites, Jonker has established a charge-jumping model to interpret the conduction mechanism of ferrites.13 This mechanism is widely adopted and needs to be discussed.10,11,14,15 In Jonker’s opinion, charges in ferrites that were induced by composition defects like Co3+ and Fe2+ in cobalt ferrite can transfer between the neighboring ions of the same element at B sites when they occasionally come close enough due to lattice vibration, although overlap of their wave functions is little. When the concentration of such charges is large, the influence of temperature on the concentration may be negligible.13 Then the relation between conductivity and temperature can be expressed as13 σdc = neμ = ne

(3)

(2)

where n represents the concentration of charges, μ the mobility, d the jump length, which equals to the distance between neighboring B sites, ν the active lattice frequency in hopping process, and E1 the activation energy involved in the required lattice deformation. Consequently, log10(σdcT) should vary linearly with 1/T. In Figure 2, the experimental σdcT was plotted versus 1/T and compared with the theoretical curve obtained by fitting the experimental data with eq 2. As seen, although the activation energy obtained (193.6 meV) is close to that previously obtained for electron hopping in cobalt ferrite (175−205 meV) and electron/hole hopping in nickel ferrite (110/280 meV) and nickel zinc ferrite (230/240 meV),13−15 eq 2 cannot describe σdc very satisfactorily. The experimental results appear to not vary in strict accordance with a straight

Figure 3. Temperature dependence of dc bulk conductivity of NZFO ceramic sintered at 1220 °C for 3 h. The line represents the linear fit of the data below 235 K with eq 4. The inset shows the hopping energy and hopping range shown as a function of temperature in a log−log coordinate system. 12968

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of free space. For N(EF) on the order of 1019 cm−3 eV−1, the charge concentration n should be at least on the same order. Such high concentration led the value of the contribution of WD to be about 100 meV, which composes about one-half of W at 235 K. Second, the random field set up in NZFO lattice would be further enhanced due to the special spinel structure, thus supplying an additional disorder energy. As known in NZFO lattice with spinel structure, about 1/2 of the B sites and 7/8 of the A sites (the interstices of oxygen tetrahedron) are unoccupied by the cations, and about 3/4 of Fe3+ occupy B sites while the other occupy A sites owing to the higher priority of Ni2+ to fill B sites.35 In consequence, for hopping charges like electrons transferring from Fe2+ to Fe3+, additional disorder energy would be induced owing to32 (i) the random distribution of Ni2+ and Fe3+ in B sites, which are much excessive; (ii) indirect hopping of the electrons attached to B sites via an A site; (iii) indirect charge exchange between Fe3+ and Fe2+ via Ni2+;14,36 and (iv) some Fe2+ entering the A site due to its position priority,35 thus distorting the oxygen environment. Therefore, in NZFO the real contribution of WD to W may be considerably larger than 100 meV and compose the main part of the activation energy. The observed polarons’ VRH at T > 130 K hence arises most probably due to both the high concentration of the hopping charges and the enhanced random field generated due to the special structure of spinel. However, further investigation on the detailed evaluation of WH and WD is needed for clearer understanding of the conduction mechanism of NZFO. In NZFO ceramic, a charge concentration (n) as high as 1019 cm−3 may result from Fe2+ generated by volatization of oxygen and zinc during calcination.17 It is similar to the case of other transitional metal oxides such as BaTiO3 and CaCu3Ti4O12 ceramic, in which insufficient oxidation of Ti3+ together with some deficiency in oxygen is usually observed.20,37 Actually, preparing ferrites with high resistivity usually requires sintering at high oxygen pressure or compensating the intrinsic defects by doping.10,38 The crucial role of oxygen can be confirmed to some extent by Figure 4, in which the high-frequency

activation energy W of VRH can be derived by applying the defining equation to eq 4: W = 0.25kT01/4T3/4. The fitting value of T0 is 8.9 × 108 K in this case. Then W can be calculated at different temperatures, which is shown in the inset of Figure 3. As seen, the activation energy W decreases from 223.3 to 143.3 meV as temperature decreases from 235 to 130 K. It well covers that of Ea, which decreases from 219 to 143 meV as temperature decreases from 231 to 130 K. It is strong evidence that polarons moving by VRH are responsible for the bulk conductivity of NZFO. Moreover, in VRH theory the most probable hopping range R is given by 31/4/[2παN(EF)kT]1/4.23 By adopting an estimated value of α, N(EF) can also be deduced from the fitting value of T0 and thus R can be obtained. Here, 1/α is taken to be the Bohr radius of the localized center (rB),26 which can be calculated from the ionization energy of the majority (Ei). Ei is obtained with the high-temperature activation energy of the believed intrinsic conduction of Ni0.5Zn0.5Fe2O4 ceramic (0.51 eV),27 which is a good estimation when the majority concentration is high. Then, rB = 7.2Ei/κ = 0.83 Å, where κ = 17 is the intrinsic permittivity of NZFO lattice.3 The calculated value of N(EF) is 1.37 × 1019 cm−3 eV−1, which implies a high charge concentration in NZFO. The value of R is shown in the inset of Figure 3. As seen, the most probable hopping range increases from 3.5 to 4.1 nm as temperature decreases from 235 to 130 K. It is worth noting that all the calculated values of R and W at different temperatures satisfy the necessary criteria for VRH: W > kT and αR > 1.24,28−30Also the minimum R at 235 K is much larger than the distance of the neighboring B sites d (d = 20.5a/4 = 0.297 nm,13 where a = 0.841 nm and is the lattice constant obtained from PDF#52-0278) and the average distance of iron ions at B sites (≈0.456 nm, estimated by 2[(a3/ 12)/(4π/3)]1/3), implying that 235 K is much lower than the maximum temperature corresponding to the shortest hopping distance permitted for VRH to occur.31 Therefore, VRH of localized polarons consistent with Mott’s 1/4 law is appropriate to interpret the bulk conduction mechanism of NZFO ceramic. For hopping conduction, the activation energy is made up of WH and WD/2, of which the former is the energy required to change the energy level of the hopping sites involved in a hopping event and the latter represents the disorder energy characterizing the energy difference among the hopping charges.32 WH would die away gradually below θD/2, where θD is the Debye temperature and usually on the order of several hundred degrees kelvin for inorganic oxides.33 If the WD term becomes important enough compared to WH at intermediate temperatures (>100 K) such that it dominates the response, the VRH mechanism would take place, owing to the fact that large hopping distance is undoubtedly favored for finding sites where the difference in charge energy is small.23 As a matter of fact, there has been much literature in which VRH manifests at temperatures covering T > 100 K, such as that in Sm- and Hosubstituted nickel ferrites and La-doped Co ferrite at 160−220 K, 1 6 , 2 9 CaCu 3 Ti 4 O 12 ceramic at 80−180 K, 2 0 Pb[(Fe1/3Sb2/3)xTiyZrz]O3 ceramic at 77−350 K,26 CdTe thin film at 100−160 K,28 reduced lithium niobate single crystals at 77 to ∼300 K,30 and Ba0.85Sr0.15TiO3 ceramic at 25−400 °C.34 Here for NZFO ceramic, the disorder energy would contribute to the activation energy in two ways. First, the energy spread of the hopping charge would increase with increasing the concentration. Its contribution to the activation energy can be estimated with the Miller−Abrahams formula 0.4e2/ (κε0n−1/3), as used for CoFe2O4,32 where ε0 is the permittivity

Figure 4. Conductivity of NZFO ceramic sintered at 1220 °C for 3 h with no annealing and that annealed in air at 600 °C for 24 h.

conductivity of NZFO ceramic is shown to decrease much after it was annealed in air at 600 °C for 24 h. Diffusion of oxygen from atmosphere and grain boundary to the body may have a positive effect to reduce the hopping electrons in the assintered NZFO ceramic.10 Figure 5 shows the dielectric relaxation of NZFO ceramic revealed with peak frequency of loss [log10( f r)] versus temperature (1000/T). For peak frequency ( f r) measured below about 259 K, the linear relationship between log10( f r) and 1/T is maintained to a significant extent, which implies that 12969

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Figure 5. Temperature dependence of relaxation frequency of NZFO ceramic sintered at 1220 °C for 3 h. The line represents the Arrhenius fit of the experimental data measured below 259 K.

Figure 6. Experimental (exp) and fitting (fit) data of the real (real) and imaginary (imag) part of permittivity of 1220 °C-sintered NZFO ceramic measured at 194 K. The fitting curves were calculated according to the given equivalent circuit, in which σ0_g = 5.84 × 10−9 S cm−1, sg = 0.46, σdc_g = 1.33 × 10−5 S cm−1, σ0_gb = 7.44 × 10−11 S cm−1, sgb = 0.83, σdc_gb= 1.11 × 10−15 S cm−1, permittivity at very high frequency ε∞ = 53.2, and thickness ratio of grain boundary to grain η = 0.01. Herein, g and gb denote grain and grain boundary, respectively.

the dielectric relaxation approximately obeys Arrhenius’ equation in this temperature range

fr = f0 e−E3 / kT

(5)

where f 0 is the relaxation frequency at infinite temperature and E3 is the activation energy of dielectric relaxation in NZFO. By fitting, f 0 and E3 were obtained as 7.51 × 108 Hz and 187.2 meV, respectively. Herein, it is worth noting that the value of E3 is close to E1, E2, and the average value of W obtained above, which implies the inherent correlation of polarization and bulk conduction in NZFO. Actually, according to the internal interfacial polarization model mentioned above, f r is approximately proportional to σdc,3,20 which may be the reason why f r shows a temperature dependence similar to that of σdc. One difference is that f r shows no obvious deviation from the linear relation of log10( f r) versus 1/T, which may be owing to the influence of the conductivity of grain boundaries and the lack of data measured at lower temperatures. Moreover, f 0 ( f 0 ≫ f r) is much lower than the lattice frequency ν (1.2 × 1013 s−1 according to the FTIR result), indicating that the concerned dielectric relaxation requires much longer characteristic time than charge hopping. It is also consistent with the interfacial polarization model in which the polarization is established through accumulation of carriers at grain boundaries which obviously requires much longer time since carriers must move from one side of a grain to the opposite by multiple hopping. Besides, in Figure 5, the slope of log10(f r) versus 1/T increases as temperature approaches and exceeds room temperature. It may be probably due to the gradual activation of motion of oxygen vacancy at high temperatures.11 On the basis of the above discussion, the Koops’ equivalent circuit, which is phenomenologically equivalent to the widely used IBL model, may be adopted to satisfactorily describe the internal dielectric response of NZFO ceramic after appropriate modification. As shown in Figure 6, grain and grain boundary are still supposed to be in series with each other. However, they are represented by three parallel elements: a conductance, a capacitance, and a constant phase element (CPE), rather than only the former two, as used in Koops’ model. The CPE is adopted to model UDR in this case. By use of the corresponding analytical equation deduced in another paper for such a circuit,4 the theoretical permittivity of grains and grain boundaries can be calculated for NZFO, which is shown in Figure 6 with data measured at 194 K as an example. As seen, the theoretical curve calculated with this circuit is in good agreement with the experimental data in the whole frequency range. The fitting value of σdc of grains (1.33 × 10−5 S cm−1) is

significantly agreeable with that obtained above from the highfrequency conductivity (1.41 × 10−5 S cm−1). σdc of grains is much higher than that of grain boundaries (1.11 × 10−15 S cm−1), which is accordant with the IBL model. The low conductivity of grain boundaries may result from reoxidation during cooling due to the easy adoption of oxygen from the atmosphere for boundaries. Obviously, as seen in Figure 6, the more conductive grains control the high-frequency response, while the much thinner grain boundaries dominate the colossal low-frequency response. Figure 7 shows the temperature dependence of permittivity of NZFO measured at different frequencies. At the low-

Figure 7. Temperature dependence of permittivity of NZFO ceramic sintered at 1220 °C for 3 h measured at different frequencies.

temperature end, the permittivity measured at different frequencies tends to a very low value of about several tens as temperature decreases. In this temperature range, the polaron hopping is frozen gradually. The permittivity approaches ε∞, which is mainly attributed to ionic and electronic polarization in the ceramic body. As temperature increases, the electron hopping is activated gradually by the lattice vibration. Consequently, the permittivity increases significantly due to the large difference between the conductivity of grains and grain boundaries. Then the value tends to be stable, which decreases with frequency owing to the relaxation of the interfacial polarization. Considering the loss peak at several hundreds of herytz in Figure 1d, the weak wide peak over 220− 320 K appearing at frequencies below 103 Hz in Figure 7 may originate from the damping resonance of Ag/NZFO interfacial 12970

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(9) Brockman, F. G.; Dowling, P. H.; Steneck, W. G. Dimensional Effects Resulting from a High Dielectric Constant Found in a Ferromagnetic Ferrite. Phys. Rev. 1950, 77, 85−93. (10) Byeon, S. C.; Hong, K. S.; Park, J. G.; Kang, W. N. Origin of the Increase in Resistivity of Manganese−Zinc Ferrite Polycrystals with Oxygen Partial Pressure. J. Appl. Phys. 1997, 81, 7835−7842. (11) Ponpandian, N.; Narayanasamy, A. Influence of Grain Size and Structural Changes on the Electrical Properties of Nanocrystalline Zinc Ferrite. J. Appl. Phys. 2002, 92, 2770−2779. (12) Kamiyoshi, K. I. Low Frequency Dispersion in Ni- and CoFerrites. Phys. Rev. 1951, 84, 374−375. (13) Jonker, G. H. Analysis on the Semiconducting Properties of Cobalt Ferrite. J. Phys. Chem. Solids 1959, 9, 165−175. (14) Elwell, D.; Griffiths, B. A.; Parker, R. Electrical Conduction in Nickel Ferrite. Br. J. Appl. Phys. 1966, 17, 587−593. (15) Satyanarayana, R.; Murthy, S. R. Electrical Conductivity and Thermoelectric Power of Nickel−Zinc Ferrites. Cryst. Res. Technol. 1985, 20, 1109−1116. (16) Bharathi, K. K.; Markandeyulu, G.; Ramana, C. V. Structural, Magnetic, Electrical, and Magnetoelectric Properties of Sm- and HoSubstituted Nickel. J. Phys. Chem. C 2011, 115, 554−560. (17) Van Uitert, L. G. dc Resistivity in the Nickel and Nickel Zinc Ferrite System. J. Chem. Phys. 1955, 23, 1883−1888. (18) Lunkenheimer, P.; Bobnar, V.; Pronin, A. V.; Ritus, A. I.; Volkov, A. A.; Loidl, A. Origin of Apparent Colossal Dielectric Constants. Phys. Rev. B 2002, 66, 052105. (19) Pizzitutti, F.; Bruni, F. Electrode and Interfacial Polarization in Broadband Dielectric Spectroscopy Measurements. Rev. Sci. Instrum. 2001, 72, 2502−2504. (20) Zhang, L.; Tang, Z. J. Polaron Relaxation and Variable-RangeHopping Conductivity in the Giant-Dielectric-Constant Material CaCu3Ti4O12. Phys. Rev. B 2004, 70, 174306. (21) Jonscher, A. K. Universal Relaxation Law; Xi’an Jiaotong University: Xi’an, 2008. (22) Elliott, S. R. AC Conduction in Amorphous Chalcogenide and Pnictide Semiconductors. Adv. Phys. 1987, 36, 135−217. (23) Mott, N. F.; Davis, E. A. Electronic Processes in Non-crystalline Materials; Clarendon: Oxford, 1979. (24) Bharadwaja, S. S. N.; Venkatasubramanian, C.; Fieldhouse, N.; Ashok, S.; Horn, M. W.; Jackson, T. N. Low Temperature Charge Carrier Hopping Transport Mechanism in Vanadium Oxide Thin Films Grown Using Pulsed DC Sputtering. Appl. Phys. Lett. 2009, 94, 222110. (25) Efros, A. L.; Shklovskii, B. I. Coulomb Gap and Low Temperature Conductivity of Disordered Systems. J. Phys. C: Solid State Phys. 1975, 8, L49−L51. (26) Osak, A. Hopping Electrical Conductivity in Ferroelectric Pb[(Fe1/3Sb2/3)xTiyZrz]O3. Ferroelectrics 2011, 418, 52−59. (27) El-Sayed, A. M. Electrical Conductivity of Nickel−Zinc and Cr Substituted Nickel−Zinc Ferrites. Mater. Chem. Phys. 2003, 82, 583− 587. (28) Sharma, K.; Al-Kabbi, A. S.; Saini, G. S. S.; Tripathi, S. K. Electrical Conduction Mechanism in Nanocrystalline CdTe (ncCdTe) Thin Films. Appl. Phys. A: Mater. Sci. Process. 2012, 108, 911− 920. (29) Bharathi, K. K.; Ramana, C. V. Improved Electrical and Dielectric Properties of La-Doped Co Ferrite. J. Mater. Res. 2011, 26, 584−591. (30) Dhar, A.; Singh, N.; Singh, R. K.; Singh, R. Low Temperature DC Electrical Conduction in Reduced Lithium Niobate Single Crystals. J. Phys. Chem. Solids 2013, 74, 146−151. (31) Bottger, H.; Bryesi, V. V. Hopping Conductivity in Ordered and Disordered Solids (I). Phys. Status Solidi B 1976, 78, 9−56. (32) Austin, G.; Mott, N. F. Polarons in Crystalline and NonCrystalline Materials. Adv. Phys. 1969, 18, 41−102. (33) Karmaka, A.; Majumdar, S.; Giri, S. Tuning A-Site Ionic Size in R0.5Ca0.5MnO3 (R = Pr, Nd and Sm)Robust Modulation in dc and ac Transport Behavior. J. Phys.: Condens. Matter 2011, 23, 495902.

polarization. The increase of permittivity at the high-temperature end results from activated band conduction probably.27

IV. CONCLUSIONS In summary, the dielectric properties of Ni0.5Zn0.5Fe2O4 ceramic prepared from powders synthesized by the citric acid combustion method were investigated in depth. NZFO ceramic exhibits a colossal permittivity as high as 104−106 at temperatures from 130 to 473 K. The Debye-like dielectric dispersion is mainly attributed to the internal polarization of NZFO ceramic rather than the interfacial polarization at the electrode/ceramic interface. Its bulk conductivity is confirmed to originate from variable-range hopping of localized polarons, which may be closely associated with the intrinsic oxygen vancancy. These polarons are frozen at low temperature and activated at high temperature. As temperature decreases from 235 to 130 K, their hopping energy decreases from 223 to 113 meV, while the hopping range increases from 3.5 to 4.1 nm. The direct correlation of polaron conduction and colossal permittivity of NZFO is definitely established by a modified Koops’ equivalent circuit based on the internal barrier layer (IBL) model, which is well-confirmed by the experimental data.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86-571-87952324. Fax: +86-571-87952324. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Natural Science Foundation of China under grant Nos. 51272230 and 50872120, Zhejiang Provincial Natural Science Foundation (Grant No. Z4110040), and the National Key Scientific and Technological Project of China (Grant No. 2009CB623302), respectively.

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