Metal-semiconductor transition in NiFe2O4 nanoparticles due to reversecationic distribution by impedance spectroscopy

M. Younas,1 M. Nadeem,1,a) M. Atif,2 and R. Grossinger21EMMG, Physics Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan2Institute of Solid State Physics, Technical University of Vienna, Wiedner Hauptstrasse 8-10,A-1040 Vienna, Austria

(Received 1 December 2010; accepted 24 March 2011; published online 6 May 2011)

We have investigated the magnetic and electrical response of the sol-gel synthesized NiFe2O4

nanoparticles. Changes in the impedance plane plots with temperature have been discussed andcorrelated to the microstructure of the material. Thermally activated hopping carriers betweenFe3!-Fe2! and Ni2!-Ni3! ions have been determined for a decrease in the resistance of the sampleand a change in the conduction mechanism around 318 K. The mixed spinel structure and brokenexchange bonds due to small size effects are due to the canted spin structure at the surface of thenanoparticles. The magnetization is found to be influenced by the surface spin canting andanisotropy. We have established the semiconducting to metallic transition (SMT) temperature to bearound 358 K in terms of localized and delocalized eg electrons along with a transition from lessconductive [Fe3!–O2"–Fe3!] and [Ni2!–O2"–Ni2!] linkage to more conductive [Fe3!–Fe2!] and[Ni2!–Ni3!] linkage at the octahedral B site. A decrease in the dielectric constant with temperaturehas been discussed in terms of the depletion of space charge layers due to the repulsion ofdelocalized eg electrons from the grain boundary planes. The anomalies in tangent loss andconductivity data around 358 K are discussed in the context of the SMT.VC 2011 American Instituteof Physics. [doi:10.1063/1.3582142]

I. INTRODUCTION

Spinel ferrite nanoparticles by virtue of their unique elec-tronic, magnetic, and physical structure may be harnessed fortechnological applications.1,2 Nano ferrites are an importantclass of materials because of their high resistivity and loweddy current losses.3 Bulk spinel ferrites are described by theformula (A)[B]2O4, where (A) and [B] represent the tetrahe-dral and octahedral sites, respectively. Nanocrystalline ferritesystems usually have a mixed spinel structure having thechemical formula, #M2!

1"dFe3!d $%M2!

d Fe3!2"d&O2"4 . The divalent

metal ion M2! can occupy the either tetrahedral (A) or octahe-dral [B] sites or both sites of the spinel structures, dependingupon the nature of the system. The inversion parameter, d, isdefined as the fraction of the (A) sites occupied by Fe3! cati-ons and its value depends on the method of preparation.4,5

NiFe2O4 is a well-known inverse spinel structure, with Ni2!

ions occupying only the B sites. Chinnasamy et al.6 haveshown that nanocrystalline NiFe2O4 exhibits a mixed spinelstructure with Ni2! ions occupying both (A) and [B] sites.NiFe2O4 nanoparticles with a mixed spinel structure havebeen shown to exhibit interesting electrical, magnetic, gas,and humidity sensing properties.6,7

The NiFe2O4 sample exhibits paramagnetic, superpara-magnetic, or ferrimagnetic behavior depending on themicrostructure.8 Scherrer9 observed ferromagnetic andsuperparamagnetic behavior in NiFe2O4 nanoparticles withgrain sizes of 17 and 10 nm, respectively. A reduction in the

saturation magnetization of NiFe2O4 due to a reduction ingrain size has been reported to result from the noncollinear-ity of the magnetic moments at the surface.10 Core-shellmorphology is appropriate to explain the magnetic propertiesof the nanoparticles. Chinnasamy et al.6 reported the highvalue of magnetocrystalline anisotropy in the mixed spinelNiFe2O4 sample with a canted spin structure at the surfaceand the core. Several methods have been used for the prepa-ration of ferrite nanoparticles such as ball milling, thermaldecomposition, and the sol-gel technique.11,12 The propertiesof the ferrites are very sensitive to the synthesis techniques.The sol-gel method is a versatile technique to vary the prop-erties of the material by controlling different parameterssuch as temperature, time of reaction, pH of the medium,and the reagent’s concentration.13 Atif et al.4 observed morereverse cationic distribution in the ZnFe2O4 nanoparticlesprepared in urea (i.e., a basic medium) rather than in citricacid (i.e., an acidic medium). In the present study we pre-pared NiFe2O4 nanoparticles in a basic medium and carriedout magnetic and electrical measurements to determine anypossible change in the conduction mechanism. To the best ofour knowledge, any possible correlation between the electri-cal parameters and the microstructure for NiFe2O4 nanopar-ticles above room temperature has not yet been reported.

Impedance spectroscopy is a powerful technique in solidstates because of its ability to differentiate the transport char-acteristics in grains and grain boundaries.14 The grains andthe grain boundaries are the two main components that com-prise the microstructure and the correspondence between thegrains and grain boundaries is important in understandingthe overall properties of these materials.15 Impedance

a)Author to whom correspondence should be addressed. Electronic mail:mnadeemsb@gmail.com.

0021-8979/2011/109(9)/093704/8/$30.00 VC 2011 American Institute of Physics109, 093704-1

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spectroscopy can be used to study the electrical behavior ofdifferent microstructures (phases) inside a polycrystallinematerial. Using the impedance technique, data equivalent tothe real and imaginary parts of complex electrical quantitiesare measured as a function of the frequency of the appliedelectric field.16 These complex quantities include electricalimpedance, dielectric permittivity, and loss tangent, tan d.The electric and dielectric properties of the ferrites are pre-dominantly controlled by the grain boundaries.17 The dielec-tric properties of the NiFe2O4 nanoparticles will beconstructive for extending the range of applications. Theelectrical properties of ferrites provide supportive informa-tion about the behavior of the localized electric charge car-riers and an understanding of the dielectric polarizationmechanism. Cation–cation interactions are distinguishedfrom cation–anion–cation interactions by affecting the elec-trical and magnetic properties of oxides containing transitionmetal elements.18 In this respect, impedance spectroscopyhas been successfully employed to explore the possible roleof these interactions in changing the electrical and magneticproperties. The temperature did not exceed 373 K to inhibitany possible grain growth during experimentation.

II. EXPERIMENTAL

NiFe2O4 nanoparticles were prepared by the sol-gelmethod. Analytical grade Ni(NO3) . 6H2O, Fe(NO3)3 . 9H2Oand urea were used for material preparation. We separatelydissolved 0.1 M of Ni(NO3) . 6H2O and Fe(NO3)3 . 9H2O in aminimum amount of distilled water. This solution was thenmixed in the aqueous solution of urea in a molar ratio of 1:3.The mixed solution was heated to a temperature of 338–343 Kwith vigorous stirring until the gel was formed, which was sub-sequently dried at 393 K for 3 h in an oven. The dried gel washeat treated at 573 K for 3 h to remove volatile species. Thenthe powder was pressed into a pellet 13 mm in diameter and1.5 mm in thickness. Finally, the pellet was sintered at873 K for 4 h. The structural characterization was performedby an x-ray diffractometer (XRD) having Cu Ka radiation(1.5418 A). The intensities were recorded for 20o' 2h' 70o

with a step scan of 0.02o with a time of 1 s/step. The measure-ments of the hysteresis loops were performed by using a physi-cal property measurement system (PPMS-9 T, QuantumDesign) applying a magnetic field of 5 T.

Impedance spectroscopy on the sintered pellet of NiFe2O4

was performed in the frequency and temperature range of1' frequency' 107 Hz and 298 K' temperature' 373 K,respectively, using an Alpha-N analyzer (Novocontrol, Ger-many). The surfaces of both sides of the pellet were properlycleaned and contacts were made by silver paint on oppositesides of the pellet, which were cured at 423 K for 3 h. Beforethe impedance experiments, the dispersive behavior of theleads were carefully checked to exclude any extraneous induc-tive and capacitive coupling in the experimental frequencyrange. The ac signal amplitude used for all of these studieswas 0.2 V. WINDETA software was used for data acquisition,which was fully automated by interfacing the analyzer with acomputer. ZVIEW software was used for the fitting of the meas-ured results. The sample was arranged inside a homemade

sample holder and a dc power supply was connected to thesample holder to stabilize the temperature. Measurementswere made after stabilizing the temperature for about 10 minprior to each reading.

III. RESULTS AND DISCUSSION

Figure 1 shows the XRD pattern of the synthesized nickelferrite nanopowder. All XRD peaks are indexed well with thestandard pattern for NiFe2O4 reported in PCPDF card #74-2081. The average crystallite size has been calculated fromthe most intense peak (311) using Scherer’s formula d( kk/bcos h where d is the particle size, b is the full width at halfmaximum of the peak (311) and k is an instrumental con-stant.19 The average calculated particle size has been found tobe 226 3 nm. The lattice parameter (8.339 A), computedusing respective (hkl) values, is less than that of the bulk ma-terial. This reduction in lattice parameter may be attributed tothe increased degree of inversion, more surface energy, andsurface tension which can lead to the distortion of the latticeconstant.4,20 Fig. 2 shows the field dependent magnetizationof the NiFe2O4 sample measured at different temperatures inan applied field up to 5 T. From these measurements, it hasbeen found that the magnetization does not saturate at themaximum available field (i.e., 5 T) and the values of magnet-ization obtained at 300, 350, and 400 K are 15, 14, and 13emu/g, respectively. The room temperature magnetizationvalue is considerably smaller than the bulk value of 56 emu/gfor nickel ferrite.21 This can be explained on the basis of thecore-shell morphology of the nanoparticles with a ferrimag-netically aligned core surrounded by the surface shell, whichis found to be structurally and magnetically disordered due tothe nearly random distribution of cations and the canted spinarrangement. The origin of this surface disorder may be dueto broken exchange bonds, high anisotropy on the surface, ora loss of the long-range order in the surface. Furthermore,canted or disordered spins at the surface of the nanoparticlesare difficult to align along the field direction causing an unsat-urated magnetization in these particles.22–24 As a consequence

FIG. 1. X-ray diffraction pattern of the NiFe2O4 sample recorded at roomtemperature.

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of the frustrated superexchange interactions in the surfaceshell, our prepared nickel ferrite sample exhibits a reduced un-saturated magnetization which is attributed to the weakeningof the AB exchange interactions due to the effect of spin cant-ing that dominates over the effect of site exchange of the cati-ons in the surface shell.25

Figures 3(a) and 3(b) show the complex impedanceplane plots of the NiFe2O4 sample at different temperaturesand the arrow shows the direction of the increase in fre-quency. At each temperature, impedance plane plots showtwo well resolved semicircular arcs, a larger one at low fre-quency and a smaller one at the higher frequency side. Theappearance of two arcs in impedance plane plots at each tem-perature indicate the presences of two types of relaxationphenomena with sufficiently different relaxation times(s(RC), where R is the resistance and C is the capacitanceof the associated phase.16 The size of the semicircular arcsdecreases with the increase in temperature and shows itsminima around 358 K. A further increase in temperaturecauses an increase in the diameter of the impedance planeplots as seen in Fig. 3(b). The centers of both of the semicir-cular arcs have been found to be depressed below the realaxis indicating the heterogeneity and deviation from the idealbehavior.16 We define this temperature (358 K) as the semi-conducting to metallic transition (SMT) temperature. The

fitting parameters derived for the equivalent circuit will bediscussed in the next paragraph.

In order to correlate the electrical properties of theNiFe2O4 sample with the microstructure of the material, anequivalent circuit model (RgQg) (RgbQgb), shown in the insetof Fig. 3(a) has been employed to interpret the impedanceplane plots. Here R, Q, g and gb are the resistance, the con-stant phase element, grain interiors and grain boundaries,respectively. The constant phase element (CPE) is used toaccommodate the nonideal behavior of the capacitancewhich may have its origin in the presence of more than onerelaxation process with similar relaxation times.16 The ca-pacitance of the CPE is given by the following relation,C ( Q1=nR#1"n$=n, where the parameter n estimates the noni-deal behavior having a value of zero for pure resistive behav-ior and is unity for capacitative behavior.26,27 In these typesof ferrites, the grain boundary resistance is generally higherin comparison to the grains.3 Additionally, the arc represent-ing the grain boundaries generally lies on the lower fre-quency side since the relaxation time of the grain boundariesis much larger than that of the grains.28 Therefore, we assignsmaller (high frequency) and larger (low frequency) semicir-cular arcs to the grains and grain boundaries, respectively.29

The parameters Rg, Rgb, Qg, Qgb, ng, and ngb were obtainedfor each temperature by fitting the impedance plane plots(within 1% fitting error). Figure 4(a) implies that slight var-iations in parameters n and C for the grain and grain bounda-ries in the 298–338 K range is indicative of theinhomogeneous distribution of the energy of the trap centers.With an increase in temperature, there are visible increasingand decreasing trends in the values of ng and ngb, respec-tively, in the 338–358 K range. These trends signify that thegrain capacitance (Cg) is likely to approach ideal behaviorand the grain boundary (Cgb) deviates from the ideal behav-ior as shown in Fig. 4(b). A decrease in the capacitance ofthe grains may be due to the vanishing of defects such as therelease of trapped charges followed by the accumulation ofthese charges at the grain boundaries, thereby increasing itscapacitance. Above 358 K (i.e., the SMT temperature), bothCg and Cgb parameters start saturating. Saturation in thecapacitances of the grains and grain boundaries may be dueto the combined effect of the delocalized charge carries andspin alignments.

Figures 5(a) and 5(b) illustrate the variations in the resis-tances of the grain and grain boundaries with temperature.

FIG. 3. (Color online) (a) Impedanceplane plot of the NiFe2O4 sample at roomtemperature. Inset shows the equivalentcircuit model. Arrow shows the directionof increase in frequency. (b) Impedanceplane plot at some selected temperatures.Inset shows the impedance plane plotbetween 363–373 K.

FIG. 2. (Color online) Magnetization against applied field at differenttemperatures.

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The inset of Fig. 5(b) shows the variations in the total resist-ance of the sample with temperature. The decrease in the re-sistance of grains and grain boundaries has been suggested tobe due to the thermal activation of the localized charges.Two types of thermal activations, i.e., carrier density in thecase of band conduction and carrier mobility in case of hop-ping, are responsible for the reduction in the resistive proper-ties with temperature.15 With the increase in temperatureabove 338 K, the grain resistance shows increasing trendswhile the grain boundary and total resistance (shown in theinset of Fig. 5) still show decreasing trends. The balancebetween the mobility and density of the thermally activatedhopping carriers plays a vital role in determining the changein resistance with temperature. Above 338 K, there is adecrease in the density of thermally activated hopping car-riers within the grains but the mobility of the hopping car-riers increases with temperature. The increased value of themobility compensates for the decrease in the density of thehopping carriers and we observe a decrease in the total resist-ance of the sample with a temperature up to 358 K as shownin the inset of the Fig. 5(b). An increasing trend in the resist-ance of the grain boundaries beyond 358 K shows its metal-lic behavior. On the whole, the conduction mechanism canbe implicit by considering the potential of the grain boundaryand energy of the eg electrons. In ferrites, transport phenom-ena usually arise by the hopping of localized d electronsbetween valence distributions of cations that normallyoccupy the oxygen octahedral site.18 The electrostatic inter-action between anion and cation electrons cause a splittingof the cation 3d level into less stable doubly degenerate egelectrons and more stable triply degenerate t2g electrons.

30 IfEk is the energy of eg electrons, U is the potential of the grainboundaries, n is the number density of the eg electrons, thenmathematically, n ( nee/=kTe, where e is the charge on a sin-gle electron, U is the potential applied by the grain bounda-ries, k is the Boltzmann constant, Te is the temperature of egelectrons, and n0 is the number density of electrons atU) 0.27 If Ek> eU then the electrons will be delocalizedand actively participate in the conduction mechanism butwhen Ek< eU, then eg electrons will be localized. It isinferred here that below 358 K, in the presence of some non-magnetic disorder (i.e., electronic trap center) and magneticdisorder (i.e., disorientation of the surface and core spins) eg

electrons will be localized, satisfying the condition ofEk< eU and with an increase in temperature up to 358 K, thehopping probability of the eg electrons increases, therebydecreasing the resistance of the sample. However, with a fur-ther increase in temperature above 358 K, localized statesbecome delocalized along with alignments of the core/sur-face spins and effective conducting channels appear. Con-ducting channels facilitate the movement of charge carriersthereby increasing their mobility and we observe metal-likebehavior in this temperature range. Moreover, at the SMTtemperature, all of the eg electrons might have multipotentialvalues that give rise to a competition between localized anddelocalized charge carriers.

The activation energy for the thermally activated chargecarriers is obtained by fitting the dc conductivity data usingthe Arrhenius relation, r ( r0 exp%"Ea=kT&, where r0 is thepre-exponential factor, Ea is the activation energy, and k isBoltzmann’s constant. The resistance values of the grains(Rg), grain boundaries (Rgb), and geometrical dimensionshave been used to calculate the total dc conductivity by usingthe relation, r ( L=A:R, where r is the conductivity inS cm"1, A is area of the sample in cm2, L is length of thesample in cm, and R is the total resistance of the grains andgrain boundaries in X.31 From Fig. 5(c) a change in slope isobserved beyond 318 K, showing that a different conductionmechanism is involved. The activation energies 0.71 and0.41 eV have been calculated from the fitted data below andabove 318 K, respectively. A higher value of the activationenergy below 318 K suggests dominant hole hoppingbetween Ni2! $ Ni!3 ions at the octahedral B-site, and theNi!3 ions are in a low spin state t62g; e

1g

! "as compared to the

Fe!3 t32g; e2g

! "ions. With the increase in temperature above

318 K, the electrons gain enough energy to dominate theoverall conduction mechanism that causes a reduction in theactivation energy since electron hopping requires a lowervalue of activation energy compared to that of holehopping.31

Goodenough32 predicted the simultaneous existence ofthe both cation–cation and cation–anion–cation interactions inthe rock salt type structures such as NiO, MnO, FeO, etc.When strong cation–anion–cation interactions dominate overthe weak cation–cation interactions, these materials have semi-conducting/insulating behavior. In the case of strong cation–

FIG. 4. (Color online) (a) Variation ofparameters ng and ngb with temperature,and (b) variation of grains and grainboundary capacitances with temperaturefor the NiFe2O4 sample.

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cation interactions between octahedral B-site, these materialsshow metallic behavior, and may become semiconducting atlow temperatures. Also, the presence of cations of the sameelements with different valence states give rise to the metalliccharacter below the Curie temperature. In NiFe2O4 with nor-mal cation distribution (Fe3!)[Ni2!Fe3!]O4

2", the cation–cation interaction is dominated by the cation–anion–cationinteractions between [Fe3!–O2"–Fe3!] and [Ni2!–O2"–Ni2!].33,34 In the view of crystal field and ligand field theories,the Ni2!–O2"–Ni2! interactions are dominant which renderedthis material to be semiconducting. However, Ni2! ions maydistribute randomly on (A) and [B] sites along with Fe3! ionsdue to some reverse cationic distributions in the nanocrystal-line NiFe2O4 material. The room temperature Mossbauer spec-troscopy (the result will be shown in a forthcoming paper)revealed the sextet and relaxed magnetic structure with a verybroad linewidth. The broad linewidth is observed due to thefield distribution for small crystallite size which is about 22nm in this case. The reduced value of the hyperfine field at theB site compared to the bulk counterpart35 is the result of thedistribution of the crystallite size. The inversion parameter esti-mated from the Mossbauer spectroscopy was 0.64. Thereduced value of the tetrahedral isomer shift as compared tothe octahedral isomer shift for this material has been attributedto the difference in the coordination of the Fe3! from the fourfold site (A site) to the six fold (B site). Hence, in this materiala fraction of Fe3! and Ni2! ions migrate to the [B] and (A)sites, respectively. Shifting of the Fe3! ions causes compres-sive strains due to the smaller distance between the B-site ions

compared to the A-site ions in nanoparticles.7 These compres-sive strains may break the surface exchange bonds whichresults in a canted spin structure. The canted spin structure notonly affects the [Ni2!–O2"–Ni2!] interactions but also weak-ens the AB-exchange interactions that cause a lower value ofthe room temperature magnetization compared to the bulkcounterpart previously discussed. An increased numberof Fe3! at [B] enhances the exchange interaction between[Fe3!–O2"–Fe3!]. It is presumed here that below 258 K, anincrease in temperature causes an increase in hopping of thelocalized charge carriers between the [Fe3!–O2"–Fe3!] and[Ni2!–O2"–Ni2!] linkage at the octahedral B site, in this waygiving rise to the semiconducting character in the material.However; the affinity of the NiO for the oxidation and creationof defects such as oxygen vacancies during heating in the fer-rite lattice leads to the formation of Ni3! and Fe2! ions. Above358 K, diminishing localized states and alignments of the spinsgive rise to the efficient conductive channels in the form of[Fe3!–Fe2!] and [Ni2!–Ni3!] links. These channels cause thedelocalization of the charge carriers, and in so doing creating ametallic character above 358 K.

Figures 6(a) and 6(b) show the variation of tangent losswith frequency at some representative temperatures. Eachspectrum possesses two loss peaks with different relaxationtimes exhibiting the presence of at least two relaxations inthe system which is in accordance with the impedance planeplot results previously discussed. The larger peak in the lowfrequency region <102 Hz is attributed to the relaxation pro-cess at the grain boundaries and the smaller peak in the high

FIG. 5. (Color online) (a) Variation ofRg with temperature, (b) variation of Rgb

with temperature for the NiFe2O4 sam-ple; inset shows the variation of total re-sistance with temperature, and (c) totaldc conductivity of NiFe2O4 the solidlines are the best fit to the Arrheniusrelation.

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frequency region >104 Hz is associated with the grains.36 Inboth relaxation processes, the peak height increases andshifts toward the higher frequency side up to 358 K, asshown in Fig. 6(a). In the NiFe2O4 material,18 the relaxationis attributed to the cation–anion–cation interactions at theoctahedral B site. Now the increase in magnitude of the tan-gent loss peak with temperature is attributed to the increasein the number of thermally activated [Fe3!–O2"–Fe3!] and[Ni2!–O2"–Ni2!] linkages responsible for the relaxation;whereas the shift in the relaxation frequencies toward highervalues is due to the mobility activation of the charge carrierswith an increase in temperature. Above 358 K, the magni-tude of the loss peak in the low frequency region remains rel-atively temperature insensitive which supports ourdiscussion of delocalization of the charge carriers with anindiscriminate distribution of the energy. Some of the chargecarriers scatter from the grain boundary planes due to theincreased lattice vibrations.37 The scattering outcome in thereduced value of the mobility that has been found to be re-sponsible for the shift of the high frequency relaxation peaktoward a lower frequency as shown by the arrow in Fig. 6(b).

Figure 7(a) shows the frequency dependent real part ofthe dielectric constant at different temperatures. The trends ofthe graph show the existence of more than one type of polar-ization in NiFe2O4 nanoparticles. Typically four types ofpolarizations, interfacial, dipolar, atomic, and electronic arereported in ferrites.38 Dispersion below 102 Hz is suggested tobe due to the interfacial polarization and above 104 Hz, due torotational displacement of the dipoles. At frequencies higherthan 106 Hz, a relatively independent value of the dielectricconstant with temperature is attributed to the atomic and elec-tronic polarizations. Figure 7(a) indicates an increase in thedielectric constant with temperature up to 358 K. It is sug-gested here that thermally activated dipoles cause an increasein the interfacial and rotational polarizations by accumulatingat grain boundaries. In the view of the above SMT discussion,an increase in temperature above 358 K alters the overallspace charge capability. A decrease in the dielectric constant,as shown in the inset of Fig. 7(a), has been endorsed due tothe scattering of the charge carriers which causes a depletionin the space charge layers. At each temperature, a decrease inthe dielectric constant with frequency is observed owing tothe lower dipolar response to the ac field.39

Different types of conductivities in NiFe2O4 materialhave been reported in the literature. Baruwati et al.40 attrib-uted the n-type behavior as being due to the presence of Fe3!

in NiFe2O4 nanoparticles. The electron conduction is repre-sented as Fe3! $ Fe2!. The hole conduction is represented asNi2! $ Ni3!. Other reports41,42 also support the existence ofn-type and p-type conductivities in Ni-Zn ferrites due to thepresence of Fe2! and Ni3!, respectively. The values of theactivation energy (i.e., 0.41 and 0.71 eV) obtained in thisstudy suggest hopping and polaronic conduction between thelocalized sites.43 In the hopping process, the carrier mobilityis temperature dependent, which is usually characterized byactivation energy. Figure 7(b) shows the frequency dependentac conductivity of the NiFe2O4 sample at some representativetemperatures. At low frequency, the ac conductivity is foundto be weakly frequency dependent due to the nonequilibriumoccupancy of the trap charges.27 A further amplification offrequency reduces the occupancy of the trap centers by mak-ing them available for conduction. It facilitates the conductivestate to become more active by promoting the hopping ofelectrons and holes. The conductivity increases with increas-ing frequency and temperature up to 358 K. Above 358 K, thefrequency of the hopping ions decreases due to a reduction inthe mobility of the charge carriers after reflection from thegrain boundary plane and a decrease in conductivity as shownin inset of Fig. 7(b) is observed. Trends in conductivity withtemperature supports our results of the dielectric constants asboth the conductivity and the dielectric constant runs parallel.

In order to obtain a clear understanding of the conduc-tion mechanism, we have divided the conductivity graphover three frequency regions: (I) 1–100 Hz, (II) 3* 102–4* 103 Hz, and (III) 3* 105–4* 106 Hz. At each frequencyregion, the conductivity follows the dynamical ac power law,such that r x; T# $ ( B T# $xS T# $, where B is the parameterhaving the unit of conductivity and s is the slope of the fre-quency dependent region, 0.0' s' 1.18 Fitting of the experi-mental data yields a value of s whose dependence ontemperature is a function of the conduction mechanism.Figure 7(c) shows the variation of the slope parameter, s,with different temperatures. For region (I), there is no changein s with temperature due to a nonequilibrium occupancy ofthe trap charges. In region (II) there is a linearly decreasingtrend of s with temperature suggesting a correlated barrier

FIG. 6. (Color online) (a) Variation oftangent loss with frequency. The direc-tion of the arrow shows the increase intemperature, and (b) variation of tangentloss with frequency with the arrow in thedirection of the increase in temperature.

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hopping conduction model in this material. At higher fre-quencies in region (III), value of s first decreases reaching aminimum value, and then starts increasing again as shown inFig. 7(c). This behavior of s is in accordance with the over-lapping large polaron tunneling model of ac conduction.12

The higher values of activation energy in our case also sup-port this argument.17 The cations surrounded by closepacked oxygen anions can be treated as isolated from eachother due to little direct overlap of the charge clouds andhence, the localized eg electron model is appropriate. Thislocalization give rise to the formation of the polaron and thecharge transport may be considered between the nearestneighbor sites.12,44 The polaronic conduction in this materialhas been assumed between Fe3! and Fe2! due to the pres-ence of defects (i.e., oxygen vacancies, vacancies, agglomer-ates, and nanovoids) at nanolevels.17 Apparently, themechanism of ac conduction in the nanostructure NiFe2O4 isdifferent in different frequency ranges. It is expected thatthe correlated barrier hopping conduction mechanismdominates in this material owing to the presence of the[Fe3!–O2"–Fe3!] and [Ni2!–O2"–Ni2!] linkage in the lat-tice. The formation of hopping ion pairs depends upon theoccupancy of Ni-ions at the octahedral B-site. However, aclear understanding of the conduction mechanism in thisnanostructure NiFe2O4 needs further investigation.

IV. CONCLUSIONS

It has been shown that impedance spectroscopy is an excel-lent technique to investigate the electrical transition with the

possible correlation to the microstructure of the material. Grainand grain boundary phases are well resolved by impedanceplan plots. The parameters Rg, Rgb,Qg,Qgb, ng, and ngb coupledwith the grain and grain boundaries are explained using anequivalent circuit model. Thermal activation of trappedcharges/dipoles has been found to be responsible for decreasingthe resistance of the grain and grain boundaries and an increasein the value of the dielectric constant and tangent loss. Thechange in slope of the Arrhenius plot around 318 K has beendiscussed on the basis of hopping between Fe3!–Fe2! andNi2!–Ni3! ions and hopping has been suggested as a dominantac conduction mechanism in this material. As the magnetiza-tion study illustrated, surface spin canting of the nanoparticlesdue to the broken exchange bond and anisotropy is responsiblefor the weakening of the AB-exchange interaction and hence alower value of room temperature magnetization. Semiconduc-tor to metallic transition around 358 K has been reported anddiscussed in terms of the transition from localized charge car-rier [Fe3!–O2"–Fe3!]/[Ni2!–O2"–Ni2!] linkages to delocal-ized charge carrier [Fe3!–Fe2!]/[Ni2!–Ni3!] linkages.

ACKNOWLEDGMENTS

One of the authors, M. Atif, acknowledges the HigherEducation Commission (HEC), Islamabad Pakistan, for thegrant of the PhD scholarship.

1S. Son, M. Taheri, E. Carpenter, V. G. Harris, and M. E. McHenry,J. Appl. Phys. 91, 7589 (2002).

2M. Sugimoto, J. Am. Ceram. Soc. 82, 269 (1999).

FIG. 7. (Color online) (a) Variation ofdielectric constant with log f; the direc-tion of the arrow shows the increase intemperature; inset shows a decrease inthe dielectric constant with temperature.(b) Variation of ln(r) with ln(f); insetshows the decrease in conductivity withtemperature, and (c) variation of theslope parameter (s) with temperatures atdifferent frequencies.

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3N. Ponpandian, P. Balaya and A. Narayanasamy, J. Phys. Condens. Matter14, 3221 (2002).

4M. Atif, S. K. Hasanian, and M. Nadeem, Solid State Commun. 138, 416(2006).

5L. D. Tug, V. Kolesnichenko, G. Caruntu, D. Caruntu, Y. Remond, V. O.Golub, C. J. O’Connor, and L. Spinu, Physica B 319, 116 (2002).

6C.N. Chinnasamy, A. Narayanasamy, N. Ponpandian, K. Chattopadhyay,K. Shinoda, B. Jeyadevan, K. Tohji, K. Nakatsuka, T. Furubyashi, andI. Nakatani, Phys. Rev. B 63, 184108 (2001).

7J. Jacob and M. A. Khadar, J. Appl. Phys. 107, 114310 (2010).8R. J. Brook and W. D. Kingery, J. Appl. Phys. 38, 3589 (1967).9G. W. Scherrer, Relaxation in Glasses and Composites (Wiley, New York,1986).

10J. Z. Jaing, G. F. Goya, and H. R. Rechenberg, J. Phys. Condens. Matter11, 4063 (1999).

11M. A. Gabal and Y. M. Al Angari, Mater. Chem. Phys. 115, 578 (2009).12E. V. Gopalan, K. A. Malini, S. Sagar, D. S. Kumar, Y. Yoshida, I. A.Al-Omari, and M. R. Anantharaman, J. Phys. D 42, 165005 (2009).

13A. S. Edelstein and R. C. Cammarata, Synthesis Properties and Applica-tions (IOP, London, 1996).

14J. R. Macdonald, Impedance Spectroscopy, Emphasizing Solid Materialsand Systems (Wiley, New York, 1987).

15M. Idrees, M. Nadeem, and M. M. Hassan, J. Phys. D 43, 155401 (2010).16E. Barsoukov and J. R. Macdonald, Impedance Spectroscopy Theory,Experiments and Applications (Wiley, New York, 2005).

17V. E. Gopalan, K. A. Malini, S. Saravanan, D. Sakthi Kumar, Y. Yoshida,and M. R. Anantharaman, J. Phys. D 41, 185005 (2008).

18S. S. Ata-Allah and M. Kaiser, Phys. Status Solidi 201, 3157 (2004).19I. H. Gul, A. Z. Abbasi, F. Amin, M. Anis-ur-Rehman, and A. Maqsood,J. Magn. Magn. Mater. 311, 311 (2007).

20T. Sato, IEEE Trans. Magn. Magn. 6, 795 (1970).21J. Smit and H. P. J. Wijn, Ferrites, Physical Properties of FerromagneticOxides in Relation to their Technical Applications (Wiley, New York, 1959).

22K. Haneda, Can. J. Phys. 65, 1233 (1987).23A. H. Morrish, K. Haneda, and P. J. Schurer, J. Phys. Colloq. 37, C6 (1976).

24L. Chao, A. J. Rondinone, and Z. J. Zhang, Pure Appl. Chem. 72, 37(2000).

25V. Sepelak, I. Bergmann, A. Feldhoff, P. Heitjans, F. Krumeich, D.Menzel, F. J. Litterst, S. J. Campbell, and K. D. Becker, J. Phys. Chem. C111, 5026 (2007).

26M. Nadeem, M. J. Akhtar, and M. N. Haque, Solid State Commun. 145,263 (2008).

27M. Nadeem and A. Mushtaq, J. Appl. Phys. 106, 073713 (2009).28J. R. Macdonald, Impedance Spectroscopy (Wiley, New York, 1987).29E. Iguchi, N. Nakamura, and A. Aoki, J. Phys. Chem. Solids 58, 755(1997).

30I. Bunget and M. Popescu, Physics of Solid Dielectrics (Editura StiinsificaSi Enciclopedica, Bucharest, 1978).

31N. Sivakumar, A. Narayanasamy, N. Ponpandian, J. M. Greneche,K. Shinoda, B. Jeyadevan, and K. Tohji, J. Phys. D 39, 4688 (2006).

32J. B. Goodenough, Phys. Rev. B 117, 1442 (1960).33S. S. Ata-Allah, M. K. Fayek, H. S. Refai, and F. J. Mostafa, Solid StateChem. 149, 434 (2000).

34S. S. Ata-Allah and M.K Fayek. Hyperfine Interact. 128, 467 (2000).35V. Sepelak, D. Baabe, D. Mienert, D. Schultz, F. Krumerich, F. J. Litterst,and K. D. Necker, J. Magn. Magn. Mater. 257, 377 (2003).

36M. Nadeem and M. J. Akhtar, J. Appl. Phys. 104, 103713 (2008).37R. Waser, in Proceedings of the 3rd Euro-ceramic Soc. Conf., edited byP. Duran and J. F. Fernandez, Madrid 12-17 September (1993), p. 23.

38A. Verma, O. P. Thakur, C. Prakash, T. C. Goel, and R. G. Mendiratta,Mater. Sci. Eng., B 116, 1 (2005).

39M. Nadeem, A. Farooq, and T. J. Shin, Appl. Phys. Lett. 96, 212104 (2010).40B. Baruwati, K. R. Madhusudan, and S. V. Manorama, Appl. Phys. Lett.85, 14 (2004).

41A. M. El-Sayed. Mater. Chem. Phys. 82, 383 (2003).42B. V. Bhise, A. K. Ghatage, B. M. Kulkarni, S. D. Lotke, and S. A. Patil,Bull. Mater. Sci. 19, 527 (1996).

43A. M. Abdeen, J. Magn. Magn. Mater. 192, 12 (1999).44B. Vishwanathan and V. R. K. Moorthy, Ferrite Materials, Science andTechnology (Springer, Berlin, 1990).

093704-8 Younas et al. J. Appl. Phys. 109, 093704 (2011)

Downloaded 10 May 2011 to 130.160.75.92. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions