Journal ofMaterials Chemistry C

PAPER

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aMaterials Science and Technology Division

Science and Technology, CSIR, Tr

manojraamavarma@yahoo.co.ukbInstitute for Intensive Research in Basic

Kottayam-686 560, IndiacMaterials Research Laboratory, Universit

SloveniadCenter of Excellence for Biosensors, Instr

Solkan, Slovenia

† CCDC reference number 957848. Forelectronic format see DOI: 10.1039/c3tc31

Cite this: J. Mater. Chem. C, 2013, 1,6565

Received 21st June 2013Accepted 29th July 2013

DOI: 10.1039/c3tc31203h

www.rsc.org/MaterialsC

This journal is ª The Royal Society of

Re-entrant spin glass behaviour and magneto-dielectriceffect in insulating Sm2NiMnO6 double perovskite†

P. Neenu Lekshmi,a G. R. Raji,a M. Vasundhara,a Manoj Raama Varma,*a

S. Savitha Pillaib and M. Valantcd

The structure and magneto-dielectric properties of Sm2NiMnO6 double perovskite have been investigated.

The pure monoclinic bulk phase of Sm2NiMnO6 is an intrinsic B-site disordered ferromagnet showing a

second order magnetic phase transition �157 K, along with a low temperature re-entrant spin glass-like

transition (�20 K) due to the inherent coupling of Ni–Mn network with Sm3+ ion. Moreover, it is an

insulator with room temperature dc resistivity �108 U cm. Furthermore, the high dielectric permittivity

(�103) coupled with a shift in dielectric maxima towards higher temperature with frequency, analysis of

the phenomenological parameters (Tm, TB, g, DTrelax), and the validity of non-linear Vogel–Fulcher

relation, we define this ferromagnetic insulator as a relaxor-type dielectric material. Importantly, it

exhibits a positive intrinsic magneto-dielectric (MD) response �2% at 100 kHz under a low magnetic

field of 0.5 T close to 150 K. The intrinsic MD effect indicates a correlation between spin orientations on

the two magnetic sublattices (Ni and Mn) and the magneto-dielectric coupling in the ferromagnetic

regime. The insulating ferromagnetic behaviour coupled with MD effect make Sm2NiMnO6 an attractive

spintronic material.

I Introduction

Double perovskite oxides, A2B0B00O6, (A – alkaline earth metalssuch as Ca, Ba, Sr, etc., or rare earth ions of larger ionic radii, B0

and B0 0 – transition metal cations or lanthanides with smallerionic radii) have received much interest since they provide aunique opportunity to induce and control the multiferroicbehaviours in oxide systems. They display interesting proper-ties, such as metallic/half-metallic ferromagnetic and magne-toresistive properties as observed in Sr2FeMoO6 (ref. 1) (half-metallic ferromagnet), Sr2FeReO6 (ref. 2) (half-metallic ferri-magnet) and Sr2FeWO6 (ref. 3) (antiferromagnetic insulator),together with a number of interesting phenomena, includingroom temperature magnetoresistance, magneto-capacitanceand magnetostriction. The presence of mutually coupledmagnetic and dielectric properties, the so-called magneto-dielectric (MD) or magneto-capacitance (MC) effect, are current

, National Institute for Interdisciplinary

ivandrum-695 019, India. E-mail:

Sciences, Mahatma Gandhi University,

y of Nova Gorica, Nova Gorica-5000,

umentation and Process Control, 5250

crystallographic data in CIF or other203h

Chemistry 2013

focuses of interest since they provide vast scientic and noveltechnological impact.4–6 The rare earth based double perovskiteLa2NiMnO6, is a single material platform with multiple func-tions such as ferromagnetic semiconductivity, spin–phononand magneto-electric coupling near ambient temperature, andis expected to have unprecedented device applications.7 Thesecomplex physical properties arise from competing interactionsbetween magnetic (spins), structural (phonons) and polariza-tion (charges) order parameters. While most transition metalsinvolved in single perovskites are antiferromagnetic insulatorsdue to the negative super exchange interaction between thetransition metal ions,8 distorted double perovskite La2NiMnO6

is a ferromagnetic insulator due to the positive super exchangeinteraction between Ni and Mn cations.9–13 Such behaviour issignicant for exploring spintronic materials since it allows MDproperties to be achieved. Furthermore, the B-site metal ionordering in the crystallographic lattice greatly modies themagnetic, transport and MD properties of the material. Thereported large negative MD of 16%, near the ferromagnetictransition (�280 K) in bulk ordered La2NiMnO6 was assigned tothe intrinsic spin–lattice coupling.4 Recently Choudhury et al.reported a large MD coupling (8–20%) in the ferromagneticregion in a partially disordered La2NiMnO6 polycrystallinesample attributed to asymmetric hopping across the transitionmetal cations.13 However, extrinsic effects like particle size,grain boundaries, spin disorder, Maxwell–Wagner (MW) inter-facial effect etc., can also inuence the dielectric response undermagnetic eld.14,15

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Journal of Materials Chemistry C Paper

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It has been reported that, depending on the type, charge andsize of the cation present in the B-site, some of the doubleperovskites show interesting spin glass behaviour also. Spinglasses are magnetic systems which exhibit a “freezing transi-tion” to a state of a new kind of order in which spins are alignedin random directions.16 The re-entrant spin glass (RSG) transi-tion is a well-known phenomenon of spin glasses emergingfrom either long-range ferromagnetic (FM) or anti-ferromag-netic (AFM) ordering above the spin glass transition tempera-ture. Moreover, a few reports are available for the criticalexponents at the phase transition between the intermediateordered state and the high-temperature paramagnetic state ofthe re-entrant systems. However, until now, the exact nature ofthe re-entrant transition is still unclear and highly controversialdue to complex experimental data of RSG.17–21

It has been observed that the properties of La2NiMnO6 willgenerally change noticeably with the substitution of La ion byRare-Earth (RE) elements with smaller ionic radius. Moreover,the entire series of these oxides (RE2NiMnO6) have beenreported to be ferromagnetic with a decrease in TC, or JNi–Mn,due to the larger deviation of the Ni–O–Mn bond angle from180� with the substitution of heavier RE element. But theinvestigation of RE2NiMnO6 (ref. 22–24) ceramics is relativelysparse as compared to La2NiMnO6. Sm2NiMnO6 is reported tobe ferromagnetic with a double transition in the temperaturedependence of its magnetisation curve,23,25 however, its MDstudies have not been reported until now. The present investi-gation focuses on the in-depth analysis of ac as well as dcmagnetisation measurements and here in this report, for therst time, we show the MD effect of Sm2NiMnO6. We also noticethat the present compound exhibits a higher resistivity value atroom temperature and an intrinsic MD effect which may orig-inate from the weak spin–lattice interaction. Thus the observedinsulating ferromagnetic behaviour with MD coupling makesSm2NiMnO6 an attractive spintronics material.

II Experiment

Single-phase polycrystalline Sm2NiMnO6 samples were preparedfrom polymeric precursors by the Pechini method. The analyticalgrade metal nitrate solution was mixed with a stoichiometricamount of citric acid and the resulting emerald-green chelatedsolution was stirred for about 1 hour on a hot plate at 70 �C.Ethylene glycol was added to this solution and then heated toapproximately 150 �C to allow the chelates to undergo poly-esterication as well as to remove excess water. The resultingyellowish-green-brown gel was slowly decomposed in air at320 �C. The product underwent a subsequent treatment in air at800 �C for 2 h in order to eliminate all the organic materials andnitrates. The precursor powder was then grinded and calcined atvarious temperatures, ranging from 900 to 1200 �C with inter-mediate grinding, with a nal sintering at 1300 �C. The powderX-ray diffraction pattern is obtained with a PANalytical X'pertPro diffractometer in Bragg–Brentano geometry with Cu-Ka

radiation in the 2q range of 10� to 90� with a step size of0.008�. Reitveld renement of the diffraction pattern was carriedout using the GSAS soware. Temperature dependent ac

6566 | J. Mater. Chem. C, 2013, 1, 6565–6574

susceptibility measurements, c(T), temperature dependent dcmagneticmeasurements under eld cooled and zero eld cooled,M(T) and magnetic isotherms,M(H), were performed in a SQUIDVSM magnetometer from Quantum Design. The electron trans-port (resistivity) measurements were carried out by constantvoltage method in the temperature range of 10–300 K using aknown resistor. In this method, a constant voltage source (4 V)and a known resistor was placed in series with the sample. Thenthe voltage drop across the known resistor was measured using aKiethley nanovoltmeter (2182 A) and from that the unknownresistance of the sample was calculated. For dielectric charac-terisation disk samples with a diameter of 10 mm and height of 2mm have been plated with silver paste and inserted into the coldhead of the closed cycle cryo cooler (ARS-2HV). The measure-ments have been performed with a LCR meter (Agilent E4980A)that has been compensated for the coaxial cable length and openand short circuit calibrated. The magnetic eld has been appliedto the samples by inserting them into the center of a hollowcylindrical NdFeB magnet.

III Results and analysisA Structural characterisation

The X-ray diffraction pattern of the polycrystalline Sm2NiMnO6

conrmed the presence of a single phase monoclinic structurewith P21/n space group. The Reitveld renement result conrmsthe monoclinic (P21/n) phase of Sm2NiMnO6. Since P21/n is amaximal nonisomorphic sub group of Pbnm, it is difficult todistinguish between P21/n and Pbnm space groups simply by theX-ray diffraction technique especially if the ordering is incom-plete and b is very close to 90�. However, renement usingorthorhombic Pbnm space group led to unsatisfactory results.Further, the obtained lattice parameters and volume obtainedfrom renement using monoclinic P21/n are found similar tothe reported value of monoclinic Sm2NiMnO6 double perov-skites.23,25 But, the lack of superstructure peak below 20�

suggests that the ordering is not strong enough in the currentsample. Bond valence sum (BVS) formalism was done tocalculate the valence state of Ni and Mn ions. The effectivevalence Vij between the ith and jth atoms is dened as

Vij ¼Xj

eððd0�dijÞ=0:37Þ, where dij is the bond length between i and

j atoms and d0 is the bond valence parameter that has beenempirically determined for the i–j pair.26 Furthermore, the bondvalence sum calculated from Ni–O and Mn–O bond lengths,using the soware SPuDs indicate valence uctuations betweenNi2+/Ni3+ and Mn4+/Mn3+. But the values are found to be moreclose to Ni3+/Mn3+ that is consistent with the reported oxidationstate of high temperature sintered La2NiMnO6.11 Details of thelattice parameters extracted along with renement parametersand BVS are listed in Table 1.

B Magnetic characterisation

dc magnetisation. The M(T) measurements of zero eld-cooled (ZFC) and eld-cooled (FC) cycles under the elds of100 Oe, 2 T and 5 T in the temperature range 5 to 300 K are

This journal is ª The Royal Society of Chemistry 2013

Table 1 Lattice parameters, structural refinement parameters and bond valencesum for Sm2NiMnO6 at room temperature

Sm2NiMnO6

Space group P21/n

Lattice parametersa (A) 5.3469(2)b (A) 5.5076(2)c (A) 7.6040(3)b (deg.) 90.042(9)Volume (A3) 223.93(2)Rwp 0.0467Rp 0.0364

Bond valence sumNi2+ 2.58Ni3+ 3.34Mn4+ 3.47Mn3+ 3.45

Fig. 1 Temperature dependence of field-cooled (FC) and zero-field-cooled (ZFC)dc magnetisation measured at 100 Oe, 2 Tand 5 Tand inverse susceptibilities withlinear fit to Curie–Weiss law in the high temperature region for 100 Oe.

Fig. 2 (a) Low field hysteresis loop measured at different temperatures in therange �200 Oe to +200 Oe. Inset: M vs. H curves measured up to 6 T at 300 K, (b)low field hysteresis loop measured at 65 K and 150 K in the range �200 Oe to+200 Oe. Inset: M vs. H curves measured up to 2 T at 65 K.

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shown in Fig. 1. The M(T) curve clearly indicates a doubletransition under 100 Oe eld; the rst one is a very sharptransition at higher temperatures around 156 K, resembling aparamagnetic (PM) to ferromagnetic (FM) transition, TC, andthe other one is at lower temperatures around 20 K, resem-bling a spin glass/glassy behaviour, Tf. This double transitionand the irreversibility between FC and ZFC curves vanishes athigher applied elds (H ¼ 2 T and 5 T) and both ZFC and FCcurves collapse into a single broad PM to FM like transition.The inverse magnetic susceptibility of ZFC at 100 Oe in thehigher temperature range was tted to classical Curie–Weiss(CW) law and is shown in Fig. 1. A deviation of the t to CWlaw can be clearly seen for temperatures that are signicantlyabove TC. The effective paramagnetic moment calculated fromthe CW analysis is meff � 5.76 mB F.U.�1 [F.U. – Formula Units].Moreover, the Curie constant (C) and the Weiss temperature(Q) were determined to be 4.15 emu mol�1 K�1 and 172.51 K,respectively. The positive value of Q calculated from the tsuggests the presence of predominantly ferromagneticexchange interactions. The disappearance of the double tran-sitions with the application of higher elds and eld depen-dence on TC are a clear indication of the coexistence of FM

This journal is ª The Royal Society of Chemistry 2013

phase along with minor AFM phase. This coexistence of FM–

AFM causing the spin uctuations may lead to the freezing ofspins at the lower temperatures, thereby causing the formationof the second transition at Tf, which is in turn understood interms of glassy systems.27,28 The existence of the glassy state inthe vicinity of the FM transition gives rise to two possible typesof SG behaviour: Re-entrant Spin Glass (RSG) or Cluster-Glass(CG). Furthermore, the irreversibility observed in ZFC and FCbelow TC and the remarkable shi in TC to higher tempera-tures with the application of elds, 156 K for 100 Oe, 162 Kfor 2 T and 172 K for 5 T, clearly suggest the presence of aspin disorder and competing interactions due to the coexis-tence of FM–AFM phases in the supposed ferromagneticregion, Tf # T # TC, whereas the appearance of a sharp drop inmagnetisation below Tf and the deviation from CW behaviourare indicative of RSG behaviour.29–33 Therefore the M–T datashows a possible frustrated state below the Curie temperaturein Sm2NiMnO6, which needs further evidence.

Magnetic isotherms. In the inset of Fig. 2(a) and (b), wepresent the magnetisation (M) vs. applied eld (H) curves ofSm2NiMnO6 at 300 K in the range of �60 000 Oe to +60 000 Oeand at 65 K in the range of�20 000 Oe to +20 000 Oe, respectively.TheM–H loop at 300 K is completely a straight line as in the case ofPM state. The M–H loop at 65 K has an ‘S’ like appearance, i.e. arapid increase in magnetisation value at lower magnetic elds butdoes not saturate even at applied magnetic elds of 20 000 Oe,with a small hysteresis at lower elds, indicating the co-existenceof frustrated and FM states. In order to characterise the magnetic

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ordering below TC, M(H) isotherms in the low eld regime(�200 Oe # H # +200 Oe) were also studied at different temper-atures (5, 20, 30, 65, 75 and 150 K) and are shown in Fig. 2a. Thelow eld ZFC hysteresis experiment was carried out in such a waythat the sample was cooled from 300 K to the required lowtemperature and aer taking the M–H loop the sample was againheated to 300 K. This process was repeated for each temperature inorder to avoid the thermal remanence effect that might be presentin the sample below TC. At low applied elds, the M(H) curveexhibits a typical FM-like hysteresis loop. At 150 K (Fig. 2b), thehysteresis loop shows a lower remanent magnetisation, MR, (0.03mB F.U.�1) and coercive eld, HC, (10 Oe), moreover, the virginbranch crosses the M(H) loop reecting either frustrated interac-tion, or eld induced growth of the FM phase.34 On lowering thetemperature to 75 K the magnitudes ofMR (0.17 mB F.U.

�1) andHC

(50 Oe) slightly increase, at 65 K the magnitude of HC is found tobe the same but MR (0.14 mB F.U.�1) is decreased. Moreover, thevirgin branch crosses the hysteresis loop at 65 K also (Fig. 2b).However at 30 K, the M(H) loop is similar to 75 K. At 20 K (�Tf),there is a noticeable increase in MR (around 0.21 mB F.U.�1) andthe vertex of the loop is found to be pointing to a much highermagnetisation value. Interestingly, below Tf at 5 K, the hysteresisloop shows a further decrease in MR. In a conventional spin glasssystem the magnitude of MR and HC increases with decreasingtemperature,29 but here an anomaly is observed and it is signi-cant with the development of spin canting effects below TC.29,35,36

Moreover, these features are in corroboration with those reportedin general for systems classied as RSG where the ferromagneticphase itself develops in the presence of competinginteractions.29,32,35

Fig. 3 (a) M vs. H around TC, (b) Arrott plots, M2 vs. H/M, (c) MAPs, M1/g vs. (H/M)1

log–log scale at TC¼ 158 K along with the fitting curve to eqn (3), (d) Kouvel–Fisher ptemperature dependence of Ms(0) and c0

�1 along with the fitting curves to eqn (1

6568 | J. Mater. Chem. C, 2013, 1, 6565–6574

In order to further understand the critical behaviour,we have carried out isothermal magnetisation measurementsnear TC. Fig. 3a shows a series of M(H) curves in theimmediate vicinity (152 K # T # 162 K) of the Curie temper-ature at an interval of 1 K. The gradual change of theM(H) curves and the curvature at low elds due to the co-existence of frustrated state and FM state make it difficult toextract an accurate value of TC. Fig. 3b shows Arrott plots, M2

vs. H/M, for the compound and it clearly indicates a positiveslope with non-linear curves showing curvature even athigher elds. However, the straight line extrapolated to thecurve at a temperature of 152 K shows a positive intercept atthe M2 axis whereas the 162 K shows an intercept on the H/Maxis, indicating a second order phase transition between 152 Kand 162 K. The critical behaviour of magnetic systems with asecond order magnetic phase transition near the Curietemperature is characterised by a set of interrelatedcritical exponents, b, associated with the spontaneous mag-netisation (Ms), g which is associated with initial magneticsusceptibility (c0) and d, which is related to the criticalmagnetisation isotherm at TC. They are mathematicallyrelated as:

Ms(0) ¼ m0|s|b, s < 0, T < TC (1)

c0�1 ¼

�h0

m0

�sg; s. 0;T .TC (2)

H ¼ A0Md, s ¼ 0, T ¼ TC (3)

/b using critical exponents b ¼ 0.475 and g ¼ 0.98489. Inset: critical isotherm on alots for spontaneous magnetizationMs(0) and inverse initial susceptibility c0

�1, (e)) and (2), respectively.

This journal is ª The Royal Society of Chemistry 2013

Table 2 The critical exponents obtained in this work from several methods andcomparison of critical parameters predicted by different theoretical models

TC b g d Ref.

Sm2NiMnO6

MAP 158.8 0.475 0.9849 This workKouvel–Fischer method 158.42 0.4537 This work

158.35 0.9501 This workPower law 158.34 0.4319 This work

158.38 0.9279 This work158 3.0465 This work

Wisdom scaling relation 3.0735 This workMean-eld model 0.5 1.0 3.0 453D Heisenberg model 0.365 1.336 4.80 453D Ising model 0.325 1.24 4.82 45Tricritical model 0.25 1 5 45Spin glass 1 2.2 3.1 40

Fig. 4 (a) Temperature dependence of ac susceptibility at various frequenciesunder Hac¼ 1 Oe, (b) ln(s) vs. ln(t) [where reduced temperature, t¼ (Tf� TSG)/TSG]with linear fit. Inset: ln(n) vs. Tf with the fit to Vogel–Fulcher law.

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where Ms(0) is the spontaneous magnetisation; c0�1 is the

inverse of the susceptibility; s is the reduced temperature

s ¼ TTC

� 1� �� �

; TC is the Curie temperature and m0, h0 and A0

are the critical amplitudes. For rst order ferromagnetic phasetransitions, the critical exponents are impossibly denedbecause the applied magnetic eld can shi the transitionwhich results in a eld dependent phase boundary TC(H).37,38

The analysis of static critical phenomenology near the Curietemperature is capable of giving further evidence for re-entrantbehaviour.39–41 The TC and critical exponents can be easilydetermined from several methods which include the modiedArrott plots (MAP) technique,42 the Kouvel–Fisher method43 andthe Widom scaling relation.44 The MAP technique is based onArrott–Noakes equation of state,

�H

M

�1g ¼ asþ bM

1bðHÞ (4)

where a and b are material dependent parameters. The regularArrott plot shows that the M2 vs. H/M relationship is based onthe mean-eld model of critical exponent of b¼ 0.5 and g¼ 1.0.In the case of MAP, different values of b and g are taken as trialexponents from various models for the construction of MAP[(H/M)(1/g) �M(1/b)] and then are tted into the data of the linearpart or directly tted into the initial Arrott plot.45 The Ms(0) isdetermined from the intersection of the linear extrapolation of

the straight line in the modied Arrott plots with the M1b axis,

while the c0�1 corresponds to the intersection of these lines

with theHM

� �1g

axis. An initial value of TC is determined from

the isotherm that passes through the origin. These data aretted to the exponential behaviour of eqn (1) and (2) to obtainnew values of b and g, respectively. These new values are thenused to obtain the new MAPs. This procedure is continued untilthey converge to a stable value. Finally, we obtained the besttted values as: b ¼ 0.475, g ¼ 0.9849 and TC ¼ 158.8 K and the

M1b vs.

HM

� �1g

is shown in Fig. 3c. The corresponding value of

d, obtained from the Widom scaling relation is

d ¼ 1þ g

b

� �¼ 3:0735. Thus the calculated d value is close to

the estimated, d ¼ 3.0465 value from the critical isotherm at158 K (inset Fig. 3c), which is near to TC.

In addition, we also determined the critical exponents b andg along with TC by the Kouvel–Fisher method,43

MsðTÞdMsðTÞ=dT ¼ T � TC

b(5)

c0�1ðTÞ

dc0�1ðTÞ=dT ¼ T � TC

g(6)

and also directly from the power-law predictions of eqn (1) and(2) which are given in Fig. 3d and e, respectively. The values ofTC and the critical exponents of Sm2NiMnO6 are obtainedthrough different methods and the theoretical values derived

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from several models are summarized in Table 2 for comparison.In earlier studies the critical exponents of the re-entrant systemsare reported to have values in between the classical threedimensional ferromagnetic materials and those characterisinga spin glass transition.40,41 We have got an analogous behaviour,which further supports the presence of RSG behaviour.

ac susceptibility. To further characterise the RSG behaviour,c(T) measurements were done in an applied eld Hac ¼ 1 Oe inthe temperature range 5 to 300 K at various frequencies rangingfrom 29 Hz to 999 Hz, shown in Fig. 4a. From the real, c0(T) andimaginary c0 0(T) parts of susceptibility, a high temperature

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Fig. 5 Temperature dependence of ac magnetic susceptibility at various dc biasfields under fixed Hac ¼ 1 Oe and f ¼ 88 Hz.

Fig. 6 Temperature dependence of dc resistivity. Inset: linear fit for Mott VRH in

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maxima was observed at Tp around 150 K, which shows no effecton frequency dependence, whereas a low temperature maximaat Tf around 20 K exhibits a clear shi towards high temperaturewith increasing applied frequency. Between the two maxima(Tf # T # Tp) in c0(T) a systematic plateau-like behaviour isobserved whereas in the case of c0 0(T) broad shoulders areobserved. The TC was obtained at 157 K by extrapolating the

linear part of CW t from1c0 ðTÞ (not shown).

From the c(T) frequency variation measurements, both c0(T)and c0 0(T) show strong frequency dependence at Tf, on the otherhand, the frequency dependence of the peak at Tp is found to bequite negligible. Thus it is apparent that the observed maximaat Tf indicates the presence of a frustrated magnetic state, theexistence of spin glass-like nature, however, the maxima at Tpsuggest the presence of a strong ferromagnetic interaction.Again, the double maxima observed in c(T) and the M(T)measurements are found to be similar, which further corrobo-rates RSG behaviour.29–33

For further clarication, analysis of the susceptibility data at Tfwas performed. The maximum change in the freezing tempera-ture,DTf is denoted asDTf(u)¼ DTf(u)¼ T999 Hz

f � T29 Hzf ¼ 2.3 K.

The relative shi in freezing temperature,DTf

½TfDlogðuÞ�, can be

used to describe the magnetic order of the system. This valuetypically lies between 0.005 and 0.08 for a spin glass (SG) and is 2for non-interacting super paramagnetic materials. The obtainedvalue 0.098 � 0.004 characterises our system to be more likely acluster glass type. Dynamical scaling analysis was performed

using the critical slowing down relation,17ss0

¼�ðTf � TSGÞ

TSG

��zn0

,

where s is the relaxation time corresponding to the measured

frequency�s ¼ 1

n

�. Fig. 4b shows the dependence of s with

reduced temperature, t t ¼ ðTf � TSGÞTSG

� �� �. From the analysis,

TSG, the critical spin glass ordering temperature as frequencytends to zero, s0, the characteristic relaxation time of single spinip, and the dynamic critical exponent, zn0 are determined as 14.9K, 3.1 � 10�5 and 1.98, respectively, n0 is the critical exponent of

correlation length, x ¼ Tf

TSG� 1

� ��n0" #

. For a spin-glass system,

s0 ¼ 10�13 and zn0 are typically found to lie between 4 and 12, thehigher value of s0 and lower value of zn0 implies slower spin ip-ping, attributed to the presence of randomly oriented ferromag-netic clusters. Such higher s0 values have also been observed in avariety of magnetic systems including metallic alloys and oxidesshowing RSG behaviour.31–33 Furthermore, the failure of Arrhenius

relation n ¼ n0e��

EakBTf

(not shown) implies that the dynamics are

not simply associated with the single-spinips, but rather reect acooperative character, which is cluster glass like. To investigatethe interaction among RSG clusters, the Vogel–Fulcher law17 is

proposed, n ¼ n0e��

EakBðTf�T0Þ

. Here Ea is the activation energy or

the potential barrier that separates two adjacent clusters where n0

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is the characteristic frequency of the clusters, Tf the freezingtemperature and T0 is the Vogel–Fulcher temperature, which isthe measure of inter-cluster interaction strength. The excellentagreement of this t (inset Fig. 4b), with the rened parametersn0 ¼ 2 � 103, Ea/kB ¼ 2.16 and T0 ¼ 14.6, is a clear indication ofRSG behaviour.46

To further probe the RSG behaviour, ac susceptibilitymeasurements were proceeded with super imposed dc elds(Hdc ¼ 0, 0.255, 4.53, 19.75, 49.95, 80.16 and 110.29 Oe) underHac 1 Oe and frequency 88 Hz in the temperature range 5 to 300K (Fig. 5). c0(T) and c0 0(T) show a shi in Tf towards lowertemperatures with a slight change in the magnitude while adrastic decrease in the magnitude for the Tp comes withincreasing eld. The intensity of the peak at around TC in c0 0(T)diminishes with increasing eld indicating the FM nature of thecompound. Moreover, we observe an anomaly in the interme-diate temperature region, Tf # T # Tp, in c0 0(T) whose magni-tude depends on the applied dc eld which yet again indicatesthe presence of frustration. This interpretation is supported bythe decrease in MR and the behaviour of virgin curve in the loweld hysteresis loop at 65 K. This is a clear signature of RSGbehaviour in the studied compound.31,35

C dc transport properties

Fig. 6 shows the temperature dependence of dc resistivity (rdc)measured in the temperature range 50–300 K. The dc transportproperty shows high resistance of the compounds which

the low temperature region.

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precluded the resistivity measurements below 50 K. For oxidesystems, different models have been proposed to describe thetemperature dependent charge transport behaviour which isdened by lnr f 1/n, where n ¼ 1, 2 and 4 corresponds to asimple thermal activation model, Efros–Shklovskii typehopping, and Mott's variable range hopping (VRH), respec-tively.47 Among these the resistivity data is aptly following theVRH mechanism in the low temperature region (T < 180 K) asshown in the inset of Fig. 6. In Mott's VRH, the hoppingdynamics are controlled by collective excitation of the chargecarriers and the mechanism is given by,

r ¼ r0 exp

�T0

T

�14

24

35 (7)

where r0 and T0 are constants; T0 ¼ 24pkBNðEFÞx3 �, where N(EF)

is the density of localized states at the Fermi level and x is thedecay length of the localized wave function and kB is theBoltzmann constant. The value of T0 is obtained as �1.7 � 108

K, which is of a similar magnitude as observed in transitionmetal oxides.48 By taking x as 3.95 A (the average distancebetween two neighboring Ni or Mn ions obtained from struc-tural renement), N(EF) is obtained as 8.5 � 1024 eV�1 m�1. Thehopping energy has been estimated from T0 using the formula

Ea ¼ kB4T0

1=4T3=4. It varies from 0.05 to 0.13 eV in the

temperature range of 50–180 K.

Fig. 7 (a) 30 vs. T curves at different frequencies. Inset: expanded view of low tempekHz with CW fit. Inset: modified CW fit [log(1/30 � 1/3 0

m) vs. log(T � Tm)] at 500 kH

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D Dielectric and magneto-dielectric behaviour

Fig. 7a shows the temperature dependence of the real part, 30, ofdielectric permittivity, 30(T), at several frequencies, whichexhibits two dominant frequency-dependent dielectric relaxa-tions which saturate and become relatively frequency inde-pendent at lower temperatures. The presence of strongdielectric relaxations is also seen in the corresponding lossdata, tan d(T) Fig. 7b. The peak temperature (Tm) at whichmaximum dielectric constant occurs is found to be frequency-dependent and shis to higher temperatures with an increasein the measuring frequency. Relaxor like dielectric behaviour iswell manifested from the frequency dependent peak in 30(T) andfrom the frequency dependent tan d(T). Also, the maximumvalue 3

0m of the dielectric constant decreases with increase in

frequency. A deviation from Curie–Weiss law can be clearly seenin the reciprocal of the dielectric constant (1/30) versus temper-ature, at 10 kHz as shown in Fig. 7c. The reciprocal dielectricconstant starts to follow the Curie–Weiss law above 250 K whichis dened as the burn temperature (TB). The difference betweenTB and Tm, (250 K� 228 K¼ 22 K) shows a characteristic diffusetransition. The evaluation of relaxor behaviour using a modiedCurie–Weiss law is shown in the inset of Fig. 7c. The value of g� 1.98 obviously indicates that the material has an almostcompletely diffused phase transition. Furthermore, the degreeof relaxation behaviour, where Tm(1000 kHz) and Tm(10 kHz) are thetemperatures corresponding to the maximum dielectricconstant at 1000 kHz and 10 kHz, respectively, obtained at 99 Ksuggests strong frequency dispersion. Like many relaxors, the

rature relaxation, (b) tan d vs. T curves at different frequencies, (c) 1/30 vs. T at 500z, (d) non-linear Vogel–Fulcher fitting.

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Table 3 Calculated effective magnetic moment, meff for the possible spin-stateconfigurations in Sm2NiMnO6

Spin states meff ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2mSmÞ2 þ mNi

2 þ mMn2

qMn3+ (S ¼ 2), Ni3+ (S ¼ 3/2) 6.47Mn3+ (S ¼ 2), Ni3+ (S ¼ 1/2) 5.46Mn4+ (S ¼ 3/2), Ni2+ (S ¼ 1) 5.08Mn2+ (S ¼ 2), Ni4+ (S ¼ 2) 7.86Mn2+ (S ¼ 2), Ni4+ (S ¼ 1) 6.77Mn2+ (S ¼ 2), Ni4+ (S ¼ 0) 6.15

mSm ¼ gSm

2JðJ þ 1Þ�12 ¼ 0:8452 gSm ¼ 32þ SðS þ 1Þ � LðLþ 1Þ

2JðJ þ 1Þ�

¼ 0:2857

�;

mNi=mMn ðspin-onlyÞ ¼ ½4SðS þ 1Þ�12:

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frequency dependence of the maximum in the loss tangent canbe well tted to the non-linear Vogel–Fulcher (VF) law,26

s ¼ s0 exp

�Ea

kB�Tm � Tf

�� (8)

which is used to characterize the frequency dispersion behaviourin relaxors, where s0 is the pre exponential factor; Ea is the acti-vation energy; kB is the Boltzmann constant; Tm is the tempera-ture at which maximum of 30 occurs at the angular frequency u¼2pn; s¼ u�1 and Tf is the static freezing temperature at which therelaxation time s tends to innity. The best t of VF law (Fig. 7d)to the experimental data shows a glassy behaviour analogous tothe spin glass state in magnetic materials with polarisationuctuations above Tf. The glassy behaviour is attributed to theinteraction arising from B-site cation disorder and valence uc-tuations.13,26 The parameters obtained from the non-linear t areEa ¼ 0.15 eV, s0 ¼ 2.65 ns and Tf ¼ 15.9 K.

The temperature dependent 30 measured both in the presenceand in the absence of a low external magnetic eld (0.5 T) atdifferent frequencies and similarly tan d are shown in Fig. 8a andb, respectively. The % MD [dened by MD (%) ¼ 100(D3MD/30)]and the % Magneto-Dielectric Loss [MDL (%) ¼ 100(Dtan dMD/tan d0)] are shown in the inset of Fig. 8a and b, respectively. TheMD effect demonstrates a positive MD effect below 150 K andwhich further decreases to give a colossal negative MD effectabove the transition temperature. Moreover, both MD effect andMDL increase with eld for all temperatures below the FM

Fig. 8 (a) The temperature dependent 30 measured at 0 T (closed symbols) and0.5 T (open symbols). Inset: % MD effect with temperature. (b) The temperaturedependent dielectric loss measured at 0 T (closed symbols) and 0.5 T (opensymbols). Inset: temperature dependence of % MDL effect.

6572 | J. Mater. Chem. C, 2013, 1, 6565–6574

transition but they show different signs above the FM transition,which suggests that the observed MD effect may be an intrinsiceffect.49 However, the observed colossal negative MD effect abovethe transition temperature clearly indicates the presence ofextrinsic contribution also. The intrinsic contribution originatesfrom the asymmetric hopping of charge carriers (between Ni andMn sites), whereas the extrinsic contributions may arise due toparticle size, spin disorder or Maxwell–Wagner relaxations, i.e.from accumulated charge carriers near the grain boundaries.13,49,57

IV Discussions

The double magnetic transition observed in dc and ac mag-netisations and the presence of large bifurcation in ZFC/FCmagnetisation below TC, with a sharp drop in magnetisationbelow Tf, indicates the occurrence of re-entrant behaviour.Deviation of the t to CW law for temperatures signicantlyabove TC attributes to spin uctuations associated with glassysystems.33 The various possible spin-state combinations for Niand Mn ions and the calculated total effective moment of

Sm2NiMnO6, meff ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2mSmÞ2 þ mNi

2 þ mMn2

qare shown in

Table 3. The experimental meff (5.76 mB F.U.�1) value is found tolie in between that theoretically predicted for high spin (HS)Mn3+ (t2g

3, eg1), HS Ni3+ (t2g

5, eg2) and HS Mn3+ (t2g

3, eg1), low

spin (LS) Ni3+ (t2g6, eg

1), which is likely to be due to the presenceof mixed spin states in Ni3+ (3d7 system). Ni3+ systems are closeto HS–LS transition point due to the increased covalency.Moreover, the increased charge transfer will further increase theeffects of 3d spin–orbit coupling.58

The dc magnetisation also indicates the co-existence of FM–

AFM interactions in the supposed ferromagnetic region Tf # T#

TC, which is supported by the low eld hysteresis behaviour in thetemperature range Tf # T # TC. Thus the thermomagnetic anal-ysis of ZFC and FC indicates the presence of competing FM–AFMexchange interactions in the system, which may arise due to thecombination of intrinsic disorder50 along with inherent magnetocrystalline anisotropy.23 The intrinsic disorder might be attrib-uted due to the presence of antiferromagnetic pairs such asMn3+–O–Mn3+, Ni3+–O–Ni3+, which have been introduced due tothe intrinsic antisite boundary in Ni/Mn network so that the

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ferromagnetic interaction is weakened.9,13 The inherent contri-bution arises from the spin–orbit coupling between Mn–Ninetwork and Sm3+ ion.23–25 It is proven from the past studies thatSm3+ spin order at low temperatures and the 4f Sm spins mightcause an AFM interaction23–25,51,52 with the FM Ni3+–O–Mn3+ thatmay be causing the sharp down turn at 20 K in the ZFC–M(T)curve with the eld of 100 Oe and the presence of a small peak inc(T) around 20 K. However, the appearance of hysteresis in thelow eld M(H) below Tf (T ¼ 5 K) suggests the presence of acompeting AFM–FM interaction. Moreover, the observed lowtemperature peak in the dc magnetisation depends largely on themagnitude of applied elds which further supports thecompeting AFM–FM interactions51–54 resulting in RSG behaviourin Sm2NiMnO6. Moreover, rigorous critical analysis near theCurie temperature shows the values of the exponents (b, g, d)slightly deviate from themean eld values, which in turn could bedue to the presence of competing magnetic interactions, andthereby establishes the RSG behaviour. Moreover, the detailedanalysis of ac susceptibility near Tf along with ac superimposeddc measurements strongly supports the RSG behaviour.

Resistivity shows an insulating type dependence on tempera-ture, being rdc � 108 U cm at 300 K. The three classes of modelsfor resistivity in oxides do not t the experimental data in thewhole measured temperature range (50–300 K). Among themresistivity evolution in the low temperature region (T < 180 K)follows the VRHmodel. This type of hopping conduction is typicalof phase separated systems (FM and AFM clusters) where thecharge carriers move by hopping between two localized electronicstates.55 Thus the overall resistivity behaviour is consistent withthe hopping motion of the charge carriers through such localizedstates, as observed in many disordered systems.47

The dielectric transport studies clearly show the presence ofdouble dielectric relaxations. The deviation from Curie–Weisslaw, the parameter g � 2 obtained from modied Curie–Weisst, the degree of relaxation, DTrelax � 99 K, and the validity ofnon-linear Vogel–Fulcher relationship indicate a glassy likecharacteristic and provide direct evidence for a relaxor dielectricbehaviour. This particular nature indicates that the systemfreezes to a glassy state below a certain temperature and therebytakes much longer to respond to the small external ac signal.The low temperature dielectric relaxation may arise from theasymmetric hopping of charge carriers between Ni and Mn ionswhich can be attributed to the presence of polarized nano-regions (PNRs) creating a defect related hopping mecha-nism.26,56 The PNRs are characteristics in the double perovskitestructure arising from structural disorder in the lattice, due tothe inhomogeneous distribution of the B-site cations (due to thecoexistence of two different B-site cations Ni and Mn) withvalence uctuations. The obtained activation energy from theVF t for the dielectric relaxation (�0.15 eV) is close to thehopping energy obtained from the VRHmechanism (0.13 eV for180 K) from the dc resistivity which further gives an evidence forthe presence of hopping mechanism. Again, the observedcolossal dielectric response above 150 K which may arise fromthe extrinsic Maxwell–Wagner kind relaxation, which emergesfrom the different conductivities near the grain boundaries dueto the presence of accumulated charges.13,57 Furthermore, the

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appearance of a spin glass like transition and dipolar freezingcharacter around the same low temperature regime (below 20 K)support the possibility of a multiglass state at lower tempera-tures.13,59 Interestingly a notable intrinsic positive and anextrinsic colossal negative MD response are observed below andabove the FM transition temperature, respectively. The intrinsiceffect may arise from the connection between the spin orien-tations on the two magnetic sublattices (Ni and Mn) and themagneto-dielectric coupling below the ferromagnetic transitiontemperature. Moreover, in the presence of even a low magneticeld, the spin–spin correlation is signicantly enhanced,leading to an increasing MD effect up to somewhere near theferromagnetic transition temperature. However, the MD effectfurther decreases even in the presence of the magnetic eld dueto thermal disordering of the spin orientation.13

V Conclusions

The present investigation reports polycrystalline Sm2NiMnO6

double perovskite oxide crystallises into a single phase mono-clinic structure with a phase group P21/n having intrinsic B-sitedisordered Ni3+/Mn3+ ion pairs with the characteristic features ofan insulating RSG behaviour along with relaxor dielectric prop-erties. Furthermore, the magneto-capacitance measurementseven under a lowmagnetic eld of 0.5 T at 10 kHz show a positiveintrinsic MD response (�2%) below the FM–PM transitiontemperature (�150 K) and a negative extrinsic colossal MD effectabove the transition temperature. From the experimentalevidences, we suggest the RSG behaviour in the compound arisesdue to the presence of competingmagnetic exchange interactionsinduced by intrinsic disorder along with inherent coupling of Ni–Mn network with Sm3+ ion. Moreover, the observed colossaldielectric response and the dielectric relaxation dynamics mayarise due to the existence of PNRs in a disordered surroundingwhich in turn is due to the presence of intrinsic antisite disorder.Furthermore, the observed positive MD effect indicates a corre-lation between spin orientations on the two magnetic sublattices(Ni and Mn) and the magneto-dielectric coupling in the ferro-magnetic regime. These observations suggest Sm2NiMnO6 is anattractive spintronics material since the insulating ferromagneticnature along with magneto-dielectric properties are of capitalimportance for exploring spintronic materials.

Acknowledgements

P. Neenu Lekshmi is thankful to Council of Scientic andIndustrial Research (CSIR), India for granting the Senior ResearchFellowship. M. Vasundhara and M. R. Varma acknowledgeDepartment of Science and Technology (DST), and CSIR, Indiagranted Project SURE (No. CSC0132) for the nancial support.

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