Thermopower studies of rare earth doped lanthanumbarium manganites

G. Lalitha Reddy a,b, Y. Kalyana Lakshmi a, N. Pavan kumar a, S. Manjunath Rao c,P. Venugopal Reddy a,n

a Department of Physics, University College of Science, Osmania University, Hyderabad 500007, Indiab Department of Physics, Telangana University (South Campus), Jangampally, Indiac Central Instruments Laboratory, University of Hyderabad, Hyderabad 500046, India

a r t i c l e i n f o

Article history:Received 20 December 2013Received in revised form23 February 2014Available online 13 March 2014

Keywords:Magnetic materialElectrical propertyMagnetic propertyThermopowerConduction mechanism

a b s t r a c t

Influence of rare earth doping on electrical, magnetic and thermopower studies of La0.34Re0.33-Ba0.33MnO3 compound was investigated. Ferro to paramagnetic transition and metal to insulatortransition temperatures decrease with decreasing ionic radius of the dopant ion. Electrical resistivityin the entire temperature range is explained by phase separation model. The magnitude of Seebeckcoefficient increases with increasing dopant ionic radius. A cross over from negative to positive sign hasalso been observed in thermopower data with decreasing A site ionic radius (⟨rA⟩). The low temperaturethermopower data has been explained using a qualitative model containing diffusion; magnon drag andphonon drag effects while the paramagnetic insulating part has been analyzed using small polaronhopping mechanism.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Electronic and magnetic properties of rare earth manganites,Ln1�xMxMnO3 (Ln¼rare earth, M¼alkaline earth), have received alot of attention in the last decade due to their possible technologicalapplications [1]. These compounds show various interesting andinter-related properties, such as the insulator–metal and the para-magnetic–ferromagnetic transition, charge and orbital ordering.These properties are governed by various phenomena such asZener-Double exchange, static and dynamic Jahn–Teller effect, chargeand spin dynamics, etc. [2]. Changes in magnetic properties, likeferromagnetic-to-paramagnetic (FM–PM) transition, or electronicproperties, like metal-to-insulator (M–I) transition can be tuned inseveral ways.

The physical properties of these materials are controlled by variousparameters such as amount of hole doping, average ionic radius of A-site cations (⟨rA⟩), etc. [3]. In fact, the maximum transition temperature(T¼360 K) was observed for a composition with x¼0.33 [4]. Disorderdue to ionic size mismatch between various ions at the same crystal-lographic site influences the transport properties. In the case of dopedmanganites, since the conductivity and magnetism are stronglycorrelated, it is important to consider the effect of A-site ionic size

mismatch on the CMR properties [5]. The size mismatch at A-sitegenerates internal chemical pressure within the lattice. Due to thisstructural disorder effect, the local oxygen displacement occurs,ensuing into bond angle fluctuations and bond length variations,leading to carrier localization in perovskite lattice. This distortion canbe controlled by the average size of A-site cation which in turnmodifies the Mn–O–Mn bond angle and Mn–O distances. The Mn–O–Mn bond angle is directly related to the hopping integral betweenMn3þ and Mn4þ degenerate states. Thus, the variations in ionic radiiat A-sites lead to competing phases at a particular temperatureinfluencing the electrical and magnetic transport properties ofperovskite manganites [6].

Among the manganites, barium doped manganites are inter-esting ones as they exhibit ferro magnetic behavior above roomtemperature and exhibit significant magnetoresistance (MR)values. In order to develop these materials as future devicematerials, there is a need to optimize its electrical, magneticproperties. In view of this, it is felt that there is need to undertakea systematic investigation of doping of various rare earth ions atlanthanum site of La0.67Ba0.33MnO3 system so as to vary the A-siteionic radius. Among various transport properties, thermopower isvery sensitive to local moments of charge carriers and since thenature of charge carriers based on degree of JT interaction [7] canbe predicted, studies on this phenomenon have attracted theattention of several investigators [8,9]. Moreover, a systematicanalysis of thermopower data also enables one to understand the

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Journal of Magnetism and Magnetic Materials

http://dx.doi.org/10.1016/j.jmmm.2014.03.0150304-8853/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author. Tel./fax: þ91 40 2700 9002.E-mail address: paduruvenugopalreddy@gmail.com (P.V. Reddy).

Journal of Magnetism and Magnetic Materials 362 (2014) 20–26

conduction mechanism of CMR materials. In view of this, theinfluence of doping various rare earth ions at lanthanum site onelectrical, magnetic properties and thermoelectric power ofLa0.67Ba0.33MnO3 have been investigated systematically and theresults of such an investigation are presented here.

2. Experimental details

Bulk polycrystalline samples with compositional formula,La0.34Re0.33Ba0.33MnO37δ (Re¼La, Pr, Nd, Sm and Gd) were pre-pared by citrate based sol-gel method. In this all the materials inthe form of nitrates were taken in stoichiometric ratio and weredissolved in an aqueous solution. Citric acid was added in 1:1 ratioand the pH was adjusted to 6.5–7.0 by adding ammonia. When thesolution was evaporated to 1/3rd of its volume, a gelating agentethylene glycol was added in 1:1.2 ratios and the gel was dried toobtain a black precursor. The precursor was burnt to obtain axerogel which was further calcined at a temperature of 1000 1C for4 h. Finally, the calcined powders after pelletizing were sintered at1300 1C for 4 h.

The samples were characterized structurally by X-ray diffrac-tion technique using Phillips Expert diffractometer with CuKα

(λ¼1.541 ̊) radiation at room temperature. In order to determinethe ratio of Mn3þ/Mn4þ concentration and oxygen content in thesamples, iodometric titrations [10] were carried out. To determinethe magnetic transition temperatures (TC), Magnetizationmeasurements were also performed using a Vibrating SampleMagnetometer (VSM) (Lake Shore model no 7460) over a tem-perature range 80–300 K, while the electrical resistivity andmagnetoresistance (MR) studies were carried out by an Oxfordsuperconducting magnetic system at different magnetic fields overa temperature range, 5–300 K using four probe method. Finally,thermoelectric power studies were also carried out by differentialmethod over a temperature range 80–300 K. The measurementswere carried out in nitrogen (exchange gas) atmosphere in heatingmode. The absolute Seebeck coefficient (S) values were obtainedby subtracting the Seebeck coefficient values of the electrode(copper) material.

3. Results and discussion

3.1. Structural aspects

The X-ray diffraction (XRD) measurements of all the sampleswere undertaken at room temperature and the XRD patterns areshown as inset in Fig. 1. No detectable impurity phase has beenobserved from the XRD patterns. The XRD data were refined usingrietveld refinement technique assuming Rhombohedral structurewith R3c space group. A typical XRD plot of LNBMO sample alongwith its Rietveld refined one, including the difference between theobserved and calculated ones is shown in Fig. 1. Various crystal-lographic parameters obtained from the refinement process aregiven in Table 1. It can be seen from the table that both the latticeparameters, a and c are decreasing continuously with decreasingionic radius of the dopant ion and the observed behavior may beattributed to the fact that a smaller ion is replacing a bigger one atA-site of ABO3 perovskite structure. Due to successive substitutionof rare earth ions at A-site by a smaller ion, the ionic radiusreduces continuously and oxygen tends to move towards thecenter, reducing Mn–O bond distances, distorting the lattice.As the A-site radius is reduced and Mn–O–Mn angle becomessmaller than 1801 causing local lattice distortions of MnO6 octahe-dra, the cell parameters of the unit cell are reduced [11,12]. In fact,due to successive rare earth substitution at A-site, in the present

investigation also Mn–O–Mn angle is found to decrease continu-ously (Table 1). In order to determine the ratio of Mn3þ/Mn4þ

concentration and oxygen content in the samples, iodometrictitrations were carried out and the values of average Mn valenceand oxygen content are included in Table 2. One can see from thetable that the first four samples of the series are having oxygendeficiency while the Gadolinium doped one is excess in oxygen.Generally, the oxygen non-stoichiometry is compensated by anequivalent change in Mn valence resulting in variation in numberof Mn4þ sites [13].

3.2. Magnetic behavior

As the manganites are known to exhibit excellent magneticproperties including a transition from ferromagnetic to paramag-netic, a systematic investigation of magnetization with varyingtemperature has been undertaken and the magnetization vs.temperature plots of all the samples are shown in Fig. 2(a). Fromthe figure one may observe that as the temperature is decreased,

20 40 60 80

Inte

nsity

(a.u

)

2 Theta (°)

LNBMO

20 30 40 50 60 70 80

(312

) (21

4)

(220

) (02

4)

(212

) (10

4)

(211

) (11

3)

(202

)

(201

) (00

3)

(110

) (10

2)

(101

)

Inte

nsity

(a.u

)

2 Theta(°)

LBMO

LPBMO

LNBMO

LSBMO

LGBMO

Fig. 1. (a) XRD patterns of all the samples indexed with h k l values. (b) Reitveldrefined XRD pattern of Neodymium doped LBMO manganite (circles indicateexperimental points while Red line indicates refined data and the green lineindicates difference). (For interpretation of the references to color in this figurecaption, the reader is referred to the web version of this paper.).

G.L. Reddy et al. / Journal of Magnetism and Magnetic Materials 362 (2014) 20–26 21

the magnetization remains almost constant and at a particulartemperature the magnetization increases steeply and then remainsconstant on further decrease of temperature. From the inflection point

of dM/dT vs. T plot, the ferro to paramagnetic transition temperatures(TC) were obtained and are given in Table 2. It can be seen from thetable that TC values are decreasing continuously from 330 K to 115 Kwith decreasing ionic radius of the dopant ion and the observedbehavior may be attributed to the following reason: On substitution ofa trivalent element with smaller ionic radii at Ln site, the averageA-site cation radius decreases thereby enhancing its size varianceparameter, which in turn affects Mn–O–Mn angle and average Mn–Odistance (Table 1). The A-site cation size disorder may result inrandom displacement of oxygen ions from their average crystal-lographic positions causing local distortion in MnO6 octahedra. Theincreasing value of s2 with decreasing ⟨rA⟩ causes localization ofeg electrons, which in turn prevents the long-range ferromagneticordering leading to decrease in TC values. In fact, the observed decreasein TC with s2 is consistent with earlier reports [14,15].

The magnetization vs. magnetic field measurements were alsoundertaken and the plots at T¼80 K up to 1.5 T are shown in Fig. 2(b) and it is clear that all the samples of present investigationexhibit a soft ferromagnetic behavior. The magnetic moments (m)of all the samples were calculated at 1.5 T and are given in Table 2.The m values after showing an initial increase are found to decreasewith decreasing ionic radius of the dopant ion. In fact, as theconcentration of the divalent dopant (Ba) is same for all thesamples, the values of spin-only moments arising due to collinearferromagnetic arrangement of Mn ions must been equal. Theobserved unusual behavior may be explained based on the oxygennon-stoichiometry. It is clear from Table 1 that, the first foursamples of present investigation are oxygen deficient while thelast one is excess in oxygen content. In general, the oxygendeficiency results in the reduction of Mn4þ content and createspoint defects within the structure. In the case of oxygen deficientsamples, the oxygen vacancies are distributed uniformly over thecrystal lattice, making up an oxygen-vacant superstructure. Thesesuperstructures result in domination of super exchange interactionbetween Mn3þ–O–Mn3þ leading to the enhancement of ferro-magnetic properties in these samples [16].

3.3. Electrical behavior and magnetoresistance

The variation of electrical resistivity with temperature over atemperature range, 5–300 K, is shown in Fig. 3. It is clear from theplots that all the samples undergo a metal to insulating (MI)transition and MI transition temperatures (TP) falls continuouslywith decreasing ionic radius of the dopant ion. The observedbehavior may be explained on the basis of lattice effects. Whenrare-earth elements with smaller ionic radii such as Pr to Gd aresubstituted at Ln site, the value of ⟨rA⟩ decreases resulting inmoving oxygen towards the center of the cube, thereby distortingthe lattice and changing Mn–O–Mn bond angle (θ). This change inθ provides a local trap for eg electrons causing possible phase ordomain separation. The effective charge transfer (tij¼tij cos (θ/2))

Table 1Structural parameters of rare earth doped Lanthanum barium manganites.

Sample composition La0.67Ba0.33MnO3 La0.34Pr0.33Ba0.33MnO3 La0.34Nd0.33Ba0.33MnO3 La0.34Sm0.33Ba0.33MnO3 La0.34Gd0.33Ba0.33MnO3

Sample code LBMO LPBMO LNBMO LSBMO LGBMOa ()̊¼b()̊ 5.534 5.533 5.529 5.519 5.495c ()̊ 13.525 13.519 13.511 13.486 13.413V (̊3) 358.718 358.429 357.699 355.747 350.751O (x) 0.45 0.45 0.45 0.45 0.45Mn–O–Mn 164.11(3) 164.08(4) 164.07(4) 164.06(5) 163.78(7)Mn–O ()̊ 1.9738(1) 1.97370(9) 1.96794(9) 1.9677(1) 1.9547(2)RP (%) 6.2 8.6 6.1 6.9 5.0RWP (%) 5.7 6.1 5.7 6.8 3.8REXP (%) 7.5 10.9 8.0 8.7 5.4Goodness of fit (S) 1.4 1.6 1.7 1.6 1.2

Table 2Experimental data of rare earth doped Lanthanum barium manganites.

Samplecode

TC(K)

Tp(K)

Oxygencontent

Avg. Mnvalency

% MR at5 T

m

LBMO 330 274 2.945 3.28 28 3.39LPBMO 285 207 2.971 3.3 41 3.51LNBMO 235 194 2.977 3.31 56 3.52LSBMO 155 121 2.945 3.28 87 3.19LGBMO 115 89 3.028 3.36 96 2.43

100 200 300

0

5

10

15

20

25

30

-2 -1 0 1 2

-60

0

60

120

Temperature (K)

LBMOLPBMOLNBMOLSBMOLGBMO

Mag

netiz

atio

n (e

mu/

g)

H (T)

Fig. 2. (a) Magnetization vs. temperature plots of rare earth doped LBMOmanganites (red solid lines indicate theoretical fittings using Bloch equation), (b)magnetization vs. magnetic field plots of rare earth doped LBMO manganites. (Forinterpretation of the references to color in this figure caption, the reader is referredto the web version of this paper.)

G.L. Reddy et al. / Journal of Magnetism and Magnetic Materials 362 (2014) 20–2622

between the neighboring Mn sites of the local t2g spins decreaseswith decreasing θ. Consequently, the charge localization increasesdue to reduction in the mobility of charge carriers resulting indecrease in TP values [11]. It is interesting to observe from Fig. 3that with decreasing temperature, apart from TP, a low tempera-ture minimum is also observed in the electrical resistivity below50 K. In fact, a similar type of behavior was reported earlier andvarious theories were proposed to explain the observed behavior[17–19] and will be discussed in the analysis part.

As the magnetoresistance (MR) is a fundamental property ofperovskite manganites, resistivity measurements were performedin the presence of various magnetic field up to 10 T and thepercentage of magnetoresistance (MR%) were calculated using astandard relation:

MR%¼ ðρð0Þ�ρðHÞÞ=ρð0Þn100:Fig. 4 shows the variation of MR% vs. temperature at H¼5 T for allthe samples. As the temperature is decreased from 300 K, MR%

values of all the samples are found to increase upto their metalinsulator transition temperature and remain almost constant onfurther decrease of temperature. MR% values of all the samplesobtained at their respective transition temperature at a field of 5 Tare given in Table 2. It can be seen from the table that withdecreasing ionic radius, MR% values are increasing, exhibiting amaximum value of 96% for Gadolinium doped sample which maybe exploited for magnetic sensor applications at low temperatures.As almost all the samples are exhibiting constant high MR belowtransition temperature they may be exploited for various applica-tions. The large MR% in the low temperature ferromagnetic regionmay be attributed to the inter-grain spin tunneling due to avarying environment around Mn ion at the interfaces. In fact it isknown that the small size cations cause strong scattering whilethe large size ones result in a weak scattering of the carriers. Theapplication of the magnetic field reduces the scattering andencourages tunneling of the carriers through the grains leadingto exhibition of large MR% with decreasing ⟨rA⟩ [20].

0 100 200 300

0.005

0.010

0.015

0.020

10 20 30 40 50 0.0020

0.0055

0.0060

ρ (Ω

cm

)

LNBMO

X Axis Title

0 100 200 300

0.0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60

0.01

0.05

0.06

ρ (Ω

cm

)

LSBMO

ρ (Ω

cm

)

T (K)

0 100 200 300

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 10 20 30 40 50

0.051

0.0540.090

0.095

T (K)

ρ (Ω

cm)

LBMO

T (K)

0 100 200 300

0.02

0.04

0.06

0.08

0 10 20 30 40 50 0.014

0.015

0.016

0.032

0.034

T (K)

ρ (Ω

cm)

LPBMO

T (K)

0 100 200 300

0

10

20

30

40

50

5 10 15 20 25 30 350.0

0.5

5

6

ρ (Ω

cm

)

T (K)

LGSMO

ρ (Ω

cm)

T (K)

Fig. 3. Resistivity vs. temperature plots of rare earth doped LBMO manganites at 0 T, 5 T and 8 T magnetic fields (solid lines indicate theoretical fittings using phaseseparation model). Insets in the figures represent low temperature fitting data.

G.L. Reddy et al. / Journal of Magnetism and Magnetic Materials 362 (2014) 20–26 23

3.4. Analysis of electrical resistivity with temperature

To explain the variation of the electrical resistivity withtemperature especially the low temperature resistivity minimum,various scattering mechanisms such as electron–electron, elec-tron–magnon and magnon–magnon scattering processes ( belowTP) and thermal activation process, phase separation model,hopping motion of small polarons variable range hoppingmechanism, etc. (above TP) were used by several authors [21–24]. Efforts were made to fit the resistivity data of presentinvestigation using these models. It has been found that amongthese models, a model based on phase separation [24] fits well.According to this model, the material can be viewed as a networkof junctions, each consisting of paramagnetic regions sandwichedby two adjacent ferromagnetic domains. The conductive channelcan be then modelized as a series of PI with resistivity representedby ρPI and the FM domains with ρFM along the direction of currentflow and the total resistivity is given by an equation:

ρ¼mρFMþð1�mÞρPI ð1Þ

where m and (1�m) represent the volume fractions of FM and PIregions respectively. m varies with temperature, and is expressedby a phenomenological approach [24]. To support the aboveargument an appropriate equation both in FM and PI regions hasbeen considered. The resistivity in the FM region can be ascribed

to an equation ρFM¼ρ0þρ2.5T2.5 (grain boundary effects and

electron–magnon scattering process), while in the PI region theresistivity can be described by a formula as ρPI¼ρ0T exp(Eg/kBT).Substituting the values of ρFM and ρPI, in Eq. (1) we have

ρ¼mðρ0þρ2:5T2:5Þþð1�mÞρ0T expðEg=kBTÞ ð2Þ

The experimental results have been computed using m (T) as anadjustable parameter. The fitting results of all samples are dis-played in Fig. 3 and the fitting parameters are given in Table 3. Itcan be seen that the model yields quantitative fits to the experi-mental data in the whole temperature range studied both in thepresence and absence of magnetic fields. These agreements con-firm that FM and PI regions are coexistent near TC. Further, underthe influence of external magnetic field, TP shifts towards hightemperatures decreasing in the resistivity values. It means that theapplication of magnetic field melts a part of insulating fractionconverting into FM state. This prediction is quite reasonable, as themetallic component triggered by FM is also sensitive to themagnetic field, and the sizes of FM clusters grow as magneticfield is applied especially near the transition temperature. Theparameters, ρ0, ρ2.5 and Eg are found to decrease with increasingmagnetic field. This may be attributed to the fact that under theinfluence of external magnetic field PI regions convert into FMregions more easily, and suppress the formation of polarons andspin-disorder scattering, leading to monotonous decrease of Eg,which in turn enhances TP. Therefore, it has been concluded thatassumption of series connectivity between metallic and insulatingregions is appropriate for samples of present investigation.

It is interesting to see from Fig. 3 that all the samples show ashallow minimum (Tmin) at 50 K and is found to shift towards lowtemperature side with increasing magnetic field. The depth of theminima also decreases with increasing doping concentrationwhich clearly indicates that the low temperature resistivity issensitive to both applied magnetic field and dopant concentration.The observed behavior may be explained by fitting the experi-mental data to an equation [25] which results from the combinedeffect of weak localization, electron–electron and electron–pho-non scattering mechanisms and the expression is given by

ρðTÞ ¼ ðρ0�ρ1T1=2Þþρ2T

2þρ5T5 ð3Þ

where the term in the parentheses arises due to weak localizationeffect and ρ0¼1/a and ρ1¼b/a2 are constants. The other two terms,namely ρ2T

2 and ρ5T5, arise due to electron–electron and electron–

phonon scattering respectively. It can be seen from the inset ofFig. 3 that ρ(T) data fits well to Eq. (3) both in the presence andabsence of a magnetic field and the best fit parameters are given inTable 3. The fitting parameters are found to decrease with

0 50 100 150 200 250 300

0

10

20

30

40

50

60

70

80

90

100 LBMO LPBMO LNBMO LSBMO LGBMO

% M

agne

to re

sist

ance

Temperature (K)

Fig. 4. Magnetoresistance vs. temperature plots of rare earth doped LBMOmanganites at 5 T magnetic field.

Table 3Best fit parameters of resistivity data fittings in the low temperature and entire temperature region.

Sample code/field applied ρ0 (Ω cm) ρ2.5 (Ω cm K�2.5) Eg (meV) TCmod (K) ρ0

’ (Ωm) ρ1 (Ω cm K�1/2) ρ2 (Ω cm K�2) ρ5 (Ω cm K�5)

LBMO0 T 0.074 4.89�10�6 36.8 278 0.099 0.0017 2.56�10�6 5.55�10�12

8 T 0.043 2.91�10�6 27.2 285 0.054 0.0009 2.37�10�7 1.57�10�12

LPBMO0 T 0.035 1.109�10�7 140.3 225 0.036 0.00097 1.57�10�6 1.58�10�12

8 T 0.016 4.72�10�7 81.3 238 0.0167 0.00057 1.15�10�6 �3.91�10�13

LNBMO0 T 0.005 4.15�10�8 153.7 203 0.0068 0.00024 4.23�10�7 2.62�10�13

8 T 0.002 1.14�10�8 93.8 213 0.0025 0.00013 2.51�10�7 �1.71�10�13

LSBMO0 T 0.047 1.98�10�6 161.7 128 0.0647 0.0034 5.88�10�6 2.11�10�11

8 T 0.076 6.16�10�7 124.1 167 0.0163 0.0015 1.599�10�6 �6.34�10�14

LGBMO0 T 0.72 0.0025 149.7 98 7.1955 0.8401 1.55�10�6 2.28�10�7

8 T 0.197 0.00006 117.8 143 0.8898 0.1495 4.00�10�8 4.44�10�9

G.L. Reddy et al. / Journal of Magnetism and Magnetic Materials 362 (2014) 20–2624

decreasing ionic radius and on application of magnetic fieldindicating that the weak localization, electron–electron and elec-tron–phonon scattering processes decrease with decreasing ionicradius.

3.5. Thermopower studies

The temperature dependence of thermopower (S) of all thesamples from 80 to 300 K is shown in Fig. 5(a). It can be seen fromthe figure that in the case of undoped sample, LBMO, themagnitude of S is small and positive at room temperature and itbecomes negative with decreasing temperature. On substitutingthe La-site with a smaller rare earth ion, S is found to be negativeat T¼300 K and with decreasing temperature it slowly changesfrom negative to positive and finally becomes positive. Theobserved behavior may be due to change in the nature of chargecarriers both with decreasing temperature and ionic radii. Further,the magnitude of S is found to increase with decreasing ⟨rA⟩ andsuch large S values were also observed in Sm–Sr–MnO3 manga-nites [26]. The increase in the value of S indicates the weakeningof metallicity in these compounds, as it is conventionally knownthat poor conductors usually have a larger S than that of good

conductors and the behavior is consistent with the electricalresistivity measurements.

As the temperature is decreased from room temperature toliquid nitrogen temperature, S increases exhibiting a peak at acertain temperature hereafter designated as TS (Table 4) anddecreases slowly attaining a minima on further lowering thetemperature. In fact a similar behavior was reported in the caseof Pr–Sr–Mn–O manganties [27]. It can also be seen from thefigure that the TS shift towards low temperature side and minimaslowly vanishes with decreasing ⟨rA⟩. The TS values are close totheir respective magnetic transition temperature (TC). The increasein S value at TS reflects sudden change of spin entropy due toenhancement of spin polarization caused by magnetic transition[28].The observed variation in thermopower data with decreasing⟨rA⟩ suggests that the strong electronic modifications induced bythe size effect which are correlated to overlapping of atomic Mn–Oorbitals. Further, it has also been reported that the effects of theColumbian localization play an important role in determining themagnitude of thermopower values [26]. In view of this, one mayconclude that thermopower is sensitive to cationic size of thesamples.

Similar to electrical resistivity various mechanisms contributeto thermopower in the low temperature region. An effort has alsobeen made to analyze thermopower data in the ferromagneticregion using an empirical equation containing spin wave andlattice vibration terms [29]:

S¼ S0þS1TþS3=2T3=2þS3T

3þS4T4 ð4Þ

where S0 accounts for the problem of truncating the low tem-perature data, S1T corresponds to the diffusion term, S3/2T

3/2

represents the spin wave (magnon drag) contribution, S3T3 corre-sponds to the phonon drag and S4T

4 term represents spin fluctua-tions in ferromagnetic phase [30]. The experimental data werefitted to Eq. (4) and it has been observed that the equation fits wellwith the data in the ferromagnetic region and is shown in inset ofFig. 5(a). One may also observe that S3/2 values are much largerthan those of S3 suggesting that electron–magnon scattering mightbe dominating in the low temperature region.

The temperature dependence of the thermopower of thepresent series in the insulating regime is well described usingthe following expression:

S¼ kB=e½ES=kBTþα΄� ð5Þwhere ES is the activation energy obtained from TEP data. α0 is aconstant of proportionality between the heat transfer and thekinetic energy of an electron and may be used to ascertain the typeof polarons participating in conduction process. For example, ifα0o1 the charge carriers responsible for thermopower might bedue to small polarons, while if α042, they are large polarons[31,32]. From the linear fit of the curves the activation energies forthermopower (ES) were determined and are given in Table 4, whileS vs. 1/T plots are shown in Fig. 5(b). It is clear from the table thatES and Eρ values are found to increase with the substitution ofsmaller rare-earth ion but decrease in the case of Gd doped one.The enhancement in the values of both the activation energies

0.002 0.004 0.006 0.008 0.010 0.012

-40

0

40

80

120

160

300200100

-40

0

40

80

120

160

100 150

0

50

100

150

LSBMO LGBMO

T-1 (K-1)

LBMO LPBMO LNBMO LSBMO LNBMO

T (K)

S (m

icro

V/K

)

S (µ

V/K

)

T (K)

a

b

Fig. 5. (a) Seebeck coefficient vs. temperature plots of rare earth doped LBMOmanganites. Inset represents low temperature fitting data. (b) High temperaturefitting data (solid lines indicate theoretical fittings).

Table 4Best fit parameters of thermopower data fittings in the low temperature and high temperature region.

Sample code S0 (μV K�1) S1 (μV K�2) S3/2 (μV K�5/2) S3 (μV K�4) S4 (μV K�5) TS (K) Eρ (meV) ES (meV) α0

LBMO 121.55 �4.465 0.370 �0.00007 1.75�10�7 – 36.8 – –

LPBMO 13.73 �0.215 0.003 �2.78�10�7 1.23�10�8 266 140.3 3.38 �0.138LNBMO 9.26 �0.234 �0.015 �7.58�10�7 5.07�10�10 247 153.7 3.85 �0.163LSBMO �135.10 10.47 �1.191 0.0004 �1.08�10�6 185 161.7 53.8 �2.300LGBMO �3048.02 168.93 �17.161 0.0044 �0.00001 167 149.7 46.9 �1.990

G.L. Reddy et al. / Journal of Magnetism and Magnetic Materials 362 (2014) 20–26 25

may be attributed to the fact that due to doping of smaller rareearth ions at Ln site decreases the average A-site ionic radii ⟨rA⟩resulting in bending of Mn–O–Mn bond angle which inturn mighthave narrowed down the bandwidth enhancing the effective massof the charge carrier. Due to this, the effective band gap increaseswith decreasing ⟨rA⟩, while decrease in the activation energies inthe case of LGBMO might be due to excess in the oxygen content inthe sample. Therefore, higher energies are needed for the chargecarries to overcome this band gap. The difference in activationenergies obtained from the resistivity and thermopower datareflects that the charge transport occurs due to the hopping ofcarriers. Further, it is also clear from the table that the calculatedvalues of α0 are less than unity and the result strongly supports thevalidity of using small polaron hopping mechanism to explain theelectrical resistivity as well as the thermopower data of thesematerials in the high temperature regime.

4. Conclusions

Influence of rare earth doping on the electrical, magneticproperties and thermopower of LBMO manganite has been stu-died. All the samples are found to have Rhombohedral structurewith R3c space group. The variation of electrical resistivity in theentire temperature region exhibited by the samples of the presentinvestigation has been explained using phase separation model. Asthe MR% is found to increase with decreasing ionic radii both at TPand in the low temperature ferromagnetic region, the samplesmay be exploited for sensor applications. Finally, the variation ofthermopower data in the low temperature region has beenexplained by considering diffusion, phonon drag and magnon dragphenomena, while that in the high temperature region isexplained within the framework of small polaron hoppingmechanism.

Acknowledgments

First author, G. Lalitha, thank UGC, Govt., of India, for awardingDr. D. S. Kothari post doctoral fellowship and Y. Kalyana Lakshmithank CSIR, for awarding a Research Associateship. The authorsalso thank the Centre Director, Dr. Ajay Gupta and Dr. RajeevRawat, UGC-DAE Consortium for Scientific Research, Indore (CSR),India, for providing MR facilities.

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