Thermopower studies of rare earth doped lanthanum barium manganites

Thermopower studies of rare earth doped lanthanum barium manganites

Journal of Magnetism and Magnetic Materials 362 (2014) 20–26 Contents lists available at ScienceDirect Journal of Magnetism and Magnetic Materials j...

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

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Thermopower studies of rare earth doped lanthanum barium 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, India Department of Physics, Telangana University (South Campus), Jangampally, India c Central Instruments Laboratory, University of Hyderabad, Hyderabad 500046, India b

art ic l e i nf o

a b s t r a c t

Article history: Received 20 December 2013 Received in revised form 23 February 2014 Available online 13 March 2014

Influence of rare earth doping on electrical, magnetic and thermopower studies of La0.34Re0.33Ba0.33MnO3 compound was investigated. Ferro to paramagnetic transition and metal to insulator transition temperatures decrease with decreasing ionic radius of the dopant ion. Electrical resistivity in the entire temperature range is explained by phase separation model. The magnitude of Seebeck coefficient increases with increasing dopant ionic radius. A cross over from negative to positive sign has also been observed in thermopower data with decreasing A site ionic radius (〈rA〉). The low temperature thermopower data has been explained using a qualitative model containing diffusion; magnon drag and phonon drag effects while the paramagnetic insulating part has been analyzed using small polaron hopping mechanism. & 2014 Elsevier B.V. All rights reserved.

Keywords: Magnetic material Electrical property Magnetic property Thermopower Conduction mechanism

1. Introduction Electronic and magnetic properties of rare earth manganites, Ln1 xMxMnO3 (Ln¼rare earth, M¼alkaline earth), have received a lot of attention in the last decade due to their possible technological applications [1]. These compounds show various interesting and inter-related properties, such as the insulator–metal and the paramagnetic–ferromagnetic transition, charge and orbital ordering. These properties are governed by various phenomena such as Zener-Double exchange, static and dynamic Jahn–Teller effect, charge and spin dynamics, etc. [2]. Changes in magnetic properties, like ferromagnetic-to-paramagnetic (FM–PM) transition, or electronic properties, like metal-to-insulator (M–I) transition can be tuned in several ways. The physical properties of these materials are controlled by various parameters such as amount of hole doping, average ionic radius of Asite cations (〈rA〉), etc. [3]. In fact, the maximum transition temperature (T¼360 K) was observed for a composition with x¼ 0.33 [4]. Disorder due to ionic size mismatch between various ions at the same crystallographic site influences the transport properties. In the case of doped manganites, since the conductivity and magnetism are strongly correlated, it is important to consider the effect of A-site ionic size

n

Corresponding author. Tel./fax: þ 91 40 2700 9002. E-mail address: [email protected] (P.V. Reddy).

http://dx.doi.org/10.1016/j.jmmm.2014.03.015 0304-8853/& 2014 Elsevier B.V. All rights reserved.

mismatch on the CMR properties [5]. The size mismatch at A-site generates internal chemical pressure within the lattice. Due to this structural 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 can be controlled by the average size of A-site cation which in turn modifies the Mn–O–Mn bond angle and Mn–O distances. The Mn–O– Mn bond angle is directly related to the hopping integral between Mn3þ and Mn4þ degenerate states. Thus, the variations in ionic radii at A-sites lead to competing phases at a particular temperature influencing the electrical and magnetic transport properties of perovskite manganites [6]. Among the manganites, barium doped manganites are interesting ones as they exhibit ferro magnetic behavior above room temperature and exhibit significant magnetoresistance (MR) values. In order to develop these materials as future device materials, there is a need to optimize its electrical, magnetic properties. In view of this, it is felt that there is need to undertake a systematic investigation of doping of various rare earth ions at lanthanum site of La0.67Ba0.33MnO3 system so as to vary the A-site ionic radius. Among various transport properties, thermopower is very sensitive to local moments of charge carriers and since the nature of charge carriers based on degree of JT interaction [7] can be predicted, studies on this phenomenon have attracted the attention of several investigators [8,9]. Moreover, a systematic analysis of thermopower data also enables one to understand the

(312) (214)

(220) (024)

(212) (104)

(211) (113)

LPBMO LBMO

20

30

40

50

60

70

80

2 Theta(°)

LNBMO

40

60

80

2 Theta (°)

3. Results and discussion

The X-ray diffraction (XRD) measurements of all the samples were undertaken at room temperature and the XRD patterns are shown as inset in Fig. 1. No detectable impurity phase has been observed from the XRD patterns. The XRD data were refined using rietveld refinement technique assuming Rhombohedral structure with R3c space group. A typical XRD plot of LNBMO sample along with its Rietveld refined one, including the difference between the observed and calculated ones is shown in Fig. 1. Various crystallographic parameters obtained from the refinement process are given in Table 1. It can be seen from the table that both the lattice parameters, a and c are decreasing continuously with decreasing ionic radius of the dopant ion and the observed behavior may be attributed to the fact that a smaller ion is replacing a bigger one at A-site of ABO3 perovskite structure. Due to successive substitution of rare earth ions at A-site by a smaller ion, the ionic radius reduces continuously and oxygen tends to move towards the center, reducing Mn–O bond distances, distorting the lattice. As the A-site radius is reduced and Mn–O–Mn angle becomes smaller than 1801 causing local lattice distortions of MnO6 octahedra, 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

(202)

LNBMO

20

3.1. Structural aspects

(201) (003)

LSBMO

Intensity (a.u)

Bulk polycrystalline samples with compositional formula, La0.34Re0.33Ba0.33MnO3 7 δ (Re¼ La, Pr, Nd, Sm and Gd) were prepared by citrate based sol-gel method. In this all the materials in the form of nitrates were taken in stoichiometric ratio and were dissolved in an aqueous solution. Citric acid was added in 1:1 ratio and the pH was adjusted to 6.5–7.0 by adding ammonia. When the solution was evaporated to 1/3rd of its volume, a gelating agent ethylene glycol was added in 1:1.2 ratios and the gel was dried to obtain a black precursor. The precursor was burnt to obtain a xerogel which was further calcined at a temperature of 1000 1C for 4 h. Finally, the calcined powders after pelletizing were sintered at 1300 1C for 4 h. The samples were characterized structurally by X-ray diffraction technique using Phillips Expert diffractometer with CuKα (λ ¼1.541 ̊) radiation at room temperature. In order to determine the ratio of Mn3 þ /Mn4 þ concentration and oxygen content in the samples, iodometric titrations [10] were carried out. To determine the magnetic transition temperatures (TC), Magnetization measurements were also performed using a Vibrating Sample Magnetometer (VSM) (Lake Shore model no 7460) over a temperature range 80–300 K, while the electrical resistivity and magnetoresistance (MR) studies were carried out by an Oxford superconducting magnetic system at different magnetic fields over a temperature range, 5–300 K using four probe method. Finally, thermoelectric power studies were also carried out by differential method over a temperature range 80–300 K. The measurements were carried out in nitrogen (exchange gas) atmosphere in heating mode. The absolute Seebeck coefficient (S) values were obtained by subtracting the Seebeck coefficient values of the electrode (copper) material.

LGBMO

21

Intensity (a.u)

2. Experimental details

(101)

conduction mechanism of CMR materials. In view of this, the influence of doping various rare earth ions at lanthanum site on electrical, magnetic properties and thermoelectric power of La0.67Ba0.33MnO3 have been investigated systematically and the results of such an investigation are presented here.

(110) (102)

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

investigation also Mn–O–Mn angle is found to decrease continuously (Table 1). In order to determine the ratio of Mn3 þ /Mn4 þ concentration and oxygen content in the samples, iodometric titrations were carried out and the values of average Mn valence and oxygen content are included in Table 2. One can see from the table that the first four samples of the series are having oxygen deficiency while the Gadolinium doped one is excess in oxygen. Generally, the oxygen non-stoichiometry is compensated by an equivalent change in Mn valence resulting in variation in number of Mn4 þ sites [13]. 3.2. Magnetic behavior As the manganites are known to exhibit excellent magnetic properties including a transition from ferromagnetic to paramagnetic, a systematic investigation of magnetization with varying temperature has been undertaken and the magnetization vs. temperature plots of all the samples are shown in Fig. 2(a). From the figure one may observe that as the temperature is decreased,

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Table 1 Structural 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 a (̊ ) ¼ b(̊ ) c (̊ ) 3 V (̊) O (x) Mn–O–Mn Mn–O (̊ ) RP (%) RWP (%) REXP (%) Goodness of fit (S)

LBMO 5.534 13.525 358.718 0.45 164.11(3) 1.9738(1) 6.2 5.7 7.5 1.4

LPBMO 5.533 13.519 358.429 0.45 164.08(4) 1.97370(9) 8.6 6.1 10.9 1.6

LNBMO 5.529 13.511 357.699 0.45 164.07(4) 1.96794(9) 6.1 5.7 8.0 1.7

LSBMO 5.519 13.486 355.747 0.45 164.06(5) 1.9677(1) 6.9 6.8 8.7 1.6

LGBMO 5.495 13.413 350.751 0.45 163.78(7) 1.9547(2) 5.0 3.8 5.4 1.2

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

TC (K)

Tp (K)

Oxygen content

Avg. Mn valency

% MR at 5T

m

LBMO LPBMO LNBMO LSBMO LGBMO

330 285 235 155 115

274 207 194 121 89

2.945 2.971 2.977 2.945 3.028

3.28 3.3 3.31 3.28 3.36

28 41 56 87 96

3.39 3.51 3.52 3.19 2.43

Temperature (K) 30

100

200

300

25 20 LBMO LPBMO LNBMO LSBMO LGBMO

15

Magnetization (emu/g)

10 5 0 120

60

0

-60 -2

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 the table that TC values are decreasing continuously from 330 K to 115 K with decreasing ionic radius of the dopant ion and the observed behavior may be attributed to the following reason: On substitution of a trivalent element with smaller ionic radii at Ln site, the average A-site cation radius decreases thereby enhancing its size variance parameter, which in turn affects Mn–O–Mn angle and average Mn–O distance (Table 1). The A-site cation size disorder may result in random displacement of oxygen ions from their average crystallographic positions causing local distortion in MnO6 octahedra. The increasing value of s2 with decreasing 〈rA〉 causes localization of eg electrons, which in turn prevents the long-range ferromagnetic ordering leading to decrease in TC values. In fact, the observed decrease in TC with s2 is consistent with earlier reports [14,15]. The magnetization vs. magnetic field measurements were also undertaken and the plots at T ¼80 K up to 1.5 T are shown in Fig. 2 (b) and it is clear that all the samples of present investigation exhibit 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 decrease with decreasing ionic radius of the dopant ion. In fact, as the concentration of the divalent dopant (Ba) is same for all the samples, the values of spin-only moments arising due to collinear ferromagnetic arrangement of Mn ions must been equal. The observed unusual behavior may be explained based on the oxygen non-stoichiometry. It is clear from Table 1 that, the first four samples of present investigation are oxygen deficient while the last one is excess in oxygen content. In general, the oxygen deficiency results in the reduction of Mn4 þ content and creates point defects within the structure. In the case of oxygen deficient samples, the oxygen vacancies are distributed uniformly over the crystal lattice, making up an oxygen-vacant superstructure. These superstructures result in domination of super exchange interaction between Mn3 þ –O–Mn3 þ leading to the enhancement of ferromagnetic properties in these samples [16]. 3.3. Electrical behavior and magnetoresistance

-1

0

1

2

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

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

The variation of electrical resistivity with temperature over a temperature range, 5–300 K, is shown in Fig. 3. It is clear from the plots that all the samples undergo a metal to insulating (MI) transition and MI transition temperatures (TP) falls continuously with decreasing ionic radius of the dopant ion. The observed behavior may be explained on the basis of lattice effects. When rare-earth elements with smaller ionic radii such as Pr to Gd are substituted at Ln site, the value of 〈rA〉 decreases resulting in moving oxygen towards the center of the cube, thereby distorting the lattice and changing Mn–O–Mn bond angle (θ). This change in θ provides a local trap for eg electrons causing possible phase or domain separation. The effective charge transfer (tij ¼tij cos (θ/2))

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

T (K)

T (K) 0

100

200

200

0.034

300 0.08

0.090

0.20

0

0.051 0

10

20

30

40

0.06

0.015 10

20

30

40

50

0.014

T (K)

50

0.04

T (K)

ρ (Ωcm)

0.016

0.054

0.25

ρ (Ωcm)

100

0.032

0.30

0.15

0

300

0.095

0.35

23

0.10

LPBMO

LBMO 0.0060

ρ (Ω cm)

0.4

ρ (Ω cm)

0.020

0.06

LSBMO

0.0055

0.3

0.05

0.015 10

20

30 40 X Axis Title

0.0020

50

0.01 0

0.010

0.02

0.2 10

20

30

40

50

60

T (K)

ρ (Ω cm)

0.05

0.1

0.005 0.0

LNBMO 0

100

200

300

0

100

200

300

6

50

ρ (Ω cm)

ρ (Ωcm)

40 30

5

0.5 0.0

20

5

10

15

20

25

30

35

T (K)

10

LGSMO

0 0

100

200

300

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 phase separation model). Insets in the figures represent low temperature fitting data.

between the neighboring Mn sites of the local t2g spins decreases with decreasing θ. Consequently, the charge localization increases due to reduction in the mobility of charge carriers resulting in decrease in TP values [11]. It is interesting to observe from Fig. 3 that with decreasing temperature, apart from TP, a low temperature minimum is also observed in the electrical resistivity below 50 K. In fact, a similar type of behavior was reported earlier and various 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 of perovskite manganites, resistivity measurements were performed in the presence of various magnetic field up to 10 T and the percentage of magnetoresistance (MR%) were calculated using a standard relation: MR% ¼ ðρð0Þ  ρðHÞÞ=ρð0Þn100: Fig. 4 shows the variation of MR% vs. temperature at H ¼5 T for all the samples. As the temperature is decreased from 300 K, MR%

values of all the samples are found to increase upto their metal insulator transition temperature and remain almost constant on further decrease of temperature. MR% values of all the samples obtained at their respective transition temperature at a field of 5 T are given in Table 2. It can be seen from the table that with decreasing ionic radius, MR% values are increasing, exhibiting a maximum value of 96% for Gadolinium doped sample which may be exploited for magnetic sensor applications at low temperatures. As almost all the samples are exhibiting constant high MR below transition temperature they may be exploited for various applications. The large MR% in the low temperature ferromagnetic region may be attributed to the inter-grain spin tunneling due to a varying environment around Mn ion at the interfaces. In fact it is known that the small size cations cause strong scattering while the large size ones result in a weak scattering of the carriers. The application of the magnetic field reduces the scattering and encourages tunneling of the carriers through the grains leading to exhibition of large MR% with decreasing 〈rA〉 [20].

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3.4. Analysis of electrical resistivity with temperature To explain the variation of the electrical resistivity with temperature especially the low temperature resistivity minimum, various scattering mechanisms such as electron–electron, electron–magnon and magnon–magnon scattering processes ( below TP) and thermal activation process, phase separation model, hopping motion of small polarons variable range hopping mechanism, etc. (above TP) were used by several authors [21– 24]. Efforts were made to fit the resistivity data of present investigation using these models. It has been found that among these models, a model based on phase separation [24] fits well. According to this model, the material can be viewed as a network of junctions, each consisting of paramagnetic regions sandwiched by two adjacent ferromagnetic domains. The conductive channel can be then modelized as a series of PI with resistivity represented by ρPI and the FM domains with ρFM along the direction of current flow and the total resistivity is given by an equation: ρ ¼ mρFM þð1 mÞρPI

ð1Þ

where m and (1  m) represent the volume fractions of FM and PI regions respectively. m varies with temperature, and is expressed by a phenomenological approach [24]. To support the above argument an appropriate equation both in FM and PI regions has been considered. The resistivity in the FM region can be ascribed 100

LBMO LPBMO LNBMO LSBMO LGBMO

90

% Magneto resistance

80 70 60 50 40 30 20

to an equation ρFM ¼ρ0 þ ρ2.5T2.5 (grain boundary effects and electron–magnon scattering process), while in the PI region the resistivity can be described by a formula as ρPI ¼ ρ0T exp(Eg/kBT). Substituting the values of ρFM and ρPI, in Eq. (1) we have ρ ¼ mðρ0 þ ρ2:5 T 2:5 Þ þ ð1  mÞρ0 T expðEg =kB TÞ

The experimental results have been computed using m (T) as an adjustable parameter. The fitting results of all samples are displayed in Fig. 3 and the fitting parameters are given in Table 3. It can be seen that the model yields quantitative fits to the experimental data in the whole temperature range studied both in the presence and absence of magnetic fields. These agreements confirm that FM and PI regions are coexistent near TC. Further, under the influence of external magnetic field, TP shifts towards high temperatures decreasing in the resistivity values. It means that the application of magnetic field melts a part of insulating fraction converting into FM state. This prediction is quite reasonable, as the metallic component triggered by FM is also sensitive to the magnetic field, and the sizes of FM clusters grow as magnetic field is applied especially near the transition temperature. The parameters, ρ0, ρ2.5 and Eg are found to decrease with increasing magnetic field. This may be attributed to the fact that under the influence of external magnetic field PI regions convert into FM regions more easily, and suppress the formation of polarons and spin-disorder scattering, leading to monotonous decrease of Eg, which in turn enhances TP. Therefore, it has been concluded that assumption of series connectivity between metallic and insulating regions is appropriate for samples of present investigation. It is interesting to see from Fig. 3 that all the samples show a shallow minimum (Tmin) at 50 K and is found to shift towards low temperature side with increasing magnetic field. The depth of the minima also decreases with increasing doping concentration which clearly indicates that the low temperature resistivity is sensitive to both applied magnetic field and dopant concentration. The observed behavior may be explained by fitting the experimental data to an equation [25] which results from the combined effect of weak localization, electron–electron and electron–phonon scattering mechanisms and the expression is given by ρðTÞ ¼ ðρ0  ρ1 T 1=2 Þ þρ2 T 2 þ ρ5 T 5

10 0 0

50

100

150

200

250

300

Temperature (K) Fig. 4. Magnetoresistance vs. temperature plots of rare earth doped LBMO manganites at 5 T magnetic field.

ð2Þ

ð3Þ

where the term in the parentheses arises due to weak localization effect and ρ0 ¼1/a and ρ1 ¼ b/a2 are constants. The other two terms, namely ρ2T2 and ρ5T5, arise due to electron–electron and electron– phonon scattering respectively. It can be seen from the inset of Fig. 3 that ρ(T) data fits well to Eq. (3) both in the presence and absence of a magnetic field and the best fit parameters are given in Table 3. The fitting parameters are found to decrease with

Table 3 Best fit parameters of resistivity data fittings in the low temperature and entire temperature region. Sample code/field applied LBMO 0T 8T LPBMO 0T 8T LNBMO 0T 8T LSBMO 0T 8T LGBMO 0T 8T

ρ0 (Ω cm)

ρ2.5 (Ω cm K  2.5)

Tmod (K) C

ρ’0 (Ω m)

ρ1 (Ω cm K  1/2)

0.074 0.043

4.89  10  6 2.91  10  6

36.8 27.2

278 285

0.099 0.054

0.0017 0.0009

2.56  10  6 2.37  10  7

5.55  10  12 1.57  10  12

0.035 0.016

1.109  10  7 4.72  10  7

140.3 81.3

225 238

0.036 0.0167

0.00097 0.00057

1.57  10  6 1.15  10  6

1.58  10  12  3.91  10  13

0.005 0.002

4.15  10  8 1.14  10  8

153.7 93.8

203 213

0.0068 0.0025

0.00024 0.00013

4.23  10  7 2.51  10  7

2.62  10  13  1.71  10  13

0.047 0.076

1.98  10  6 6.16  10  7

161.7 124.1

128 167

0.0647 0.0163

0.0034 0.0015

5.88  10  6 1.599  10  6

2.11  10  11  6.34  10  14

0.72 0.197

0.0025 0.00006

149.7 117.8

98 143

7.1955 0.8898

0.8401 0.1495

1.55  10  6 4.00  10  8

2.28  10  7 4.44  10  9

Eg (meV)

ρ2 (Ω cm K  2)

ρ5 (Ω cm K  5)

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

decreasing ionic radius and on application of magnetic field indicating that the weak localization, electron–electron and electron–phonon scattering processes decrease with decreasing ionic radius.

3.5. Thermopower studies The temperature dependence of thermopower (S) of all the samples from 80 to 300 K is shown in Fig. 5(a). It can be seen from the figure that in the case of undoped sample, LBMO, the magnitude of S is small and positive at room temperature and it becomes negative with decreasing temperature. On substituting the La-site with a smaller rare earth ion, S is found to be negative at T ¼300 K and with decreasing temperature it slowly changes from negative to positive and finally becomes positive. The observed behavior may be due to change in the nature of charge carriers both with decreasing temperature and ionic radii. Further, the magnitude of S is found to increase with decreasing 〈rA〉 and such large S values were also observed in Sm–Sr–MnO3 manganites [26]. The increase in the value of S indicates the weakening of metallicity in these compounds, as it is conventionally known that poor conductors usually have a larger S than that of good

T (K) 100

200

LBMO LPBMO LNBMO LSBMO LNBMO

120

300 100

0 100

150 T (K)

40

S (microV/K)

0

a

-40 160

LSBMO LGBMO

120

S ¼ kB =e½ES =kB T þ α΄

80 40 0 -40

ð4Þ

where S0 accounts for the problem of truncating the low temperature data, S1T corresponds to the diffusion term, S3/2T3/2 represents the spin wave (magnon drag) contribution, S3T3 corresponds to the phonon drag and S4T4 term represents spin fluctuations in ferromagnetic phase [30]. The experimental data were fitted to Eq. (4) and it has been observed that the equation fits well with the data in the ferromagnetic region and is shown in inset of Fig. 5(a). One may also observe that S3/2 values are much larger than those of S3 suggesting that electron–magnon scattering might be dominating in the low temperature region. The temperature dependence of the thermopower of the present series in the insulating regime is well described using the following expression:

50

80

conductors and the behavior is consistent with the electrical resistivity measurements. As the temperature is decreased from room temperature to liquid nitrogen temperature, S increases exhibiting a peak at a certain temperature hereafter designated as TS (Table 4) and decreases slowly attaining a minima on further lowering the temperature. In fact a similar behavior was reported in the case of Pr–Sr–Mn–O manganties [27]. It can also be seen from the figure that the TS shift towards low temperature side and minima slowly vanishes with decreasing 〈rA〉. The TS values are close to their respective magnetic transition temperature (TC). The increase in S value at TS reflects sudden change of spin entropy due to enhancement of spin polarization caused by magnetic transition [28].The observed variation in thermopower data with decreasing 〈rA〉 suggests that the strong electronic modifications induced by the size effect which are correlated to overlapping of atomic Mn–O orbitals. Further, it has also been reported that the effects of the Columbian localization play an important role in determining the magnitude of thermopower values [26]. In view of this, one may conclude that thermopower is sensitive to cationic size of the samples. Similar to electrical resistivity various mechanisms contribute to thermopower in the low temperature region. An effort has also been made to analyze thermopower data in the ferromagnetic region using an empirical equation containing spin wave and lattice vibration terms [29]: S ¼ S0 þ S1 T þ S3=2 T 3=2 þ S3 T 3 þ S4 T 4

150 S (µV/K)

160

25

b

0.002

0.004

0.006

0.008

0.010

0.012

T-1 (K-1) Fig. 5. (a) Seebeck coefficient vs. temperature plots of rare earth doped LBMO manganites. Inset represents low temperature fitting data. (b) High temperature fitting data (solid lines indicate theoretical fittings).

ð5Þ

where ES is the activation energy obtained from TEP data. α0 is a constant of proportionality between the heat transfer and the kinetic energy of an electron and may be used to ascertain the type of polarons participating in conduction process. For example, if α0 o 1 the charge carriers responsible for thermopower might be due to small polarons, while if α0 4 2, they are large polarons [31,32]. From the linear fit of the curves the activation energies for thermopower (ES) were determined and are given in Table 4, while S vs. 1/T plots are shown in Fig. 5(b). It is clear from the table that ES and Eρ values are found to increase with the substitution of smaller rare-earth ion but decrease in the case of Gd doped one. The enhancement in the values of both the activation energies

Table 4 Best 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 LPBMO LNBMO LSBMO LGBMO

121.55 13.73 9.26  135.10  3048.02

 4.465  0.215  0.234 10.47 168.93

0.370 0.003  0.015  1.191  17.161

 0.00007  2.78  10  7  7.58  10  7 0.0004 0.0044

1.75  10  7 1.23  10  8 5.07  10  10  1.08  10  6  0.00001

– 266 247 185 167

36.8 140.3 153.7 161.7 149.7

– 3.38 3.85 53.8 46.9

–  0.138  0.163  2.300  1.990

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may be attributed to the fact that due to doping of smaller rare earth ions at Ln site decreases the average A-site ionic radii 〈rA〉 resulting in bending of Mn–O–Mn bond angle which inturn might have narrowed down the bandwidth enhancing the effective mass of the charge carrier. Due to this, the effective band gap increases with decreasing 〈rA〉, while decrease in the activation energies in the case of LGBMO might be due to excess in the oxygen content in the sample. Therefore, higher energies are needed for the charge carries to overcome this band gap. The difference in activation energies obtained from the resistivity and thermopower data reflects that the charge transport occurs due to the hopping of carriers. Further, it is also clear from the table that the calculated values of α0 are less than unity and the result strongly supports the validity of using small polaron hopping mechanism to explain the electrical resistivity as well as the thermopower data of these materials in the high temperature regime. 4. Conclusions Influence of rare earth doping on the electrical, magnetic properties and thermopower of LBMO manganite has been studied. All the samples are found to have Rhombohedral structure with R3c space group. The variation of electrical resistivity in the entire temperature region exhibited by the samples of the present investigation has been explained using phase separation model. As the MR% is found to increase with decreasing ionic radii both at TP and in the low temperature ferromagnetic region, the samples may be exploited for sensor applications. Finally, the variation of thermopower data in the low temperature region has been explained by considering diffusion, phonon drag and magnon drag phenomena, while that in the high temperature region is explained within the framework of small polaron hopping mechanism. Acknowledgments First author, G. Lalitha, thank UGC, Govt., of India, for awarding Dr. D. S. Kothari post doctoral fellowship and Y. Kalyana Lakshmi thank CSIR, for awarding a Research Associateship. The authors also thank the Centre Director, Dr. Ajay Gupta and Dr. Rajeev Rawat, UGC-DAE Consortium for Scientific Research, Indore (CSR), India, for providing MR facilities.

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