Materials Research Bulletin 62 (2015) 153–160

Structural and transport properties of double perovskite Dy2NiMnO6

Sadhan Chanda *, Sujoy Saha, Alo Dutta, T.P. SinhaDepartment of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata 700009, India

A R T I C L E I N F O

Article history:Received 10 June 2014Accepted 8 November 2014Available online 11 November 2014

Keywords:A. CeramicsB. Sol–gel chemistryC. Impedance spectroscopyD. Dielectric propertiesE. Electronic structure

A B S T R A C T

The double perovskite oxide Dy2NiMnO6 (DNMO) is synthesized in nano and bulk phase by the sol–gelcitrate method. The Rietveld refinement of X-ray diffraction pattern of the sample at room temperatureshows the monoclinic P21/n phase. Dielectric relaxation of the sample is investigated in the impedanceand electric modulus formalisms in the frequency range from 50 Hz to 1 MHz and in the temperaturerange from 253 to 415 K. The Cole–Cole model is used to explain the relaxation mechanism in DNMO. Thefrequency-dependent maxima in the imaginary part of impedance are found to obey an Arrhenius lawwith activation energy of 0.346 and 0.344 eV for nano and bulk DNMO, respectively. A significant increasein conductivity of bulk DNMO has been observed than that of the nanoceramic. Electronic structures andmagnetic properties of DNMO have been studied by performing first principles calculation based ondensity functional theory.

ã 2014 Elsevier Ltd. All rights reserved.

Contents lists available at ScienceDirect

Materials Research Bulletin

journal homepage: www.else vie r .com/ locat e/mat resbu

1. Introduction

Multifunctional double perovskite oxides (DPOs) Ln2NiMnO6

[Ln = lanthanides] have gained immense research interest in therecentyearsduetotheirrichphysicalpropertieswhichmakethemasthe prospective materials for technological applications [1–13]. Inthis family La2NiMnO6 having ferromagnetic order temperature ofabout 280 K is a rare example of a single material platform withmultiple functions, inwhichthe spins, electric charges, and dielectricproperties can be tuned by magnetic and/or electric fields. Thedielectric relaxor behaviour is also observed in Nd2NiMnO6by Shi et.al [4]. These properties make this series of materials suitable forpossible applications in spintronic devices, such as magneticmemories and magnetodielectric capacitors [2,6].

Most of the reported Ln2NiMnO6 DPOs have been prepared byhigh temperature solid-state reaction technique from their corre-sponding pure oxides. But in many cases this technique suffers fromthe problem of the presence of some unreacted rare earth oxides asimpurities in the materials and sometimes the formation ofundesirable phases [7]. It is observed that probability of gettingthe impurity phases increases when the ionic radius of the rare earthelement in this series decreases [11,12]. In this respect whilesynthesising Tb2NiMnO6 by solid state reaction technique, theexistence of an impurity phase of Tb2O3 is reported by Nair et al. [11].Similarly, Y2NiMnO6 [12] has not been synthesised in single phase

* Corresponding author. Tel.: +91 33 23031191/9836626460; fax: +91 3323506790.

E-mail addresses: sadhan.physics@gmail.com, schanda.cob@gmail.com(S. Chanda).

http://dx.doi.org/10.1016/j.materresbull.2014.11.0210025-5408/ã 2014 Elsevier Ltd. All rights reserved.

because radius of Y3+ is almost equal to Dy3+. Thus, synthesizing apure phase material of this family with lower ionic radius (such as Y,Dy–Lu compounds) is challenging.

Among the various Ln2NiMnO6 DPOs studied so far, Dy2NiMnO6

(DNMO) is a ferromagnetic material with Tc� 105 K. Asai et al. havestudied the crystal structure and magnetic properties of DNMOand concluded that superexchange interaction Ni2+–O–Mn4+ isresponsible for ferromagnetism in this material [7]. The theoreticaleffort for understanding the various microscopic properties ofDNMO is not available in the literature. To our knowledge, thereexists no report of plane wave based basic electronic structurecalculation of DNMO.

In the present work, we have successfully synthesised a purephase of DNMO by sol–gel citrate method. The dielectric propertiesof the sample have been investigated by alternating currentimpedance spectroscopy (ACIS) in a frequency range from 50 Hz to1 MHz and in the temperature range from 253 K to 415 K. The studyof the influence of sintering conditions (effects of grain size) on theelectrical properties of the ceramic has also been reported. Wehave carried out the spin polarised density functional theorycalculations using full potential linearized augmented plane wave(FPLAPW) method implemented in WIEN2k [14] to understand theferromagnetic insulating behaviour in this compound.

2. Experimental

2.1. Sample preparation

DNMO in powder form was synthesized by the sol–gel citratemethod [15,16]. At first, reagent grade Dy(NO3)3�6H2O (Alfa Aesar),

Fig. 1. Rietveld refinement plot of DNMO-1 at room temperature. A schematicpresentation of the DNMO monoclinic unit cell is shown in the inset. The Ni atomsare located at the centres of the NiO6 (orange) octahedra. The Mn atoms are locatedat the centres of the MnO6 (green) octahedral. (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version of this article.)

154 S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160

Ni(NO3)2�4H2O (Alfa Aesar), and Mn(NO3)2�6H2O (Alfa Aesar) weretaken in stoichiometry ratio and separately dissolved in de-ionizedwater by stirring with a magnetic stirrer. The obtained clearsolutions were then mixed together. Citric acid (CA) and ethyleneglycol (EG) were added to this solution drop wise according to themolar ratio of {Dy3+, Ni2+ + Mn2+}:{CA}:{EG} = 1:1:4 to form apolymeric-metal cation network. The solution was stirred at 348 Kusing a magnetic stirrer for 4 h to get a homogeneous mixture andthen the solution was dried at 393 K to obtain the gel precursor. Atthe end, combustion had taken place in the gel which hadproduced a black fluffy powder of the material. The powder wascalcined at 1073 K in air for 5 h and cooled down to roomtemperature (RT � 300 K) at a cooling rate of 1 K/min. The calcinedsample was pelletized into discs of thickness = 1.5 mm anddiameter = 8 mm using polyvinyl alcohol as binder. Finally, thesepellets were sintered at 1073 and 1423 K for 10 h in air and cooleddown to RT by cooling at the rate of 1 K/min. From now onwards,we have abbreviated DNMO-1 and DNMO-2 for the samplessintered at 1073 and 1423 K, respectively.

2.2. Sample characterization

The determination of lattice parameters and the identification ofthe phase at RT was carried out using a X-ray powderdiffractometer (Rigaku Miniflex II) having Cu-Ka radiation in the2u range of 15–80� by scanning at 0.02� per step. The refinement ofcrystal structure was performed by the Rietveld method with theFullprof program [17]. The background was fitted with 6-coefficients polynomial function, while the peak shapes weredescribed by pseudo-Voigt profiles. Throughout the refinement,scale factor, lattice parameters, positional coordinates (x, y, z), andthermal parameters were varied and the occupancy parameters ofall the ions were kept fixed. The particle size and selected areaelectron diffraction (SAED) pattern of the sample (DNMO-1) werestudied by the high resolution transmission electron microscopy(HRTEM) (FEI Tecnai G2, 200 KV). The scanning electron micro-scope (FEI Quanta 200) was used for investigation of thehomogeneity of the synthesized samples. The optical spectrumof the material was collected by a Shimadzu UV–vis spectrometer.

For electrical measurements, both the sides of sintered pelletswere polished. Two thin gold plates were used as electrodes. Theimpedance, conductance, and phase angle were measured using anLCR meter (HIOKI) in the frequency range from 50 Hz to 1 MHz atthe oscillation voltage of 1.0 V. The measurements were performedover the temperature range from 253 K to 415 K using an inbuiltcooling–heating system. The temperature was controlled by anEurotherm 2216e programmable temperature controller con-nected with the oven. Each measured temperature was keptconstant with an accuracy of �1 K. The complex dielectric modulusM* (=jvCoZ*) was obtained from the temperature dependence ofthe real (Z0) and imaginary (Z00) components of the compleximpedance Z* (=Z0 + iZ00), where v is the angular frequency(v = 2 pn) and i =

ffiffiffiffiffiffiffi�1

p. Co = eoA/d is the empty cell capacitance,

where A is the sample area, and d is the sample thickness. The I–Vcharacteristics of DNMO were measured in the temperature rangefrom 213 K to 473 K using a source measure unit (Keithley 236).

2.3. Computational details

The experimental lattice parameters are used as the input forthe FPLAPW calculations of DNMO. The muffin-tin (MT) radii forDy, Ni, Mn, and O are taken as 2.21, 1.96, 1.91, and 1.65 au (atomicunit), respectively. To take into account the exchange andcorrelation effects, generalized gradient approximation (GGA) asparametrized by Perdew et al. [18] has been applied. No shape

approximation corresponding to potential is taken into account. Inthe calculations, we have used a parameter RMTKmax = 7, whichdetermines matrix size (convergence), where Kmax is the planewave cut-off and RMT is the smallest of all atomic sphere radii. Forthe self-consistent calculation with the plane wave basis4 � 4 � 4 Monkhorst-Pack [19] k point mesh is used. The iterationprocess is continued until calculated total energy and chargedensity of the crystal converged and becomes less than 0.01 mRy/unit cell and 0.001 e/a.u.3, respectively. For the 3d transition metal(Ni and Mn) and rare earth element (Dy) the correlation effect oflocalized d and f electrons are considered. We have applied theeffective Coulomb potential (UNi � 3d = UMn�3d = 2 eV and UDy�4f = 4eV) in GGA + U [20] calculations. The value of U is optimized suchthat the moments of the magnetic ions and optical band gap aresatisfactorily described with respect to the experimental results.

3. Results and discussion

3.1. Structural analysis

The X-ray diffraction pattern of DNMO-1 is shown in Fig. 1,where the symbols represent the experimental data and the solidline represents the best fit to the diffraction data obtained byRietveld refinement for monoclinic symmetry (space group P21/n).The curve at the bottom represents the difference betweenexperimental pattern and the calculated one. The refined latticeparameters, a = 5.2425(4) Å, b = 5.5468(5) Å, c = 7.5025(7) Å, and themonoclinic angle b = 90.042(2)� are in reasonable agreement withthe same series of materials such as Tb2NiMnO6 [11] andLn2NiMnO6 (Ln¼Nd, Sm) [9]. The stability of DNMO to a firstapproximation is determined by the ratio of Dy—O to B—O (B¼Ni,Mn) bond lengths, which can be expressed as the tolerance factorTf = ðrDy þ r0Þ=ð

ffiffiffi2

pððrNi þ rMnÞ=2 þ r0ÞÞ (where rDy, rNi, rMn, and ro are

ionic radii of dysprosium, nickel, manganese, and oxygen,respectively). Here Dy has co-ordination number eight insteadof 12. The reduced coordination number of Dy is a result of some ofthe anions moving too far away for lower symmetry DPO due tooctahedral tilting which causes the first coordination sphere aboutthe Dy cation to change. It has been proposed by Woodward [21]that any anion more than 3.00 Å away from the A-cation of DPOs(general formula A2B0B00O6) may be considered to be outside thecoordination sphere. It is found that Tf = 0.85 for DNMO usingrDy = 1.027 Å, rNi= 0.69 Å, rMn= 0.53 Å, and ro = 1.4 Å [22]. A sche-matic presentation of the DNMO cell is shown in the inset of Fig. 1with the distribution of ions at crystallographic positions 4e for

Fig. 2. (a) The transmission electron microscopy (TEM) image of particles, (b) itscorresponding high resolution-TEM (HR-TEM) image, and (c) selected area electrondiffraction (SAED) pattern.

Table 2Lattice constant, grain size, porosity, and activation energy for DNMO-1 and DNMO-2 samples.

Samples Lattice parameters(Å)

Density Porosity(%)(gm/cc)

Grain size(mm)

Ea(eV)

DNMO-1 a = 5.2425,b = 5.5469

6.87 15.5 0.178 � 0.023 0.364

c = 7.5026,b = 90.042

DNMO-2 a = 5.2446,b = 5.5477

7.45 8.5 0.289 � 0.067 0.344

c = 7.5044,b = 90.045

S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160 155

Dy3+ ions, 2c for Ni2+ ions, 2d for Mn4+ ions and 4e for O2� ions asgiven in Table 1. Each Ni2+ and Mn4+ ions are surrounded by six

Table 1Structural parameters for DNMO as obtained from Rietveld analysis of XRD pattern.

Space group = p21/n,a = 5.2425(4) Å, b = 5.5468(5) Å, c = 7.5025(7) Å, and b = 90.042(2)�

Atoms Site x y

Dy 4e 0.5202(6) 0.5692(3)

Ni 2c 0.0 0.5

Mn 2d 0.5 0.0

O1 4e 0.395(3) 0.957(3)

O2 4e 0.202(9) 0.195(8)

O3 4e 0.190(7) 0.081(5)

BVS: Dy = 2.8, Ni = 2.57, Mn = 3.115

Rp = 2.72; Rwp = 3.46; Rexp = 3.33; x2 = 1.08.

O2� ions, constituting NiO6 and MnO6 octahedra, respectively. Aquantitative estimate of the valence states of the cations wasobtained by calculating the bond valence sums (BVS). The finalstructure parameters along with important bond distances, bondangles associated with NiO6 and MnO6 octahedra and BVS ofDNMO are listed in Table 1. The measured lattice parameters,density and porosity of the samples sintered at different temper-atures are given in Table 2. The density of the samples increases asthe sintering temperature increases from 1073 to 1473 K. On theother hand, porosity (P) of the samples decreases with the increaseof sintering temperature.

The HRTEM micrographs of DNMO-1 are shown in Fig. 2(a–c).The particles are found to be segregated as observed from Fig. 2(a).The sizes of the particles are estimated to be in the range from 80 to110 nm. Fig. 2(b) indicates the homogeneous orientation of thelattice planes with interplanar spacing of 0.27 nm which correlateswith the d spacing value of (0 2 0) plane of the XRD pattern. TheSAED pattern (Fig. 2(c)) shows bright spots indicating that particlesare well crystalline in nature.

The surface morphology of DNMO samples is revealed by SEM,as shown in Fig. 3(a) and (b). It is clear that the grain size increaseswith increasing the sintering temperature. The mean grain sizesare about 0.178 � 0.023 and 0.289 � 0.067 mm for DNMO-1 andDNMO-2 samples, respectively. It is observed that with theincrease in sintering temperature, the number of pores decreasedand the rate of grain growth apparently increased.

3.2. Optical analysis

The UV–vis absorption spectrum of DNMO-1 is shown in Fig. 4.The energy band gap is determined using absorption spectrumwith the help of Tauc relation [23,24] given by

ahn ¼ A hn � Eg� �n (1)

where hy is the energy of the incident photon, a is the absorptioncoefficient, and A is a characteristic parameter independent of thephoton energy, Eg is the optical band gap and the value of n is 1/2 or

z Bond length Bond angle

0.253(1) Ni-O1(x2) = 1.84 <Ni-O1-Mn> = 144.64�

0.0 Ni-O2(x2) = 2.08 <Ni-O2-Mn> = 152.25�

0.0 Ni-O3(x2) = 2.02 <Ni-O3-Mn> = 138.70�

0.265(6) Mn-O1 (x2) = 2.09�0.020(7) Mn-O2 (x2) = 1.840.081(5) Mn-O1 (x2) = 2.05

Fig. 3. SEM images of surface morphologies of (a) DNMO-1 and (b) DNMO-2.

16

8MΩ

)

25 3 K 28 9 K 32 5 K 35 2 K 37 0 K 38 8 K 41 5 K

12

1

Z' (

MΩ

)

156 S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160

2 for the direct or indirect transition respectively. Using thisrelation, a graph is plotted between (ahy)2 and hy as shown inFig. 4. The extrapolation of the linear absorption-edge part of thisgraph with a straight line to (ahy)2 = 0 axis gives the value of theband gap. The value of the optical band gap of the material fordirect transition is found to be �1.62 eV. It is to be mentioned that

0.5 1.0 1.5 2.0 2.5 3.00

2

4

(αhν

)2 (m

-2eV

2 )

hν (eV)

Eg = 1.62 eV

Fig. 4. UV–vis absorption spectrum for direct transition ((ahy)2 vs. hy).

no significant change is observed in the UV–vis absorptionspectrum of the DNMO-2 sample.

3.3. Dielectric relaxation

The dielectric relaxation of DNMO can be broadly analyzed interms of (i) dipolar and (ii) conductivity relaxation mechanisms.For dielectric relaxation originating from dipole motion, thedielectric response can be described as a direct relationshipbetween the dielectric constant (e* = e0 � ie00) and the admittance.For conductivity relaxation, the dispersion of the dielectricconstant is determined by a locally inhomogeneous potentialbarrier with long-range charge-carrier diffusion, and the dielectricresponse can be described as a relationship between electricmodulus (M* = M0 + iM00 = 1/e*) and the impedance (Z* = Z0 + iZ00). Wehave applied the second approach to study the dielectric relaxationof DNMO. The angular frequency dependence of real (Z0) andimaginary (Z00) parts of complex impedance of DNMO-1 at varioustemperatures are shown in Fig. 5. At a particular temperature, Z0

decreases monotonically with increasing frequency upto a certainfrequency and then becomes frequency independent (Fig. 5(a)). Itis evident from Fig. 5(b) that the spectrum of Z00 at eachtemperature exhibits one relaxation peak whose peak frequency,vm, increases with increasing temperature. It should be noted thatthe similar spectrum are also observed in the sample DNMO-2 (notshown). This behaviour suggests a possibility that the spectralintensity of the dielectric relaxation observed in DNMO isthermally activated. The total resistance decreases with anincrease in temperature across the entire frequency range, whichshows the semiconducting behaviour of the material.

It is clear that the width of the peaks in Fig. 5(b) cannot beaccounted for in terms of a mono-dispersive relaxation process,but points towards the possibility of a distribution of relaxationtimes. In order to account for it, fitting of the impedance data wasperformed with the help of the Cole–Cole relation, defined as [25]

3 4 5

12

8

4

4

0

Z' ( Fit ting

0

3 4 5 6

log ω (r ad s-1)

log ω (r ad s-1)

Z''

(MΩ

)

log ω (r ad s-1)

0.5

0

0

3 4 5 6 7

(b)

Z''

(MΩ

)

(a)

Fig. 5. Frequency (angular) dependence of Z0 (a) and Z00 (b) of DNMO at varioustemperatures. The solid lines are fits of the Cole–Cole relation.

Fig. 7. Frequency (angular) dependence of normalized peaks, Z00/Z00m and M00/M00m

for DNMO-1 at 415 K. The scaling behaviour of the Z00 of DNMO-1 is shown in the

S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160 157

Z� ¼ Rg

1 þ jvtg� �1�a (2)

where Rg and tg are the resistance and characteristic relaxationtime respectively corresponding to grain effect, and a is adimensionless exponent that denotes the angle of tilt of thecircular arc from the real axis. The best fitting of the impedancedata with Eq. (2) is shown by solid lines in Fig. 5 for Z0 and Z00. Thevalues of a lie in the range between 0.23 and 0.18 in thetemperature range of 253–415 K.

To get an idea about the type of relaxation response in thesematerials, it is necessary to find out the activation energy ofrelaxation process. At a temperature T, the most probablerelaxation frequency (vm) corresponding to the peak position inZ00 vs. log v is proportional to exp(�Ea/kBT) (Arrhenius law). Thelinear fit of the experimental data as shown by the solid lines inFig. 6 gives the activation energy of 0.364 and 0.344 eV for DNMO-1and DNMO-2, respectively. Such a value of activation energyindicates that the conduction mechanism in the samples may bedue to the polaron hopping based on the electron carriers [26]. Thefact that the lower activation energy in DNMO-2 than that ofDNMO-1 is due to the increase in density (decrease in porosity) ofthe sample with increase in sintering temperature which gives abetter contact between the particles and provides an easypercolation path for the charge carrier conduction [27].

In Fig. 7, the variation of normalized parameters M00/M00m and Z00/

Z00m as a function of logarithmic frequency measured at 415 K forDNMO-1 is shown. The position of the peak in the Z00/Z00m is slightlyshifted to lower frequency region in relation to the M00/M00

m peak.This is also observed in DNMO-2 (not shown). A comparison of theimpedance with electric modulus data allows the determination ofthe grain response in terms of localized or non-localizedconduction [28]. The Debye model is related to an ideal frequencyresponse of localized relaxation. The non-localized process knownas the dc conductivity is dominated at low frequencies. Theoverlapping peak position of M00/M00

m and Z00/Z00m curves is anevidence of delocalized or long-range relaxation [28]. For DNMOthe M00/M00

m and Z00/Z00m peaks almost overlap suggesting the majorcomponents from long-range relaxations.The inset of Fig. 7 showscomplex plane impedance plot, (Z* plot), for the DNMO-1, plottingthe imaginary part Z00 against the real part Z0 at temperature 415 K.A point on this curve represents a given measurement of Z0 (v) andZ00 (v), at a specific angular frequency v (=2pf). In the compleximpedance plot, one expects a separation of the grain effect from

4.0

4.5

5.0

5.5

6.0

log ω

m (

rad

s-1)

2.4 2.6 2.8 3.0 3.2 3.4

3.0

3.5

4.0

4.5DNMO2

Ea = 0.36 eV

1000 /T (K-1)

Ea = 0.34 eV

DNMO1

Fig. 6. The temperature dependence of the most probable relaxation frequencyobtained from the frequency-dependent imaginary part of the impedance curvesfor DNMO-1 and DNMO-2: here, the symbols are the experimental data and thesolid lines are the least-squares straight-line fit. (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version of this article.)

surface (grain boundary and/or electrode) effect as the surfacepolarization is highly capacitive phenomenon and is characterizedby large relaxation time than the polarization mechanism in thegrain. This fact usually results in the appearance of two separatearcs of semicircle in the Z00 vs. Z0 plots (one representing the bulkeffect at high frequencies while the other represents surface effectin lower frequency range). The presence of a single semicircular arcpassing through the origin in the entire frequency region indicatesthat the relaxation mechanism in DNMO is purely a grain effect. Ifwe scale each Z00 with Z00m and each v with vm, the entire curvescollapse into a single master curve as shown in the inset of Fig. 7.The scaling nature of Z00 implies that the relaxation shows the samemechanism in the entire temperature range.

3.4. dc and ac conductivity

To study the long range relaxation phenomena in DNMO, wehave also adopted the dc and ac conductivity formalisms. Fig. 8shows I–V characteristics obtained at different temperatures forDNMO-1. The dc conduction study also supports the insulatingbehaviour of the material. It should be noted that the similarcharacteristics are also observed in the sample DNMO-2 (notshown). The corresponding Arrhenius plot is shown in the inset ofFig. 8. The temperature dependence of dc conductivity of DNMO-1 for polaron hopping can be explained by [25]

sdc ¼n0a2e2vLO

kBTexp �WH þ eg=2

kBT

� �

¼ A0

Texp �WH þ eg=2

kBT

� �(3)

where e denotes the electronic charge, n0 expð�eg=2kBTÞ is thenumber of small polaron per unit volume, a is the characteristicintersite hopping distance, vLO is the optical phonon frequency, WH

is the hopping energy of a polaron, and eg is the energy gapbetween the energy states which participate directly in theelectrical transport. The dc activation energy ðWH þ eg=2Þ asobtained from the linear fit of the experimental data (shown in theinset of Fig. 8) is found to be 0.37 eV which is very close toactivation energy required for relaxation process as obtained fromthe impedance analysis. These results imply that the nature ofcharge carriers responsible for dielectric relaxation peaks and dcconduction belongs to the same category, indicating that thepolarization relaxation has a close relation to the conductivity in

0 10 20 30 40 50

0.08

0.04I (m

A)

V (volt )

248 K 288 K 318 K 333 K 353 K

0.0

2 3 4

-4

-2

0

σ dcT

(S

m-1K

)

1000/T (K-1)

Fig. 8. Current vs voltage characteristics at different temperature for DNMO-1.Temperature dependence of dc conductivity of DNMO-1 is shown in the inset.

158 S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160

the grain interior. In such situation the band gap energy forelectrical conduction eg can be calculated from the differencebetween the dc activation energy and hopping energy of smallpolaron. In the case of dielectric relaxation, the activation energy isthe hopping energy [25], i.e., Ea= WH. Thus the value of eg is foundto be 0.058 eV. The least-mean-square analysis also yieldsAo = 5.06 � 106K V�1 cm�1.

Fig. 9 shows a log–log plot of the frequency dependence of acconductivity for DNMO at various temperatures. The value of acconductivity decreases with decreasing frequency and becomesindependent of frequency after a certain value. Extrapolation ofthis part to lower frequencies will give the dc conductivity (sdc). Itis to be mentioned that, at low frequencies, random diffusion ofcharge carriers via hopping gives rise to a frequency-independentconductivity. At high frequencies, s(v) exhibits dispersion,increasing in a power-law fashion. The real part of conductivitys in such a situation can be expressed as [29]

-5

-4

log

σ ac (

Sm-1

)

log ω (rad s-1)

25 3 K 28 9 K 32 5 K 35 2 K 37 0 K 38 8 K 41 5 K Fitti ng

log

σ ac (

Sm-1

)

4 6

-4.5

-4.0

-3.5

(b) 370_ DNMO-2 415_ DNMO-2 370_ DNMO-1 415_ DNMO-1

(a)

Fig. 9. (a) Frequency (angular) dependence of ac conductivity of DNMO-1 at varioustemperatures. Solid lines are fits of the power law. (b) Frequency (angular)dependence of ac conductivity of DNMO-1 and DNMO-2 for the temperatures370 and 415 K.

s vð Þ ¼ sdc 1 þ vvH

� �n� �(4)

where vH is the hopping frequency of the charge carriers, and n isthe dimensionless frequency exponent. This relation correspondsto the hopping conduction of charge carriers.

Hopping of charge carriers takes place through localizationpositions separated by energy barriers of various heights. Thenumber of charge carriers that have high relaxation time due tohigh energy barrier which respond in the low-frequency regimemight be lower than the number of charge carriers with lowrelaxation time, and this has resulted in low values of conductivityat low frequencies. The temperature-dependent parameter nrepresents the number of many-body interactions among chargecarriers and defect states. In a fixed frequency range, n ! 1 asT ! 0 and decreases with increasing temperature, indicating fewerinteractions. The experimental conductivity spectra of DNMO isfitted to Eq. (4) with sdc and vH as variables, keeping in mind thatthe values of the parameter n are weakly temperature dependent.The best fit of the conductivity spectra is shown by solid lines inFig. 9(a) with the values of n lying in the range between 0.88 and0.95 for the temperature range from 253 to 415 K. A comparison ofthe frequency dependent ac conductivity for DNMO-1 and DNMO-2 at the temperature 370 and 415 K has been shown in the Fig. 9(b).It is observed that the electrical conductivity increases withincreasing sintering temperature which can be ascribed to thedecrease in porosity as shown in Fig. 3. With increasing sinteringtemperature, the relative density of the materials increases,ensuring a better contact between the particles, which isdemonstrated through higher relative conductivities.

3.5. Electronic and magnetic structure

The spin polarized total density of states (DOS) per formula unitof DNMO obtained by only GGA calculations is shown in Fig.10. Thezero of the energy is set at the top of the valence band. Withoutaccounting for Coulomb repulsion i.e., U = 0, the GGA calculationspredict that the ground state of DNMO has half-metallic characterwith a finite density of states at the Fermi level (set at 0 eV) in thedown spin channel and a band gap of size 1.4 eV in the up spinchannel. This half-metallic behaviour does not agree with ourexperimental results which show that DNMO is an insulator with adirect energy band gap of 1.62 eV. It is well known that LDA andGGA cannot describe the correct ground state for perovskite oxidesand other highly correlated compounds [30,31]. Hence, specialconsiderations are required for the correlation effect of d and felectrons of Ni, Mn, and Dy in DNMO. We have therefore

Fig. 10. The spin-polarized total density of states calculated within GGA for DNMO.

0

50

50

0

0

12

12

0

0.0

1.5

4

0

0.0

0.7

eg

eg

eg

eg

t2g

t2g

t2g

t2g

DNMO

-10 -8 -6 -4 -2 0 2 4 6

0.7

0.0

O-p

Mn-d

Ni-d

Energy (eV)

Dy-f

0

2

DO

S (

Stat

es/e

V c

ell)

3

0

Fig. 11. The spin-polarized total and partial density of states calculated withinGGA + U for DNMO.

S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160 159

considered the GGA + U approach, where a Hubbard term (U) isintroduced for the strong on-site Coulomb repulsion among thevarious states [30].The spin polarized total DOS with partial DOS ofDy-f, Ni-d, Mn-d and O-p states of DNMO obtained from GGA + Ucalculations is shown in Fig. 11. The GGA + U calculations predictcorrectly the insulating electronic structure of DNMO. The opticalband gap is found to be �1.5 eV which is almost equal to theexperimental value observed by UV–vis absorption spectrum ofDNMO. It is observed from the partial DOS of Ni-d and Mn-d thatthe octahedral crystal field in the surroundings of Ni and Mn atomssplits the Ni- and Mn-d manifolds into t2g and eg levels. In the up-spin channel, the Ni-t2g and Ni-eg levels are found in the energyrange from �6 eV to EF with the significant mixing with Mn-dstates and O-2p states. In the down spin channel, Ni-t2g states liefrom �1.2 to �0.5 eV in the valence band, while Ni-eg states liefrom 1.5 to 3.0 eV in the conduction band. This leads to the

conclusion that the nominal oxidation state of Ni is d8 : t3"2g e2"g t3#2g

in DNMO. In the up-spin channel the Mn-t2g states are localizedbetween Ni-t2g and Ni-eg states and filled, while the Mn-eg stateslie from 1.5 to 2.8 eV and remain empty. In the down-spin channel,both Mn-t2g and Mn-eg states are located in the energy range from1.5 to 5.0 eV. This corresponds to the nominal valence of Mn4+

d3 : t3"2g e0g

in DNMO, which shows a good agreement of the

results reported by Asai et. al [7]. Exchange splitting between t2gup and t2g down, and between eg up and eg down are also observedfor both Ni and Mn ions. The exchange splitting between eg up andeg down states for Ni and Mn is 1.2 and 1.0 eV respectively, and theexchange splitting between t2g up and t2g down states for Ni andMn is 0.5 and 2.5 eV respectively. The calculated magneticmoments at Ni and Mn-sites are found to be 1.56 and 2.87 mB/f.u., respectively which also support the Ni2+ and Mn4+ states in

DNMO. The sum of the magnetic moments of Ni and Mn in DNMOis found to be 4.43 mB/f.u. Since the magnetic interaction betweenthe magnetic cations Ni and Mn takes place through the O anion, O-site possesses some magnetic moment of 0.18 mB/f.u. The rest ofthe moment comes from Dy3+ ions in DNMO as the total magneticmoment are found to be 15.0 mB/f.u. This is in a good agreementwith the experimental results obtained in DyNi0.5Mn0.5O3 by Asaiet. al [7].

4. Conclusions

In summary, we have synthesised double perovskiteDy2NiMnO6 in nano and bulk phases by the sol–gel citrate methodand systematically investigated its structural, dielectric, andmagnetic properties. The Rietveld refinement of X-ray diffractionpattern of the sample at room temperature (300 K) shows themonoclinic P21/n phase. The value of the optical band gap of thematerial for direct transition is found to be �1.62 eV. The dielectricrelaxation (a conduction process) of the sample is investigated inthe impedance and electric modulus formalisms in the frequencyrange from 50 Hz to 1 MHz and in the temperature range from253 to 415 K. The Cole–Cole model is used to explain the relaxationmechanism in DNMO. The frequency-dependent maxima in theimaginary part of impedance are found to obey an Arrhenius lawwith activation energy of 0.346 and 0.344 eV for nano and bulkDNMO respectively. The dc and ac conductivity formalisms revealthat small polaron hopping process is responsible for conduction inDNMO. With increasing sintering temperature, the relative densityof the materials increases and porosity decreases, ensuring a bettercontact between the particles, which is demonstrated throughhigher relative conductivities. The GGA + U calculated resultsobtained from FPLAPW method suggest that the ground state ofthe material is a ferromagnetic insulator.

Acknowledgements

Sujoy Saha acknowledges the financial support provided by theUGC, New Delhi (India) in the form of SRF. Alo Dutta thanks toDepartment of Science and Technology for providing the financialsupport through DST Fast Track Project under grant no. SR/FTP/PS-032/2010.

References

[1] N.S. Rogado, J. Li, A.W. Sleight, M.A. Subhraminian, Adv. Mater. 17 (2005) 2225.[2] D. Choudhury, P. Mandal, R. Mathieu, A. Hazarika, S. Rajan, A. Sundaresan, U.V.

Waghmare, R. Knut, O. Karis, P. Nordblad, D.D. Sarma, PRL 108 (2012) 127201.[3] M. Sonobe, K. Asai, J. Phys. Soc. Jpn. 61 (1992) 4193.[4] C. Shi, Y. Hao, Z. Hu, J. Phys. D: Appl. Phys. 44 (2011) 245405.[5] S. Zhao, L. Shi, S. Zhou, J. Zhao, H. Yang, Y. Guo, J. Appl. Phys. 106 (2009) 123901.[6] K. Devi Chandrasekhar, A.K. Das, C. Mitra, A. Venimadhav, J. Phys.: Condens.

Matter 24 (2012) 495901.[7] K. Asai, K. Fujiyoshi, N. Nishimori, Y. Satoh, Y. Kobayashi, M. Mizoguchi, J. Phys.

Soc. Jpn. 67 (1998) 4218.[8] K.D. Truong, M.P. Singh, S. Jandl, P. Fournier, J. Phys.: Condens. Matter 23 (2011)

052202.[9] W.Z. Yang, X.Q. Liu, H.J. Zhao, Y.Q. Lin, X.M. Chen, J. Appl. Phys. 112 (2012)

064104.[10] C. Moure, J. Tart aj, A. Moure, O. Peña, Bol. Soc. Esp. Ceram. 48 (2009) 199.[11] H.S. Nair, D. Swain, N. Hariharan, S. Adiga, C. Narayana, S. Elzabeth, J. Appl.

Phys. 110 (2011) 123919.[12] M. Mouallem-Bahout, T. Roisnel, G. Andre, D. Gutierrez, C. Moure, O. Peña,

Solid State Commun. 129 (2004) 255.[13] R.J. Booth, R. Fillman, H. Whitaker, A. Nag, R.M. Tiwari, K.V. Ramanujachary, J.

Gopalakrishnan, S.E. Lofland, Mater. Res. Bull. 44 (2009) 1559.[14] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented

PlaneWave + Local Orbitals Program for Calculating Crystal Properties (Techn.Universität Wien Vienna, 2001)

[15] S. Chanda, S. Saha, A. Dutta, T.P. Sinha, Mater. Res. Bull. 48 (2013) 1688.[16] S. Saha, S. Chanda, A. Dutta, T.P. Sinha, J. Sol–Gel Sci. Technol. 69 (2014) 553.[17] J. Rodriguez-Carvajal, Physica B 192 (1993) 55.[18] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.

160 S. Chanda et al. / Materials Research Bulletin 62 (2015) 153–160

[19] H.J. Monkhorst, J.D. Pack, Phys Rev. B 13 (1976) 5188.[20] V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, G.A. Sawatzky, Phys. Rev.

B 48 (1993) 16929.[21] P.M. Woodward, Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem. 53

(1997) 44.[22] R.D. Shannon, Acta Crystallogr. 32 (1976) 751.[23] J. Tauc, R. Grigorovici, A. Vancu, Phys. Status Solidi 15 (1966) 627.[24] E.A. Davis, N.F. Mott, Philos. Mag. 22 (1970) 903.

[25] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341.[26] E. Iguchi, K. Ueda, W.H. Jung, Phys. Rev. B 54 (1996) 1743.[27] P. Thongbai, T. Yamwong, S. Maensiri, J. Appl. Phys. 104 (2008) 074109.[28] R. Gerhardt, J. Phys. Chem. Solids 55 (1994) 1491.[29] D.P. Almond, A.R. West, Nature 306 (1983) 456.[30] V.I. Anisimov, F. Aryasetiawan, A.I. Lichtenstein, J. Phys. Condens. Matter. 9

(1997) 767.[31] L. Chen, T. Li, S. Cao, S. Yuan, F. Hong, J. Zhang, J. Appl. Phys. 111 (2012) 103905.