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Thermopower studies of Pr0.67D0.33MnO3 manganite system

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2007 J. Phys. D: Appl. Phys. 40 721

(http://iopscience.iop.org/0022-3727/40/3/005)

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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 40 (2007) 721–729 doi:10.1088/0022-3727/40/3/005

Thermopower studies of Pr0.67D0.33MnO3manganite systemG Venkataiah, Y Kalyana Lakshmi and P Venugopal Reddy1

Department of Physics, Osmania University, Hyderabad – 500 007, India

E-mail: pvenugopalreddy@yahoo.com

Received 22 June 2006, in final form 14 November 2006Published 19 January 2007Online at stacks.iop.org/JPhysD/40/721

AbstractWith a view to explaining the structural and electrical transport behaviour ofsome rare earth manganites, having the general formula Pr0.67D0.33MnO3(D = Ca, Sr, Pb and Ba), a systematic investigation of the electricalresistivity, thermopower and magnetic properties has been undertaken.These materials were prepared using the citrate–gel route by sintering at900 C. All the materials were characterized by x-ray diffraction, scanningelectron microscopy, etc measurements. The x-ray data were analysed usingthe Rietveld method and the variation of various parameters involved in theprocess as explained. The average crystallite size of the materials has beenestimated using the peak broadening method, while TC and TP values weredetermined from ac magnetic susceptibility and electrical resistivitymeasurements, respectively. Finally, the magnetoresistance (MR)measurements were also carried out over a magnetic field of 1–7 T and thedata clearly exhibit the extrinsic MR in ferromagnetic metallic region.

The influence of average A-site cation radius 〈rA〉 and cation mismatchparameter σ 2 on thermoelectric power (TEP), MR, electrical and magnetictransitions has been analysed. The TEP data at low temperatures (T < TP)have been analysed by considering the magnon concepts, while the hightemperature (T > TP) data were explained by the Mott’s small polaronconduction mechanism. The effects of 〈rA〉 and σ 2 on polaron activation andhopping energies were also studied systematically.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

The phenomenon of colossal magnetoresistance (CMR)[1] observed among perovskite manganites having thecompositional formula, Ln1−XDXMnO3, (where Ln = La, Pr,Nd, Eu, Y, etc and D = Ca, Sr, Pb, Ba, etc) with x = 0.33 hasled to several interesting properties. The underlying physicsbehind these remarkable properties is not yet understood well.Although, the double exchange (DE) model [2] can explainqualitatively the simultaneous occurrence of ferromagneticand metallic behaviour below the metal–insulator transitiontemperature (TP), it cannot explain several aspects, namelyspin–lattice or charge–lattice interactions, i.e. Jahn–Teller (JT)interaction and polarons, which significantly contribute tothe several aspects of electrical transport, especially at high

1 Author to whom correspondence should be addressed.

temperatures (T > TP) [3, 4]. Therefore, it is essential toinvestigate the phenomenon of electrical transport in terms ofpolarons.

It is known that whenever divalent ions such as Ca,Sr, Pb and Ba are doped either in La-based manganites orin Nd-based ones, they behave like doped antiferromagneticsemiconductors which, at very low temperatures, acquirespontaneous magnetization and metallic conductivity if dopinglevels are sufficiently high and display a resistivity peak in thevicinity of the ferro-to-paramagnetic transition temperature(TC). In fact, the CMR manifests in these materials bysuppressing the resistivity peak under the influence of anexternal magnetic field. In contrast to this type of behaviour,surprisingly some of the basic properties of a few Pr-basedmanganites differ drastically from others. For example,Pr1−xCaxMnO3 manganite remains insulating for any dopinglevel at T = 0. However, an external magnetic field causes

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P P M O

Inte

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Figure 1. XRD pattern of Pr0.67Pb0.33MnO3, observed intensities areshown by dots () and the calculated ones using the Rietveld methodare shown by the solid line and the line at the bottom indicates thedifference between the experimental and refined patterns.

the metamagnetic transition from an antiferromagnetic state toa ferromagnetic state simultaneously with the transition frominsulating state to a highly-conductive state [5]. Thus thistype of field-induced transitions can be considered a specialtype and obviously the CMR phenomenon exhibited by themis also of a special type. Therefore, Pr-based manganites arethe right candidates to investigate the phenomenon of MR attemperatures well below TC under different magnetic fields.

Among various transport properties, thermopower is asimple and sensitive one for analysing the charge carrierdynamics [6]. Further, as thermopower is very sensitive tolocal moments of charge carriers and since one can predictthe nature of charge carriers based on the degree of JTinteraction [7], studies on this phenomenon have attracted theattention of several investigators [7–13]. In fact, a systematicanalysis of thermopower data also enables one to understandthe conduction mechanism of CMR materials. In view of this,thermopower studies of CMR materials are very important andalso interesting. Therefore, a systematic investigation of MRand thermopower of Pr0.67D0.33MnO3(where D = Ca, Sr, Pband Ba) manganites has been undertaken and the results ofsuch an investigation are presented here.

2. Experimental details

Polycrystalline manganites, with compositional formulaPr0.67D0.33MnO3 (where D = Ca, Sr, Pb and Ba), wereprepared by the sol–gel route, taking corresponding metalnitrates as the starting materials in a stoichiometric ratio.Later, these nitrate solutions were converted into citrates andthe PH was adjusted between 6.5 and 7. After getting a solon slow evaporation, a gelating reagent ethylene glycol wasadded and heated on a hot plate between 160 and 180 Cto get a gel. Finally, the resulting powder was pressed intocircular pellets, which were sintered in air at 900 C for4 h. All the materials were characterized by x-ray diffraction(XRD) (Philips Xpert diffractometer) by analysing the datausing the DBWS Rietveld refinement method [14] and theaverage crystallite sizes were estimated by the peak broadeningtechnique. The average grain sizes of the materials werealso estimated by the scanning electron microscope (SEM)

technique (Philips FEIXL30 ESEM). ac susceptibility (χ ′)measurements were carried out over a temperature range80–300 K. The electrical resistivity and MR measurementswere performed using a JANI’S ‘supervaritemp’ cryostat inapplied magnetic fields of 1–7 T, over the temperature range70–300 K using the four-point probe method. Finally, adynamic two probe differential method was employed for themeasurement of the thermopower [15]. The samples wereattached with silver paint between two copper electrodes withadjustable temperature gradient and were monitored usingcopper–constantan thermocouples. The assembly was placedin a closed liquid nitrogen cryostat; nitrogen atmosphere isused as an exchange mainly to maintain uniform temperatureand to avoid condensation of moisture. The measurementswere carried out in the heating mode. The measuredthermopower data were corrected by subtracting thermopowervalues of copper, so as to obtain absolute thermopower valuesof samples.

3. Results and discussions

3.1. X-ray diffraction studies

The XRD data of all the samples were recorded at roomtemperature and analysed using the Rietveld method. A typicalplot of XRD pattern of Pr0.67Pb0.33MnO3 sample along withits refined one and the difference between these two patternsare shown in figure 1. The refinement is done, assuming anorthorhombic structure with Pbnm space group and based onthe refined patterns, it has been concluded that all the materialsof the present investigation are having a single phase, withoutany detectable impurity. Further, using the refined patterns, theunit cell and other fitting parameters of all the samples werecomputed and are given in table 1. It is clear from the tablethat all the three unit cell parameters are found to increase asA-site cation varies from Ca to Ba and the observed behaviourmight be due to the fact that substitution of a larger ion expandsthe unit cell in all the three directions enhancing the unit cellparameters within the same space group.

The average crystallite size values were evaluated usingthe XRD data and while doing so, the instrumental andmicro-strain broadening were taken into consideration. Theinfluence of synthesis and processing conditions is reflectedin the structural strain of the samples. The broadening ofreflections due to micro strains was considered to have anangular dependence of the form

βStrain = ε tan θ, (1)

where βStrain is the peak shift due to strain, ε (= d/d) isthe coefficient related to strain and θ is Bragg angle. Themicro strains include the effects of structural defects such asdislocations, stacking faults, twin boundaries and intergrowths.The dependence of size effect can be given by the Schererformula:

βSize = Kλ/t cos θ, (2)

where K is the grain shape factor (for a spherical grainK = 0.89), λ is wavelength of Cu Kα radiation (λ = 1.5406 Å)and t is thickness of the crystallite. In the present study,broadening of all the prominent peaks has been taken into

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Table 1. Crystallographic data of Pr-based manganites.

Sample Pr0.67Ca0.33MnO3 Pr0.67Sr0.33MnO3 Pr0.67Pb0.33MnO3 Pr0.67Ba0.33MnO3

Sample code PCMO PSMO PPMO PBMOSpace group Pbnm Pbnm Pbnm PbnmProfile fitting function Pseudo-Voigt Pseudo-Voigt Pseudo-Voigt Pseudo-Voigta (Å) 5.4274 5.4500 5.4741 5.4995b (Å) 5.4401 5.4794 5.5087 5.5222c (Å) 7.6652 7.7054 7.7406 7.7772Volume (Å3) 226.32 230.10 233.42 236.19Pr/(Ca,Sr,Pb,Ba) x 0.9974 0.9962 0.9952 0.9985(0.67/0.33) y 0.0309 0.0163 0.0125 0.0026O (1) x 0.0753 0.0810 0.0582 0.0483

y 0.4800 0.4742 0.4964 0.4262O (2) x 0.7243 0.7213 0.7134 0.7349

y 0.2769 0.2859 0.2894 0.2853z −0.0175 −0.0174 −0.0291 −0.0246

RP (%) 23.63 22.98 21.14 22.81RWP (%) 32.59 31.16 30.75 31.54REXP (%) 29.70 28.13 27.92 28.69Goodness of fit 1.10 1.11 1.10 1.10No of data points 6000 6000 6000 6000

Note: The atoms are located at the following Wyckoff positions Pr (Ca/Sr/Pb/Ba) 4(c): (x, y, 1/4); Mn 4(b):(1/2, 0, 0); O (1) 4(c): (x, y, 1/4) and O (2) 8(d): (x, y, z).

Table 2. Experimental data of Pr-based CMR manganites.

〈D〉 (nm)Samplecode XRD SEM

〈rA〉(Å)

σ 2

(Å2)TC

(K)TP

(K)T = TC − TP

(K)Max(MR%)

PCMO 110 135 1.179 0.22 × 10−6 149 — — 99PSMO 100 125 1.222 0.37 × 10−2 293 206 87 51PPMO 140 165 1.235 0.64 × 10−2 226 168 58 64PBMO 115 120 1.275 1.87 × 10−2 175 <70 <105 86

Figure 2. SEM photographs of (a) PCMO, (b) PSMO, (c) PPMO and (d) PBMO samples. The bar shown indicates 1µm length scale.

consideration. The instrumental broadening effect has beeneliminated by subtracting the value of full width at half maxima(βo) corresponding to a standard sample (SiO2) from βSize atrespective Bragg peaks. The complete expression for the fullwidth at half maxima is a linear combination of strain and sizebroadenings and is given by

βSize,Strain = ε tan θ + Kλ/t cos θ. (3)

A plot between βSize,Strain cos θ and sin θ gives a straight lineand from the value of intercept on the y-axis, the averagecrystal size has been calculated and it has been found thatthe average crystalline size (〈D〉) values are in the range 110–165 nm and are given in table 2. In order to verify the accuracyof the results, the SEM measurements were also undertakenand SEM images of the samples of present investigation areshown in figure 2. It is interesting to note from the table that the

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Figure 3. Variation of ac susceptibility with temperature of Pr-based manganites.

average grain size values obtained from the SEM micrographsare found to be in close agreement with the values computedfrom the XRD measurements.

3.2. Magnetic and electrical behaviour

In order to determine the TC values, ac susceptibilitymeasurements were carried out and the variation ofsusceptibility (χ ′) with temperature is shown in figure 3.TC values were obtained from the inflection point ofdχ ′/dT versus T curves and are given in table 2. Fromthe electrical resistivity measurements, the metal–insulatortransition temperatures (TP) were also obtained and are givenin table 2. It is clear from the table that magnetic transitiontemperatures (TC), after an initial increase are found todecrease with increasing A-site ionic radius 〈rA〉 and theobserved behaviour is in contrast to the generally observedbehaviour of continuous increase of TC with increasing 〈rA〉.

Now the observed anomalous variation of TC with varyingA-site ionic radii may be explained qualitatively using a modelbased on cation mismatch. It was reported that mismatchof cation sizes on A-site influences both the electrical andmagnetic properties of manganites [16, 17]. As a matter offact, the effect of size mismatch or disorder on TP and TC for afixed average 〈rA〉 with optimal hole doping was investigatedby Rodriguez-Martinez and Attfield [16] and they reportedthat with increasing size variance, Curie temperature fallsmonotonically with a corresponding fall in the CMR effect.The fall of TC in the case of manganites has been attributedto the large size mismatch. Further, size disorder induceslattice strain causing the random displacement of oxygen ions,thereby resulting in distortion of MnO6 octahedra and hencelocalization of electrons [18]. As a matter of fact, a largemismatch in the size of A-site cations results in a randomarrangement of Mn3+ and Mn4+ ions, thereby reducing TC.

The phenomena of size mismatch at A-site is quantifiedby a term called the size variance parameter (σ 2) [16] and is

given by the formula

σ 2 = yir2i − 〈rA〉2, (4)

where yi (yi = 1) is fractional occupancy and ri correspondto the radii of the various A-site cations. The values ofaverage A-site radii 〈rA〉 and variance parameter (σ 2) havebeen calculated for all the four samples from the standard ionicradii [19] of ninefold coordination and are given in table 2.

It is clear from the results that in the case of PCMOsample, due to a negligibly small size variance parameter(σ 2 ≈ 0.22 × 10−6 Å2) and also due to an almost equal sizeof Pr3+ (1.179 Å) and Ca2+ (1.18Å), the mismatch effect onboth the electrical as well as magnetic properties is found tobe absent. In view of this, perhaps the PCMO sample mightbe exhibiting charge ordered (CO) state [10]. Thus, due tothe presence of CO state in the sample, it might be having alarge value of resistivity values (of the order of M cm) at lowtemperatures. In fact, one may notice the absence of metallicstate in the case of PCMO sample in figure 4 and the observedbehaviour is in conformity with the reported ones [11,15,20].

Further from the magnetic susceptibility measurements ofPCMO one can understand that below 150 K a ferromagneticphase is present, while the electrical resistivity plot shows asimple insulating behaviour. Thus the behaviour exhibited bythis sample is anomalous when compared with the normallyobserved ferromagnetic metallic (FMM) nature below TP orTC in case of several other manganites. The reason for thisbehaviour may be explained based on the phase separationscenario as follows. In general, PCMO samples exhibitCO phase below 150 K and as the temperature is decreasedbelow 150 K, the CO phase might undergo a transition fromthe paramagnetic state to an antiferromagnetic state with aknown pseudo-charge-exchange ordering [10]. Therefore,one may assume that the PCMO sample of the presentinvestigation at temperatures below 150 K might be having ashort range ferromagnetic phase within the antiferromagneticmatrix exhibiting insulating behaviour.

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Figure 4. Resistivity versus temperature of (a) PCMO, (b) PSMO, (c) PPMO and (d) PBMO samples at applied magnetic fields of 0, 1, 3and 7 T.

In the case of PSMO sample, although there is a differencein the values of cationic radii of Pr3+ (1.179 Å) and Sr2+

(1.31 Å) and also the high value of σ 2 (≈ 0.37 × 10−2 Å2), themismatch effect on both the electrical and magnetic transitionsis expected; it has not been observed and the observedbehaviour may be explained as outlined below. According toRodriguez-Martinez and Attfield [16], in the case of manganitematerials, when 〈rA〉 values are higher than 1.22 Å, cationmismatch (σ 2) starts showing its influence, thereby affectingthe magnetic as well as electrical properties including theirtransition temperatures. In the present investigation, as theA-site average ionic radius 〈rA〉 of PSMO sample is 1.222 Å,even though the value of σ 2 is high, its influence is absent.In contrast to the behaviour exhibited by PCMO and PSMOsamples, PPMO and PBMO samples are found to be affectedby the mismatch effect due to the large difference in their cationradii (Pr3+ = 1.179 Å; Pb+2 = 1.35 Å and Ba+2 = 1.47 Å) andhigher 〈rA〉 values of 1.235 Å and 1.275 Å, respectively.

Further, it can also be seen from the table that thereis a large difference in the values of TC and TP and, as amatter of fact, a similar difference between these two transitiontemperatures was reported earlier [21–23]. The observeddifference between the two transition temperatures could beattributed to the surface strain induced grain boundary effectsas well as the phase segregation. It is pointed out thatthe presence of antiferromagnetic insulating regions near thegrain boundaries, although it may not modify the values ofTC (governed by the ferromagnetic core), may influence theelectrical transition temperature (TP) resulting in shifting theirvalues to lower temperatures [21]. Further, the large differencebetween TC and TP may have a strong correlation with the MRat low temperatures.

A systematic investigation of Nd-based manganites wasundertaken in this laboratory earlier [23]. Although, thestructural and magnetic properties of Pr0.67Ca0.33MnO3 andNd0.67Ca0.33MnO3 are found to be similar, there is a differencein their electronic properties. For example, while a metallicphase is exhibited by Nd0.67Ca0.33MnO3, no such behaviouris exhibited by Pr0.67Ca0.33MnO3. Secondly, although cationmismatch is present in the case of Nd-based materials, onlya negligibly small cation mismatch at A-site is present.Therefore, one may conclude that both the systems are havingdifferent types of properties. Finally, in the case of Pr-basedmanganites extrinsic MR is found to dominate, while in Nd-based manganites, both intrinsic as well as extrinsic MR arefound to coexist.

3.3. Magnetoresistance

Resistance measurements were carried out in the magneticfields of 1, 3 and 7 T, in the temperature range 70–300 K and theplots of resistivity versus temperature are shown in figure 4.It can be seen from the figures that the resistivity at a giventemperature is found to decrease with increasing field andthat TP values are found to move towards high temperatureside. The observed behaviour may be attributed to the fact thatthe applied magnetic field induces delocalization of chargecarriers, which in turn suppresses the resistivity causing localordering of the magnetic spins. Due to this ordering, the FMMstate may suppress the paramagnetic insulating (PMI) regime,thereby resulting in polarization of conduction electrons (e1

g)

inside the magnetic domains which are easily transferredbetween the pairs of Mn3+ and Mn4+ via oxygen. Due to thesereasons, the peak temperature (TP ) shifts towards the hightemperature side with the application of magnetic field [23].

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PCMO PSMO PPMO PBMO

MR

%

T(K)

(a)

PCMO PSMO PPMO PBMO

MR

%

T(K)

(b)

Figure 5. Variation of per cent of MR with temperature of Pr-basedmanganites, (a) in the presence of 1 T, (b) in the presence of 7 T.

The percentage of MR is defined as

MR% = ρ(0) − ρ(H)

ρ(0)× 100, (5)

where ρ(0) is the resistivity without magnetic field and ρ(H) isthe resistivity in a field. The MR values for 7 T field of all thesamples were calculated and are given in table 2. In the caseof PCMO, PSMO and PBMO the maximum MR values arefound to be around 100 K, while in the case of PPMO sampleit is found to be in the vicinity of TP(≈ 165 K). It is interestingto note from the table that the samples with low TC are foundto exhibit large MR and vice versa, which is in agreement withthe universal MR–TC relationship [24].

The variation of MR with temperature in the presence ofmagnetic fields 1 and 7 T is shown in figure 5. It is clear fromthe figures that the samples of the present investigation arefound to exhibit large magnetoresistance at low magnetic fields(LFMR). This LFMR appears to be high in the low temperatureregime and decreases with increasing temperature. In fact asimilar behaviour is observed even in the 7 T field and may beexplained on the basis of a qualitative model.

The phenomena of MR have two distinct contributions[21]. The first one is the intrinsic MR, which arises dueto the suppression of spin fluctuations, when the spins arealigned in the sample on the application of magnetic field.This MR has highest value near the ferromagnetic transitiontemperature and decreases with decreasing temperature andis generally observed among single-crystalline bulk as well asthin films. In the polycrystalline samples, there is an additionalMR, which is extrinsic in nature, arising due to inter-grainspin polarized tunnelling (ISPT), across the grain boundariespresent in the sample. This MR contribution usually increasesas the temperature decreases and is usually found in nano-crystalline materials. Rivas et al [25] pointed out that the sol–gel prepared samples sintered at low temperatures (900 C)with particle size 150 nm show more extrinsic nature of MR.Until recently, it was believed that the former mechanism is

responsible for the MR at high fields and the latter one atlow fields. But recent experiments have shown that high fieldresponse is also due to the existence of the grain boundariesand the nature of grain boundary is a key ingredient inthe mechanism of electrical transport, as it constitutes thebarrier through which carriers cross or tunnel. In the presentinvestigation, all the samples were sintered at 900 C for 4 hand the particle sizes of all the samples, except in the case ofPPMO, are found to be ≈150 nm. It is also clear from figure 5that all the samples, except PPMO are found to exhibit extrinsicMR. However, PPMO, is found to exhibit extrinsic MR only ina magnetic field of 7 T. In the case of PPMO as the particle sizeis found to be 165 nm, it might have exhibited maximum MRin the vicinity of TP. It is also clear from figure 5 that PPMOshows a large MR well below TP along with maximum MR atTP. This might be due to the simultaneous presence of bothintrinsic as well as extrinsic MR in the field of 7 T. Further, it isclear from figure 4 that the resistivity values of the samples ofthe present investigation are approximately 1000 times largerthan the single crystals values [26, 27]. The higher resistivityobtained in the samples of the present investigation mighthave originated from inter-grain phases and their morphology,elastic and magnetoelastic strain, etc. In view of this, one mayconclude that the samples of the present investigation mightexhibit to a large extent an extrinsic nature of MR arising dueto ISPT.

It is interesting to note from figure 5 that MR behaviour ofPCMO is different from other samples. Although significantMR has been observed at 1 and 3 T fields, surprisingly alarge stable MR of 99% has been observed only at 7 T overa wide temperature range (80–150 K) and the reason for thisbehaviour might be attributed to the melting of charge orderingphenomenon. At low fields, both the charge and spin orderedstates might not have been disturbed completely, while at highmagnetic fields of the order of 7 T, both the states might havebeen melted completely resulting in the exhibition of a verylarge MR. Although, the CO state melted in the presence of7 T field, metal–insulator transition temperature could not beobserved probably due to insufficient magnetic fields.

3.4. Thermoelectric power

Measurement of the thermo emf induced by a temperaturegradient across a sample provides complementary informationabout the resistivity [28]. The Seebeck coefficient (S) isdefined as V/T , the thermoelectric voltage per degreeof temperature difference. Thermoelectric power (TEP)measurements were carried out over a temperature range 80–300 K and Seebeck coefficient (S) values have been computedat different temperatures. The variation of S with temperatureof all the samples is shown in figure 6 and it is interesting tonote that two samples, namely PCMO and PPMO, are foundto exhibit both negative and positive S values, while the othertwo, PSMO and PBMO, exhibit only positive S, throughout thetemperature range of investigation. The observed behaviourmay be attributed to the degree of JT distortion. In the absenceof static JT distortion, the charge carriers are predicted to beelectrons, while under the influence of sufficiently large staticJT distortion, the charge carriers behave as holes [29].

It can also be seen from figure 6 that as the temperaturedecreases from 300 to 80 K, S decreases slowly attaining a

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Figure 6. Variation of S with T of Pr-based manganites.

Table 3. The best fit parameters, obtained from the thermopower data of Pr-based manganites.

Sample S0 S3/2 S4 EP ES WH = EP − ES α′

code (µV K−1) (µV K−5/2) (µV K−5) (meV) (meV) (meV)

PCMO 2.5676 −0.0091 1.2601 × 10−8 160.28 9.19 151.09 −0.3727PSMO −1.5099 0.0021 −1.0829 × 10−9 83.44 2.61 80.83 −0.0876PPMO −1.7348 0.0032 −4.8785 × 10−8 143.75 8.84 134.91 −0.3535PBMO −8.6993 0.0196 −3.6523 × 10−8 166.78 13.34 153.44 −0.5025

minimum value in the vicinity of TP. However, on furtherdecrease of temperature, the S value is found to increasesharply exhibiting a broadened peak except in the case ofPCMO. The broad peak is found to be in the temperature region150–200 K and, as a matter of fact, similar broad peaks werereported earlier [13, 30–33]. The observed broad peak may beexplained on the basis of the spin-wave theory. According tothis theory, in ferromagnets and antiferromagnets, electrons arescattered by spin waves, giving rise to magnons. In a mannersimilar to the scattering of phonons resulting in phonon drageffects, the electron magnon interaction produces a magnondrag effect. As the magnon drag effect is approximatelyproportional to the magnon specific heat, one may expectthe variation of S with temperature as T 3/2 for ferromagneticmaterials [33]. In view of these arguments, one may concludethat the observed broad peaks may be attributed to the magnondrag effect.

3.4.1. Low temperature (T < TP) behaviour. Similarly tothe electrical conduction, several factors, namely impurity,complicated band structure, electron–electron, magnonscattering, etc, affect the TEP data at low temperatures (T <

TP). In view of these facts, the ferromagnetic metallic part ofthermopower data was fitted to an equation:

S = S0 + S3/2T3/2 + S4T

4, (6)

where S0 is a constant that accounts for the low temperatureTEP data. The S3/2 term arises due to electron magnon

scattering contribution and the origin of the S4 term, whichis dominant in the high temperature region especially near thetransition temperature, might be due to spin wave fluctuationin the FM phase [13, 33, 34].

The best fit parameters obtained from equation (6) aregiven in table 3 and a typical plot is shown in figure 7. Fromthe table it is clear that S3/2 values are found to increase whileS0 is decreasing with increasing 〈rA〉. The last parameterS4 is not varying systematically. In fact, S3/2 values of thepresent investigation are comparable with those estimatedfrom specific heat studies (0.003 µV K−5/2) [13]. Further,a continuous increase in S3/2T

3/2 values with increasing〈rA〉 clearly shows a continuous increase in ferromagneticmagnon coupling strength in these materials. Similarly,S0 represents the temperature independent component ofthermopower.

3.4.2. High temperature (T > TP) behaviour. Above themetal–insulator transition temperature (TP), the variation ofthermopower with temperature follows the adiabatic smallpolaron hopping theory [35] and accordingly S is given by

S = kB/e[ES/kBT + α′], (7)

where ES is the activation energy obtained from TEP data whileα′ is a sample dependent constant. The value of α′kBT givesthe kinetic energy of the charge carriers and the magnitudeof α′ can be used to ascertain the type of polarons present

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G Venkataiah et al

50 100 150 200 250 300

-1.2

0.0

1.2

2.4

3.6S

(µV

/K)

T(K)

Figure 7. Variation of thermopower S (µV K−1) with temperature T(K) of PPMO. The solid line gives the best fit to the equationS = S0 + S3/2T

3/2 + S4T4.

0.004 0.006 0.008 0.010 0.012

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

S(µ

V/K

)

T-1(K-1)

Figure 8. A typical plot of S (µV K−1) versus T −1 (K−1) of PSMO.The solid line gives the best fit to the equationS = KB/e[ES/KBT + α′].

in the material. For example, if α′ < 1, the charge carriersresponsible for thermopower might be small polarons, whileif α′ > 1, they might be large polarons [36, 37]. The hightemperature TEP data are found to fit well with equation (5)and from fitting parameters, the ES and α′ were obtainedand are given in table 3. A typical plot of S versus 1/T

is shown in figure 8. Further, the polaron hopping energy,defined by the equation WH = EP − ES, has been calculatedfor all the samples and are also included in table 3. HereEP is the activation energy obtained from the resistivity data(not discussed in this paper). The values of EP, ES and WH

are in close agreement with the reported ones [36, 37]. Thedifference in activation energies obtained from the resistivityand thermopower data reflects that the charge transport occursdue to the hopping of carriers rather than semi-conductinglike the activated conduction. Further, it is also clear fromthe table that the calculated values of α′ are less than 1 andthe result strongly supports the validity of using the smallpolaron hopping mechanism to explain the electrical resistivityas well as the thermopower data of these materials in the hightemperature regime.

4. Conclusions

It has been concluded that the anomalous variation of both theelectrical and magnetic transition temperatures with increasingA-site cation radius may be attributed to the cation mismatcheffect. Secondly, as Pr0.67Ca0.33MnO3 is found to exhibitMR of 99%, one may exploit the material for some deviceapplications. The broad peak in TEP data of some of thesamples of the present investigation may be attributed to themagnon drag effect and is analogous to the phonon drageffect. Finally, it has also been concluded that the variationof thermopower at low temperatures may be due to spin wavefluctuations while that at high temperatures (T > TP) may bedue to small polaron hopping mechanism.

Acknowledgments

The authors are grateful to the DRDO, Government ofIndia, for supporting the present research work through theresearch project no ERIP / ER / 0103326 / M / 01. Theauthors also thank Dr V Prasad of the Indian Institute ofScience, Bangalore, for providing facilities to undertakemagnetoresistance measurements.

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