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Glassy dielectric response in Tb2NiMnO6 double perovskite with similarities to a Griffiths

phase

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2013 EPL 104 67002

(http://iopscience.iop.org/0295-5075/104/6/67002)

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December 2013

EPL, 104 (2013) 67002 www.epljournal.org

doi: 10.1209/0295-5075/104/67002

Glassy dielectric response in Tb2NiMnO6 double perovskitewith similarities to a Griffiths phase

Hariharan Nhalil1(a)

, Harikrishnan S. Nair1,2 (a)

, H. L. Bhat1,3 and Suja Elizabeth

1

1 Department of Physics, Indian Institute of Science - Bangalore 560012, India2 Julich Center for Neutron Sciences and Peter Grunberg Institute, JARA-FIT,Forschungszentrum Julich GmbH - 52425 Julich, Germany3 Center for Soft Mater Research - Jalahalli, Bangalore 560013, India

received 25 November 2013; accepted in final form 18 December 2013published online 7 January 2014

PACS 77.80.Jk – Relaxor ferroelectricsPACS 77.22.Gm – Dielectric loss and relaxationPACS 75.47.Lx – Magnetic oxides

Abstract – Results of frequency-dependent and temperature-dependent dielectric measurementsperformed on the double-perovskite Tb2NiMnO6 are presented. The real (ε1(f, T )) and imagi-nary (ε2(f, T )) parts of dielectric permittivity show three plateaus suggesting dielectric relaxationoriginating from the bulk, grain boundaries and the sample-electrode interfaces, respectively. Theε1(f, T ) and ε2(f, T ) are successfully simulated by a RC circuit model. The complex plane ofimpedance, Z′-Z′′, is simulated using a series network with a resistor R and a constant phaseelement. Through the analysis of ε(f, T ) using the modified Debye model, two different relaxationtime regimes separated by a characteristic temperature, T ∗, are identified. The temperature vari-ation of R and C corresponding to the bulk and the parameter α from modified Debye fit lendsupport to this hypothesis. Interestingly, the T ∗ compares with the Griffiths temperature for thiscompound observed in magnetic measurements. Though these results cannot be interpreted asmagnetoelectric coupling, the relationship between lattice and magnetism is markedly clear. Weassume that the observed features have their origin in the polar nanoregions which originate fromthe inherent cationic defect structure of double perovskites.

Copyright c© EPLA, 2013

Introduction. – Double-perovskite compoundsR2BB′O6 (R = rare earth; B,B′ = transition metal)display a variety of interesting properties such as ferro-magnetism [1], magnetocapacitance/magnetoresistance [2]and field-induced changes of dielectric constant [3], allof which make them potential candidates for spintronicsapplications. Theoretical predictions [4] and experimentalobservation [5] of multiferroicity have been reportedfor double perovskites. However, most investigationsof this class of compounds were focused on La-basedcompositions, for example, La2NiMnO6 which has ahigh ferromagnetic transition temperature of 280K [6,7].Ceramics of La2NiMnO6 are reported to show relaxor-likedielectric response which is attributed to Ni2+-Mn4+

charge ordering [7]. Epitaxial thin films of La2NiMnO6

are known for dielectric relaxation and magnetodielectriceffect [6]. In the present paper, we report the results ofimpedance spectroscopy of Tb2NiMnO6. The motivation

(a)Authors contributed equally to this work.

for this work stems from our previous study that showeda clear correlation between the lattice anomaly observedin the FWHM of the phonon mode and the Griffithstemperature observed through magnetization [8]. Herewe address the dielectric response of this system, itsinterpretation and appraisal based on the previousknowledge. Experimentally observed dielectric data arefaithfully reproduced using resistor network models whichhelp to extract intrinsic contributions. A characteristictemperature is identified in the ensuing analyses whichis compared with the magnetic and Raman data alreadyreported on this material. It is found that the magneticGriffiths temperature is reflected in the dielectric dataalso through this characteristic temperature.

Experimental details. – Details of synthesis, struc-ture, magnetism and Raman studies of Tb2NiMnO6 werereported earlier [8]. In order to perform dielectric mea-surements, pellets of approximate thickness 0.8mm andarea 6.8mm2 were prepared using poly-vinyl alcohol as a

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Hariharan Nhalil et al.

Fig. 1: (Colour on-line) The real part of dielectric permittivity,ε1, and the dissipation factor or loss factor, ε2, as a function oftemperature, measured with different applied frequencies in therange 100 Hz–800 Hz ((a), (b)) and 1 kHz–7 MHz ((c), (d)). Inthe low-frequency region, three different plateaus are observedwhich can arise from intrinsic, grain boundary and sample-electrode interfaces, respectively.

binder. The density of the pellet is measured to be greaterthan 95% of the theoretical density. A temperature-dependent dielectric constant was measured using a Janiscryostat in the frequency range from 1 kHz to 10MHz us-ing a 4294A precision impedance analyser with an appliedac voltage of 800mV. Dielectric experiments on thesesamples were repeated using several electrodes. Initially,silver paste was applied on both sides of the pellet andwas baked at 250 ◦C for 3–4 hours before measurement.Afterwards, the measurements were repeated using silver-and gold-plated electrodes. The data obtained with all thethree types of electrodes were consistent.

Results and discussion. – The temperature depen-dence of real and imaginary parts of dielectric permittivity,ε1(f, T ) and ε2(f, T ) of Tb2NiMnO6 in the frequency re-gion, 100Hz–800Hz, is shown in fig. 1(a), (b) and for therange, 1 kHz–7MHz in fig. 1(c), (d). Clear frequency dis-persion is observed in both plots ε1(f, T ) and ε2(f, T ) anda closer examination reveals different plateaus. Schmidtet al. [9] have shown that each relaxation is representedby a dielectric plateau, three of which are indeed seen atlow frequencies (fig. 1(a)). At high frequencies (fig. 1(c))the third plateau is not observed. The low-temperatureplateau originates from the intrinsic bulk contributionand the high-temperature plateaus could be due to thegrain boundaries and sample-electrode interface [10,11].Each relaxation can be ideally represented by one RC el-ement [12], where R and C are connected in parallel, andthree RC elements in series (upper panel of fig. 2) wereused to model the real and imaginary parts of the permit-tivity vs. T and the frequency dependence.

Fig. 2: (Colour on-line) Top: the schematic of the RC circuitused for simulating ε1 and ε2 vs. temperature plots for differentfrequencies. Bottom: simulated curves of (a) ε1 and (b) ε2vs. temperature for different frequencies. As clear from (a),three plateau-regions corresponding to εmin, εmed and εmax arepresent in the experimental data, too (fig. 1(a), (b)). Simulatedcurves of ε1 and ε2 as a function of frequencies for differenttemperatures are shown in (c) and (d).

The complex impedance is given by [13]

Z∗ = Z ′ + iZ ′′, (1)

where Z ′ and Z ′′ are the real and imaginary part of theZ∗, respectively.

For a series of three RC elements as shown in fig. 2,the real and imaginary parts of the permitivity are calcu-lated [9] as

Z∗ =R1

1 + iωR1C1+

R2

1 + iωR2C2+

R3

1 + iωR3C3, (2)

ε1 =−Z ′′

ωε0g(Z ′2 + Z ′′2), (3)

ε2 =Z ′

ωε0g(Z ′2 + Z ′′2), (4)

where ω is the angular frequency of the applied ac voltageand ε0 is the permittivity of free space and g is a geomet-rical factor (∝ area/thickness). In eq. (2), R1C1 repre-sents the intrinsic contribution, while R2C2 and R3C3 arethe external contributions from the grain boundaries and

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Glassy dielectric response in Tb2NiMnO6 double perovskite etc.

Fig. 3: (Colour on-line) Top: the R-CPE circuit used to modelthe complex plane of impedance, Z′ vs. Z′′. Bottom: theexperimental Z′ vs. Z′′ plot at 300 K shown as circles. A fit tothe observed data according to the circuit model shown aboveis given as solid line. The three different contributions to thetotal relaxation are marked. The inset shows the temperaturedependence of R0 and L0 (in the circuit) extracted from the fit.A clear divergence in slope is seen in both R0 and L0 around200 K.

the sample-electrode interface, respectively. Initially allcapacitances are treated as temperature independent andthe resistors obey an Arrhenius-type activated behavior [9]Rn = an exp(20meV/kBT). Assuming R3 � R2 � R1,the pre-exponential constants a1, a2 and a3 are taken as1, 1000, and 10000, respectively. The capacitance valuesused for the simulation are calculated from the experimen-tally observed plateaus of ε1 vs. T plots, which yieldedC1 = 1.76 pF (εlow = 20), C2 = 88.4 pF (εmed = 100), andC3 = 1.326 nF (εmax = 15000). The simulated plots forthe real and imaginary parts of the permittivity are shownin fig. 2(a), (b). The real part, ε1, has three plateaus inaccordance with the three types of relaxations: the bulk,grain boundaries and the third from the sample-electrodeinterface [9,11]. If the temperature is lowered, the intrin-sic contribution dominates and at sufficiently low T , theextrinsic contributions ceases (fig. 2(c)). The imaginarypart ε2 has two peaks, which is similar to the experimentaldata (fig. 1(b) and (d)). These features are also reflectedin the simulated frequency-dependent dielectric constant,fig. 2(c) and (d).

Impedance spectroscopy is a very powerful tool to studythe multiple relaxations observed in dielectric materials,where the real (Z ′) vs. imaginary (Z ′′) part of the compleximpedance for different frequencies are plotted together. Asubsequent analysis using the RC element model can de-convolute different types of dielectric relaxations present

Fig. 4: (Colour on-line) The complex plane of Z′ vs. Z′′ at250 K. The inset (a) shows an enlarged view of the regionwhere the bulk contribution (red line) dominates. The dataand fit at 150 K is shown in the inset (b).

in the material [13]. In the ideal case of a single relax-ation, the response is a semi-circle [14]. In real systems,the deviation from the ideal behaviour occurs and in orderto account for this non-Debye–type behavior, the ideal ca-pacitor is replaced with a constant phase element (CPE).The complex impedance of a CPE is defined as [9,15]

Z∗CPE =

1CCPE(iω)n

, (5)

where CCPE is the CPE-specific capacitance. ω is the an-gular frequency and n is a critical exponent with typicalvalues between 0.6 and 1 (for ideal capacitor n = 1). SuchCPE capacitance can be converted into real capacitanceusing a standard procedure [16]. Such a circuit model con-structed for the present work is illustrated in the top panelof fig. 3. The impedance of the sample is measured at dif-ferent temperatures and Z ′′ vs. Z ′ are plotted. The roomtemperature impedance spectra in the complex plane isshown in fig. 3 as black open circles. The data are fittedusing three R-CPE units in series corresponding to thebulk, the grain boundary and the sample-electrode con-tributions. The inductance L0 of the external leads (alsorelated to the magnetic phase) and the resistance, R0, ofthe leads and electrodes are also taken into account in thecircuit model. The curve fit to the experimental data at300K using this equivalent circuit is shown in fig. 3 as asolid line. The fit parameters are R1 = 6467±23%ohm,R2 = 23625±9%ohm, R3 = 200860±1.9%ohm, C1 =5.33 nF±2.9%, C2 = 1.62 nF±2.6%, C3 = 2.39 pF±2.1%,n1 = 0.79±1.1%, n2 = 0.98±2.4% and n3 = 0.95±1.8%.The high-frequency response originates normally from thebulk, the intermediate frequency from the grain bound-aries and the low-frequency impedance contribution fromthe sample-electrode interface [12]. Impedance data ofmagnetic materials are usually modeled by including aninductive element in the equivalent circuit wherein thepermeability and magnetic response can be roughly un-derstood from the inductance [17,18]. A combination of

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Hariharan Nhalil et al.

Fig. 5: (Colour on-line) The estimated values of R, C and nby separating the intrinsic dielectric relaxation after the anal-ysis using the resistor-capacitor models. A broad anomaly ispresent centered around 200 K (the error bars were comparableto the size of the data points).

R and L (parallel or series) is generally used for modelingthe magnetic phase [17,19]. Using the circuit shown infig. 3 we tried to extract the temperature dependence ofinductance L0 along with R0 and this is shown in the insetof the bottom panel of fig. 3. A clear anomaly is observedaround 200K, which is close to Griffith’s temperature ob-served in this material [8]. Irvine et al., for example, haveobserved that the inductance value peaks at the magneticanomaly transitions in (NiZn)Fe2O4 [17].

The intrinsic bulk contribution is analyzed using a sin-gle R-CPE unit by considering the intermediate- and low-frequency region as extrinsic. The data is fitted faithfullyup to 110K. Figure 4 shows the fit at 250K (inset (a))and 150K (inset (b)). At low temperature the bulk contri-bution dominates and the extrinsic contribution decreases.By a progressive procedure of fitting, the intrinsic responseto the dielectric relaxation was extracted. The resistance(R) and the capacitance (C) estimated from the fit areplotted against temperature, in fig. 5. A slope changeis visible in the temperature region around 200K whichcoincides with the experimentally observed Griffith’s tem-perature in this compound [8]. The spin-lattice couplingalso shows a marked change at this point. Although onecannot claim this to be magneto-electric coupling, it cer-tainly indicate a connection between the various degreesof freedom. For ideal Debye relaxation of non-interactingdipoles, the plot of ε1(T ) vs. ε2(T ) follows the Cole-Colebehaviour displaying a perfect semi-circular arc [20]. Likein many complex oxides and those with defects, deviationsfrom the ideal Cole-Cole plot are observed here; these maybe accounted for by using the modified Debye equation,

ε∗ = ε1 + iε2 = ε∞ +(ε0 − ε∞)

[1 + (iωτ)(1−α)], (6)

where ε0 and ε∞ are static and high-frequency dielec-tric constants, respectively, ω is the angular frequency,τ is the mean relaxation time and α is a parameterwhich represents the distribution of relaxation times (forideal Debye relaxation, α is zero). Equation (6) can be

Fig. 6: (Colour on-line) Frequency dependence of the realpart of the dielectric constant, ε1(T ), at different temperaturesabove T ∗ ≈ 200 K. The inset (a) shows ε1(T ) below 250 K. Thesolid lines are fits using the modified Debye equation, eq. (7).The behaviour of the dielectric function is clearly different fortemperatures above and below T ∗. The inset (b) shows thevariation of α with temperature across T ∗.

separated into the real and imaginary parts of the dielec-tric permittivity as

ε1 = ε∞ + (Δε/2)[1 − sinh(βz)

cosh(βz) + cos(βπ/2)

](7)

and

ε2 =(Δε/2) sin(βπ/2)

cosh(βz) + cos(βπ/2), (8)

where Δε = (ε0 − ε∞), z = ln(ωτ) and β = (1 − α). Thefrequency dependence of ε1(T ) for Tb2NiMnO6 at few se-lect temperatures is depicted in fig. 6 along with the curvefits using the modified Debye equation (eq. (7)). Sincethe bulk contribution will reflect in the high-frequency re-gion, fitting was performed in the high-frequency region.However, the modified Debye model was inadequate to de-scribe the behaviour of ε1 below 120K (figure not shown)and attempts to fit eq. (7) were not successful. The valueextracted for α from the fit falls between 0.18 and 0.27,which is higher than the value reported for La2NiMnO6 [7].The inset of fig. 6(b) shows the temperature variation ofα values extracted from the fit. An anomaly in the be-havior is observed in the vicinity of ∼ 200K. We de-note the temperature at which the deviation occurs as T ∗,which is close to the temperature where an anomaly in theFWHM of the Raman modes was observed in Tb2NiMnO6

(180K) [8]. This coincidence gives credence to the corre-lation between dielectric, Raman and magnetic anomaliesin this material.

The frequency dependence of ac conductivity σ ofTb2NiMnO6 is shown in fig. 7(a) and (b). This corre-sponds to two types of conduction behaviour at T < T ∗

and T > T ∗. Below 200K, conductivity decreases with theincrease in temperature reflecting an insulating behaviour.A change of slope in the ac conductivity occurs at the tem-perature at which the dielectric relaxation deviates from

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Glassy dielectric response in Tb2NiMnO6 double perovskite etc.

Fig. 7: (Colour on-line) (a) Frequency dependence of ac con-ductivity below T ∗ ∼ 200 K. (b) Frequency dependence of acconductivity at temperatures above T ∗. (c) Plot of log(fε′1) vs.log(f) for selected fixed temperatures. The inset presents thetemperature evolution of dc conductivity which shows a signif-icant change in slope close to 200 K. (d) Electrical resistance ofTb2NiMnO6 which conforms to an Arrhenius-type behaviour.

Debye-like behaviour. According to the universal dielec-tric response (UDR) [15], the relation between conductiv-ity σ′(f) and dielectric constant ε1 is given by

σ′(f) = σdc + σ0fs (9)

andε1 = tan(sπ/2)σ0f

s−1/ε0, (10)

where f is the experimental frequency, σ0 and s aretemperature-dependent constants. A stepwise increase inthe background of the loss factor reveals the contributionfrom dc conductivity (fig. 1(b) and (d)). Equation (10)can be written as

fε1 = A(T )fs, (11)

where A(T ) = tan( sπ2 )(σ0

ε0), a plot of log(fε1) vs. log(f)

results in a straight line with slope equal to s. This is pre-sented in fig. 7(c) where a clear straight line is observedat low temperatures. However, it deviates from linear-ity as temperature increases above T ∗ ≈ 200K, whencharge carriers contribute to polarization. In order tofind the dc contribution, the low-frequency ac conductivitywas extrapolated to zero frequency. The dc conductivityof Tb2NiMnO6 relates to semiconducting-like behaviourabove 200K but deviates from thermally activated be-haviour. The variation of the dc conductivity, σDC , withtemperature is shown in the inset of fig. 7(c) where thechange in slope is clearly visible close to 200K. Again,the characteristic temperature T ∗ ∼ 200K compares well

with the reported anomaly in the FWHM of Ramanmodes [8]. Figure 7(d) shows the electrical resistivity ofTb2NiMnO6 plotted in log scale against 1000/T . The re-sistivity data fits reasonably well to the Arrhenius law upto ∼ 200K. This supports the dc conductivity data de-rived from the ac conductivity and yields the activationenergy, Ea = 0.192(1) eV.

In our previous work concerning the magnetic propertiesof Tb2NiMnO6, an inhomogeneous magnetic state resem-bling the Griffiths phase was observed along with clearindications of spin-lattice coupling through Raman stud-ies [8]. We were able to extract a characteristic temper-ature T ∗ ≈ 200K where magnetic and Raman anomaliescoincided. The present dielectric response study validatedby the dielectric relaxation and the ensuing impedanceand conductivity behavior reflect the same characteris-tic temperature T ∗ in this compound. Diffuse dielectricbehaviour has been observed in nanoparticle samples ofthe double-perovskite La2NiMnO6 where disorder leadsto local polar nanoregions [21] and also in La2CoMnO6

ceramics [22] where the charge order of Co2+ and Mn4+

was the origin of relaxation. It could be assumed, in thepresent case, that clusters that posses local polarization(polar nanoregions) are formed around Ni2+ or Mn4+ dueto the cationic antisite disorder and bring about dielectricrelaxation through their mutual interaction. This is alsosupported by the fact that the frequency dependence ofthe peak temperature in dielectric data is not explainedby thermally activated behaviour. Similar to the magneticGriffiths phase where the non-analyticity of magnetizationextends above the transition temperature (in the presentcase, Tc ≈ 110K), the dielectric relaxation also identifiesthe characteristic temperature above Tc. In this context,it would be intersting to perform experimental investiga-tions using local probes like electron paramagnetic reso-nance which can give clear signatures about the Griffithsphase [23]. Combining this with the fact that the Griffithsphase can indeed make itself manifested in disordered di-electrics [24] makes this double perovskite an interestingcandidate to carry out microscopic measurements, for ex-ample using neutrons, to understand the magnetic and di-electric properties in more detail. Impedance spectroscopyand modified Debye model are used to analyse the dielec-tric response and identified a characteristic temperaturethat separates two regions of dielectric relaxation. Thisallows us to postulate a close correlation among magnetic,electronic and dielectric properties in this compound.

∗ ∗ ∗SE wishes to acknowledge the Department of Science

and Technology, India for financial support. HN wishesto thank Aditya Wagh for his help and support withdielectric measurements.

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