Influence of electron beam irradiation on electrical, structural, magnetic and thermal properties of Pr0.8Sr0.2MnO3 manganites

Influence of electron beam irradiation on electrical, structural, magnetic and thermal properties of Pr0.8Sr0.2MnO3 manganites

Physica B 502 (2016) 119–131 Contents lists available at ScienceDirect Physica B journal homepage: www.elsevier.com/locate/physb Influence of electr...

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Physica B 502 (2016) 119–131

Contents lists available at ScienceDirect

Physica B journal homepage: www.elsevier.com/locate/physb

Influence of electron beam irradiation on electrical, structural, magnetic and thermal properties of Pr0.8Sr0.2MnO3 manganites Benedict Christopher a, Ashok Rao a,n, Vikash Chandra Petwal b, Vijay Pal Verma b, Jishnu Dwivedi b, W.J. Lin c, Y.-K. Kuo c,n a

Department of Physics, Manipal Institute of Technology, Manipal University, Manipal 576104, India Industrial Accelerator Section, PSIAD, Raja Ramanna Centre for Advanced Technology, Indore 452012, M.P., India c Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan b

art ic l e i nf o

a b s t r a c t

Article history: Received 14 July 2016 Received in revised form 29 August 2016 Accepted 30 August 2016 Available online 31 August 2016

In this communication, the effect of electron beam (EB) irradiation on the structural, electrical transport and thermal properties of Pr0.8Sr0.2MnO3 manganites has been investigated. Rietveld refinement of XRD data reveals that all samples are single phased with orthorhombic distorted structure (Pbnm). It is observed that the orthorhombic deformation increases with EB dosage. The Mn–O–Mn bond angle is found to increase with increase in EB dosage, presumably due to strain induced by these irradiations. Analysis on the measured electrical resistivity data indicates that the small polaron hopping model is operative in the high temperature region for pristine as well as EB irradiated samples. The electrical resistivity in the entire temperature region has been successfully fitted with the phenomenological percolation model which is based on phase segregation of ferromagnetic metallic clusters and paramagnetic insulating regions. The Seebeck coefficient (S) of the pristine as well as the irradiated samples exhibit positive values, indicating that holes is the dominant charge carriers. The analysis of Seebeck coefficient data confirms that the small polaron hopping mechanism governs the thermoelectric transport in the high temperature region. In addition, Seebeck coefficient data also is well fitted with the phenomenological percolation model. The behavior in thermal conductivity at the transition is ascribed to the local anharmonic distortions associated with small polarons. Specific heat measurement indicates that electron beam irradiation enhances the magnetic inhomogeneity of the system. & 2016 Elsevier B.V. All rights reserved.

Keywords: Manganites Kondo-like behavior Percolation model Electron beam irradiation

1. Introduction Manganese oxides with perovskite structure provide a gateway to study the interplay of various properties such as structural, electrical, and magnetic phases of matter in a strongly correlated system. The perovskite manganites with general formula RE1  xAExMnO3 (where RE and AE are rare-earth and alkaline-earth ions, respectively) have been extensively investigated for more than two decades due to a wide variety of physical properties exhibited in these materials such as superconductivity, colossal magnetoresistance (CMR), ionic conduction, magnetism and dielectric behavior [1–4]. Generally manganites are known to show strong electron correlation. In such systems, spin, charge, orbital, and lattice degrees of freedom are strongly coupled, thereby resulting in various ground states such as ferromagnetic and charge/ n

Corresponding authors. E-mail addresses: [email protected] (A. Rao), [email protected] (Y.-K. Kuo). http://dx.doi.org/10.1016/j.physb.2016.08.053 0921-4526/& 2016 Elsevier B.V. All rights reserved.

orbital ordering states. These ground states have comparable energies so that an external disturbance can easily drive the system from one state to another. This leads to the coexistence of phases with different magnetic and electronic properties. The understanding of the fundamental origin of these ordered phases and their dynamic interplay are still an important scientific challenge. The basic physical principle of manganites is mainly due to the competition between the delocalization effects of the electronic kinetic energy and the localization effects of the Coulombic force of repulsion. When the kinetic energy is dominant, one finds a metallic ground state with ferromagnetic alignment. On the other hand, when the localization effects are dominant, insulating behavior with anti-ferromagnetic ground state is observed. There are few models that can explain the transport mechanism in manganite systems. However, most of them can be only applied to either the ferromagnetic (FM) or the anti-ferromagnetic (AFM) region. In the semiconducting region, the transport mechanism can be explained by Mott's variable range hopping (VRH) model, small polaron hopping (SPH) model, and the adiabatic small polaron

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hopping (ASPH) model [5]. In the metallic region, the transport mechanism is generally governed by the scattering mechanisms such as single magnon, electron-magnon, electron-electron and electron-phonon processes [6,7]. Recently a theoretical percolation model based on phase segregation between metallic and semiconductor regimes has been proposed [8,9]. It is established that such a model could satisfactorily describe various transport properties of manganites in the entire temperature range. Further, the Kondo like upturn observed in resistivity at low temperatures can be addressed using modified percolation model proposed by Dhahri et al. [10]. The theoretical percolation model has also been used to explain the behavior of Seebeck coefficient as a function of temperature [11–14]. However, in the case of Seebeck coefficient, the observed upturn (Kondo like) behavior has not been properly explained using percolation model. Hence, a theoretical attempt on this issue is in order. Among the rare earth based compounds, praseodymium (Pr)based CMR materials are of great interest. The parent compound PrMnO3 exhibits only anti-ferromagnetic insulator behavior whereas Pr1  xAExMnO3 (AE¼ Sr, Ca, Na) exhibits an AFM to FM phase transition. In addition to this, they also show numerous remarkable properties like metal-insulator transition (MI), charge ordering (CO), and phase separation (PS) [6,14–18]. Pr-based manganites are potential candidates for various applications such as resistance random access memories (RRAM) in the next generation of non-volatile memories which has led to dramatic improvements in the data density and reading speed of magnetic recording systems. This is mainly attributed to the bipolar resistive switching (RS) behavior observed in these compounds [19–21]. Various physical characteristics such as electronic, and magnetic properties can be tailored by applying external perturbations like magnetic field, pressure and irradiation [22–29]. The most common method used to crystallize any system is by thermal annealing, but the size of the grains increases during this process and it is perhaps difficult to have control over the grain size of the crystal. Irradiation with energetic particles such as electrons, ions, and neutrons has been one of the better and efficient methods to achieve structural control as a good alternative to thermal annealing [27–29]. Radiation-induced disorder in manganites has been investigated and it is demonstrated that irradiations with electron beam/ion beam change the Mn–O bond lengths and Mn– O–Mn bond angles which can shift the magnetic phase transition temperatures [22–26]. To the best of our knowledge, no studies have been done on the effect of electron beam irradiation on electrical, magnetic and thermal properties of Pr1  xSrxMnO3 compounds. It is well known that Pr1  xSrxMnO3 compounds show different resistivity trends which depends on the value of x. Samples with 0 rx r0.15 are canted anti-ferromagnetic, while a ferromagnetic to anti-ferromagnetic transition is observed for samples with x Z0.2. Hence Pr0.8Sr0.2MnO3 compound is of great interest and there are some reports on magnetic and electrical studies on such a system in the literature [3,30–34]. However, there is no study on thermal properties such as thermal conductivity, Seebeck coefficient, and specific heat for Pr0.8Sr0.2MnO3. In this work, we report a detailed study regarding the effect of electron beam irradiation on the structural, electrical, magnetic and thermal properties of Pr0.8Sr0.2MnO3 samples. In particular, we demonstrated that the theoretical percolation model can successfully explain the electrical and thermoelectric transport mechanism in the entire temperature range for the Pr0.8Sr0.2MnO3 system. 2. Experimental details Polycrystalline samples of Pr0.8Sr0.2MnO3 were synthesized using conventional solid state reaction method. For preparation,

stoichiometric mixture of Pr6O11, SrCO3 and MnO2 powders (99.9% Sigma-Aldrich) was ground and the fine powder was calcined thrice at 1000 °C for 24 h with intermediate grindings. From the same batch of powder, pellets were made with application of identical pressure using a hydraulic press. Then the pellets were sintered at 1300 °C for 36 h and were cooled naturally inside the furnace to room temperature. The electron beam irradiation was carried out in a 10 MeV linac (Linear particle accelerator). The accelerator was operated at beam energy of 7.5 MeV with beam power of 1.5 kW and beam parameters were optimized to deliver uniform surface dose. The irradiation was performed at room temperature for 50 kGy, 100 kGy and 200 kGy. XRD was carried out to analyze the crystal structure and microstructure of crystalline solids using Mini Flex II DESK TOP X-ray Diffractometer which uses Cu-Kα as the source (wavelength, λ ¼1.541 Å). The electrical resistivity of the samples was measured using a conventional four probe technique. The resistivity measurements were carried out in a closed cycle refrigerator as a function of temperature in the range 10–300 K. The magnetic measurements were carried out using a superconducting quantum interference device (SQUID) magnetometer and 9 T PPMS based vibrating sample magnetometer (VSM) (both Quantum Design) in both zerofield-cooled (ZFC) and field-cooled (FC) conditions at external magnetic field of 250 Oe. The hysteresis loops (M versus H) of the samples were also recorded at typical temperatures of 5 K and 300 K. Thermal conductivity and Seebeck coefficient measurements were carried out simultaneously in the temperature range 10–300 K using a direct pulse technique. Both the measurements were performed on a warming cycle. For the thermal conductivity measurements, samples were shaped to rectangular bars of dimensions of about 1.5  1.5  5.0 (mm3). One end of the sample was attached on a copper block, which functioned as a heat sink. A small calibrated chip resistor was fixed at the other end of the sample which acted like a heat source. The temperature gradient was measured using an E-type differential thermocouple fixed directly on the sample which was electrically insulated from the sample. In order to minimize the heat radiation, the temperature difference was controlled to less than 1 K. The Seebeck voltage was detected using a pair of thin Cu wires electrically connected to the sample with silver paste at the same position as the junctions of thermocouple. The elimination of stray thermal emf was achieved by applying long current pulses to a chip resistor that also serves as a heater where the pulses appear as an off-on-off sequence. Specific heat measurements were performed in the temperature range 80–350 K using an ac calorimeter. The details of these thermal measurements are given elsewhere [6,7].

3. Results and discussion 3.1. X-ray diffraction studies The X-ray diffraction data were recorded at room temperature for the pristine and as well as electron beam irradiated samples. It is revealed from Rietveld refinement analysis that all the samples were crystalline and single phased (within experimental limits of XRD) with an orthorhombic distorted structure (Pbnm). Fig. 1 shows the results of Rietveld refinement of the XRD patterns recorded for pristine and irradiated samples. The calculated pattern is in excellent agreement with the experimental data and the final refinements are satisfactory, in which R-factor and χ2 (goodness of the fit) are fairly small. Lattice parameters were calculated from the refinement. As shown in Fig. 2(a), it has been noticed that with increasing dosage of electron beam irradiation, a decrease in cell parameters (a or b or c) is observed for the lower dosage 50 kGy sample while

B. Christopher et al. / Physica B 502 (2016) 119–131

PSMO - Pristine

Intensity Ycalc Yobs-Ycalc Bragg Position

6600

3300

0

20

30

40

50

60

70

5000

2500

0

80

20

30

2 theta (deg) PSMO - 100kGy

Intensity Ycalc Yobs-Ycalc Bragg Position

8000

4000

0

20

30

40

50

60

40

50

60

70

80

2 theta (deg)

70

PSMO - 200kGy

9900

Intensity (arb. unit)

Intensity (arb. unit)

12000

Intensity Ycalc Yobs-Ycalc Bragg Position

PSMO - 50kGy

7500

Intensity (arb. unit)

Intensity (arb. unit)

9900

121

Intensity Ycalc Yobs-Ycalc Bragg Position

6600

3300

0

80

20

30

40

50

60

70

80

2 theta (deg)

2 theta (deg)

Fig. 1. Rietveld refinement plots for XRD data of the Pr0.8Sr0.2MnO3 pristine, 50 kGy, 100 kGy, 200 kGy samples.

they gradually increase for the 100 kGy and 200 kGy samples. Usually irradiation with energetic particles causes two most prominent effects to crystalline solids viz. i) creation of vacancy or point defects of displacement type and ii) excitation related processes involving relaxation of the bond due to strain or rearrangement of unstable bonds [27–29]. The initial decrease in the cell parameters is presumably due to the production of point defects for the lower dosage of 50 kGy sample. For the higher dosage samples, the relaxation of the strain dominates over the effects created by point defects in the Pr0.8Sr0.2MnO3 system. A similar behavior is seen in the case of bond length where the Mn–O bond length which first decreases for the 50 kGy sample, then an increase in bond length is observed for samples with higher dosage of electron beam (Fig. 2(b), red curve). The reason for this trend is the same as explained in the case of lattice parameters. However, we observe that the Mn–O–Mn bond angle of the studied samples increases monotonically with increase in the dosage of electron beam (Fig. 2(b), black curve). The increase in bond angle is possibly because of the strains induced by the EB irradiation [35]. The EB irradiation not only modifies the Mn-O distance and the Mn-O-Mn angle, but also could cause a distortion in the system [28,35,36]. Generally irradiation induces local distortions of the Mn-O-Mn angle in the crystal structure and consequently causes a random distribution of the magnetic exchange interactions [29]. The relaxation due to the induced strain caused by EB irradiation may result in a larger rotation of the MnO6 octahedral. It is clearly evident from the analysis of the presently investigated samples that the relation c < a < b is valid for all the samples, which is a 2

typical characteristic of an orthorhombic system and it is formed by the strong cooperative Jahn-Teller deformation which induces the charge ordering and octahedral distortion [37]. The percentage

of orthorhombic deformation D% can be obtained using the formula [37,38],

D% =

1 3

3

∑n= 1

a n − a¯ × 100 a¯

where a1 = a; a2 = b ; a3 =

(1) c 2

; a¯ =

1 3

( ) . The D% value for the abc 2

pristine sample estimated by using Eq. (1) is found to be 0.11%, and drop to about 0.09% for the irradiated sample with dosage of 50 kGy. With further increase in EB dosage, a gradual increase in D % is noticed (Fig. 2(c), black curve). As mentioned earlier, this parameter is a measure of the MnO6 octahedral distortion and also is a direct consequence of the octahedral tilting. The magnitude of the octahedron tilt φ, φ = tan−1⎡⎣ − 48 × z( OII)⎤⎦ is measured considering the positional parameter z(OII) which is obtained using Rietveld refinement [37]. It may be mentioned that the stacking of the short range Mn–O bonds along the z-direction is mainly responsible for the orthorhombic distortion [39]. The calculated values of φ and z(OII) both follow the same trend as D% which justifies that they are directly related to D%. The observed change in D% clearly indicates the presence of slight distortion in the system due to irradiation and the magnitude of distortion is higher in the sample with high dosage of irradiation. In order to verify the correlation between the structural properties with electrical properties, one-electron bandwidth (W) is estimated, where W is a measure of delocalization of electrons [35,40,41]. One-electron bandwidth is an important parameter in the ABO3 oxide materials for the existence of the charge order orbital tendency. The relative W-value is expressed as,

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5.478

released MnO6 distortion which is a direct consequence of EB irradiation.

7.728

(a)

a b

c

7.726

5.476 7.724

5.474 5.472

7.722

Cell parameter ( )

Cell parameter ( )

5.480

5.470 7.720

0

50

100

150

200

Dosage (kGy) 1.970

(b)

1.965 1.960

129.74

1.955 129.72

1.950 1.945

129.70

Bond angle Bond length

129.68

1.940

Bond length ( )

Bond Angle (deg)

129.76

1.935 1.930

129.66 0

50

100

150

200

Dosage (kGy)

(c)

0.465

231.8 3

0.460 231.6

0.455 0.450

231.4 0.120

D%

Cell Volume ( )

W (meV)

0.470

0.105

V D% W

0.090 0

50

100

150

231.2

1

105

100

90

80

Pristine 50kGy 100kGy 200kGy Fit

60

60

0

40

(2)

where γ is the Mn–O–Mn bond angle and d is the Mn–O bond length. It is observed that for sample of 50 kGy electron beam dosage, W increases slightly. With further increase in EB dosage, W decreases gradually. This implies that the energy of double exchange is weakened as the irradiation dosage is increased [35]. We conclude that the induced insulator to metal transition of Pr0.8Sr0.2MnO3 is driven not only by the Pr doping, but also by the diminishing W due to the widened Mn–O–Mn bond angle and the

20

40 60 T(K)

80

Pristine 50kGy 100kGy 200kGy

20

cos 2 ( π − γ ) d

120

75

Fig. 2. Structural parameters of the Pr0.8Sr0.2MnO3 samples against EB irradiation: (a) lattice constants, (b) bond angles and bond lengths (c) orthorhombic deformation (x-axis), one-electron bandwidth (x-axis) and cell volume (y-axis). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

3.5

The electrical resistivity as a function of temperature ρ(T) is shown in Fig. 3. It is clearly seen from the electrical resistivity data that all the samples undergo transition from the low-T metallic state to high-T insulating state. As the temperature decreases from room temperature, there is an evident hump for all the samples before the metal to insulator transition temperature (TMI), and beyond this ρ(T) curve increases till it reaches the transition temperature; thereafter a metallic behavior is observed. This indicates that the carriers are more localized around the hump region thus preventing the transition at that temperature. It is seen that all samples exhibit a similar T-dependent resistivity, even for the sample with a high dosage of EB irradiation. Such a finding implies that the localization of the charge carrier near the humplike region is robust. The observed reduction in the resistivity below TMI can be attributed to the lack of delocalized carriers that contributes for the metallic nature in the sample. We now explain the effect of irradiation on ρ(T). From Fig. 3, it is evident that resistivity decreases with increase in EB dosage up to 100 kGy. With further increase in EB dosage, resistivity increases. As mentioned earlier, EB irradiation increases the Mn–O–Mn bond angles that leads to an increase in the probability of charge carrier hopping between adjacent Mn3 þ and Mn4 þ sites, which in turn decreases the resistivity [42]. For the 200 kGy irradiated sample, the enhancement in the resistivity can be attributed to the deterioration of the octahedral structure and may as well be due to the increased strain that introduces magnetic disorder and non-magnetic phase fraction to the sample, resulting in the observed increase in resistivity. An upturn is observed in ρ(T) at low temperature (  31 K) for the pristine sample and gets gradually suppressed with irradiation. The origin of the upturn in resistivity can be associated with the competition between the weak localization effect, electron-electron scattering and electron-phonon scattering processes [10]. To understand the nature of the resistivity behavior, various theoretical models can be used. We now explain the low temperature (metallic region) and the high temperature resistivity (insulating region) behavior.

231.0

200

Dosage (kGy)

W∝

3.2. Electrical resistivity

0 0

50

100

150

200

250

300

T(K) Fig. 3. Resistivity versus temperature plot of the pristine and irradiated Pr0.8Sr0.2MnO3 samples. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

B. Christopher et al. / Physica B 502 (2016) 119–131

In case of manganites, general equation used to fit the electrical resistivity data ρ(T) can be given by the well known relation [6,7]

ρ( T ) = ρ0 + ρ2 T2 + ρ4.5 T 4.5

ρ( T ) = ρ0 + ρ1T1/2 − ρs ln T + ρp T 5 + ρ2 T2 + ρ4.5 T 4.5

(4)

where ρ1T indicates the contributions of correlated electronelectron interaction, ρslnT indicates the contributions due to Kondo-like spin dependent scattering, and ρpT5 indicates the resistivity due to electron-phonon interaction [10]. The experimental ρ(T) data of pristine and irradiated Pr0.8Sr0.2MnO3 samples were fitted to Eq. (4) and plots of the best fits are presented in Fig. 4 and the corresponding fitting parameters are listed in Table 1. We observe that by introducing these additional terms the upwards trend in electrical resistivity can be explained using Eq. (4). From the fitting we noticed that the terms ρ1T1/2 and ρslnT are considerably larger than other terms. For example at a particular temperature of about 70 K, the terms the terms ρ1T1/2 and ρsln T are almost 8–10 times larger than the remaining terms. In addition, in view of the goodness of the fit for all the samples suggests that the inclusion of the correlated electron-electron interaction 1/2

Ln(ρ/T) (Ω mm/K)

120 -1.55

110

ρ (Ω mm)

-1.86

100 90

-2.17 -2.48 5.20

80

Table 1 The parameters obtained from low temperature resistivity data and activation energy calculated from high temperature resistivity data.

(3)

where the first term ρ0 is the residual resistivity due to grain boundaries. As the polycrystalline sample contains numerous grains, grain boundaries contribute significantly to the resistivity. The second term ρ2T2 represents the contribution of electronelectron scattering process and is generally dominant up to 100 K [37,43–45]. The last term ρ4.5T4.5 arises due to the combination of electron-electron, electron-magnon and electron-phonon scattering processes [7,45–47]. For the presently investigated samples, the low temperature electrical resistivity data below the TMI was fitted using Eq. (3) and the fitting results are shown in the inset of Fig. 3 (red solid lines). We found that Eq. (3) is insufficient to explain the conduction mechanism in the entire low temperature region. In particular the upturn cannot be explained using the model. In order to explain the origin of the low-T resistivity upturn, the analysis of the data was done using a model which considers electron-electron interaction, electron-phonon interaction, and Kondo-like scattering. The Kondo effect is usually seen in magnetic alloys and has been attributed to the interaction between localized spins of magnetic impurities and the conduction electrons [10]. By considering of these factors, Eq. (3) has been modified as [10]

5.33

5.46

Pristine

50 kGy

100 kGy

200 kGy

ρ0 (Ω mm) ρ1 (Ω mm/K1.5) ρs (Ω mm) ρp (Ω mm/K5) ρ2 (Ω mm/K3) ρ4.5 (Ω mm/K5.5) Eρ (meV) ρα

277.235 95.369 211.201  5.6  10  8  0.0326 7.1  10  7 97.46 4.3  10  4

57.669 11.879 20.485  2.4  10  8  0.007 2.2  10  7 100.28 2.4  10  4

129.346 40.022 79.145  5.6  10  8  0.0198 5.2  10  7 101.54 1.8  10  4

179.682 50.869 110.741  4.2  10  8  0.0298 6.6  10  7 99.52 3.7  10  4

TMI (K)

109.2

118.3

124.3

111.6

and Kondo-like scattering is crucial to explain the low-T resistivity behavior for the Pr0.8Sr0.2MnO3 system. It is well-established that the high-T resistivity (T 4TMI) of manganites is dominated by the hopping motion of the selftrapped small polarons [37,43,48]. In order to explain the resistivity behavior in the high temperature region, we have used the adiabatic small polaron hopping model [37,43,48] which is given by the expression,

⎛ E ⎞ ρ( T ) = ρα T exp⎜ A ⎟ ⎝ kBT ⎠

Pristine 50kGy 100kGy 200kGy Kondo Fit

70 60 50

and ρα =

20

40

60

2kB ρ 3ne2a2υ α

is the residual resistivity. Here e is the electronic

charge, n is the density of charge carriers, a is the site to site hopping distance, and υ is the longitudinal optical phonon frequency. For this model to be valid, a plot of ln (ρ/T) versus 1/T should be a straight line. Inset of the Fig. 4 demonstrates that the SPH model can satisfactorily describe the characteristics of ρ(T) at high temperatures for the Pr0.8Sr0.2MnO3 system. From the theoretical fits, the activation energy values were evaluated and are listed in Table 1. It is found that the activation energy increases with increasing EB irradiation dosage upto 100 kGy, whereas EA decreases with further increase in EB dosage. It should be mentioned here that Eqs. (4) and (5) could not explain the electrical resistivity behavior near the TMI region. In order to understand the transport mechanism in the entire temperature range, Li et al. [8] have proposed a phenomenological model called percolation model which is based on the phase segregation mechanism. The percolation approach assumes that the materials are composed of both paramagnetic insulating and ferromagnetic metallic regions, whereas the semiconductor-like transport properties are exhibited in the paramagnetic region [10,44,49]. Under these considerations, the resistivity for the entire temperature range can be formulated as,

80

100

T (K) Fig. 4. Low temperature fitting of resistivity versus temperature. Inset shows the best fit in the high temperature regime.

(6)

where f is the volume fraction of ferromagnetic domains, and (1  f) is the volume fraction of paramagnetic domains. The volume fractions of paramagnetic and ferromagnetic domains satisfy the Boltzmann distribution

f=

0

(5)

where EA is the activation energy, kB is the Boltzmann constant,

ρ(T ) = ρ FM (T )f + ρ PM (T )( 1 − f )

5.59

1/1000T (K )

123

1 1 + exp

( ) ΔU kBT

(7)

where ΔU is the energy difference between paramagnetic and ferromagnetic states in this percolation approach. To explain the mechanism involved in the electrical resistivity of the entire temperature range can be rewritten as,

124

B. Christopher et al. / Physica B 502 (2016) 119–131

100

60 40

50kGy Fitted Plot

80

ρ (Ω mm)

80

ρ (Ω mm)

100

Pristine Fitted Plot

20

60 40 20

0

0 0

50

100 150 200 250 300

0

T(K)

T(K) 100kGy Fitted Plot

200kGy Fitted Plot

100

60

ρ (Ω mm)

ρ (Ω mm)

80

50 100 150 200 250 300

40 20

80 60 40 20

0

0 0

50 100 150 200 250 300

T(K)

0

50 100 150 200 250 300

T(K)

Fig. 5. Percolation model fit for resistivity data of the pristine and irradiated Pr0.8Sr0.2MnO3 samples.

Table 2 The parameters obtained using percolation fitting of resistivity data.

ρ0 (Ω mm) ρ1 (Ω mm/K1.5) ρs (Ω mm) ρp (Ω mm/K5) ρ2 (Ω mm/K3) ρ4.5 (Ω mm/K5.5) U (K/kB)

TCmod (K) R2 %

Pristine

50 kGy

100 kGy

200 kGy

217.103 87.471 151.816  3.1  10  8  0.089 6.1  10  7 5.4  10  20 172.7

81.747 3.687 2.133  1.3  10  8  0.0217 1.4  10  7 4.1  10  20 140.7

112.411 37.603 41.619  4.8  10  8  0.047 3.1  10  7 4.6  10  20 142.1

135.442 63.784 82.25  4.1 × 10  8  0.072 6.1  10  7 5.8  10  20 160.5

99.8

99.6

99.8

99.8

(

)

ρ(T ) = ρ0 + ρ1T1/2 − ρs ln T + ρp T 5 + ρ2 T2 + ρ4.5 T 4.5 f ⎛ E ⎞ + ρα T exp⎜ A ⎟( 1 − f ) ⎝ kBT ⎠

(8)

For the presently investigated Pr0.8Sr0.2MnO3 samples, we have fitted the experimental data of electrical resistivity to Eq. (8) and the results are shown in Fig. 5. It is apparent that a good agreement between the experimental data and theoretical fit. We thus conclude that the percolation model is valid to explain the electrical resistivity behavior in the entire temperature range. The fitting parameters are tabulated in Table 2. 3.3. Magnetic measurements The temperature dependent magnetization measurements under zero-field-cooled (ZFC) and field-cooled (FC) conditions are

shown in Fig. 6. All the samples show a pronounced magnetic transition from paramagnetic (PM) state to ferromagnetic (FM) state as the temperature decreases from room temperature. With further decrease in temperature, the ZFC magnetization (MZFC) curve diverges from its respective FC magnetization (MFC) curve. The temperature at which the abrupt change in the magnetization curve can be considered as the Curie temperature TC which is attributed mainly to the magnetic ordering of the Mn sublattice [50]. The Curie temperature (TC) of all the samples was calculated from the temperature derivative of the magnetization (dMFC/dT) versus temperature curve and the TC values are summarized in Table 3. We noticed that the irradiation does not have much effect on TC. It can be clearly seen from the ZFC curve that there is a change in the slope of MZFC and this step like interruption is observed at a characteristic temperature denoted by TST which decreases monotonically with dosage of irradiation. Generally, the change in the slope of MZFC or MFC observed at low temperature region occurs putatively due to the ordering of Pr moments. Such ordering of Pr moments has been found to be the characteristic feature of low doped Pr1  xSrxMnO3 and Pr1  xCaxMnO3 systems [14,16,50]. It is also seen from Fig. 6 that, at low temperatures MFC values for pristine, 50 kGy and 100 kGy samples are higher than those of MZFC, a feature commonly observed in all manganites [6,9,51]. However for the sample irradiated with 200 kGy, MFC values are smaller than those of MZFC upto a temperature of about 60 K. With further decrease in temperature MFC and MZFC curves crossover and the value of MFC is again higher than that of MZFC below 60 K. Such an unusual phenomenon is presumably due to the high dosage of EB irradiation that facilitates the magnetic domains to overcome the pinning in the 200 kGy sample. However, this feature is suppressed when the temperature is further decreased due

B. Christopher et al. / Physica B 502 (2016) 119–131

12

-0.66

8

0 100 200 300

T (K)

Pristine

4

ZFC FC

0

0.00

(dM/dT)

-0.33

Moment (emu/g)

0.00

(dM/dT)

Moment (emu/g)

12

125

-0.37

8

-0.74 0

T (K)

4

50kGy ZFC FC

0 0

50 100 150 200 250 300

0

50 100 150 200 250 300

T (K)

T (K) 16

-0.6 0

8

100 200 300

T (K)

100kGy

4

ZFC FC

0

0.00

(dM/dT)

-0.3

12

Moment (emu/g)

(dM/dT)

0.0

Moment (emu/g)

100 200 300

-0.33

12

-0.66 0

8

100 200 300

T (K)

200kGy

4

ZFC FC

0 0

50 100 150 200 250 300

0

50 100 150 200 250 300

T (K)

T (K)

Fig. 6. Temperature dependence of magnetization for the pristine and irradiated Pr0.8Sr0.2MnO3 samples.

Table 3 The parameters deduced from the magnetic studies of pristine as well as EB irradiated samples.

μeff ( μB

)

14

Pristine

50 kGy

100 kGy

200 kGy

161.4 53.0 8.57  0.0043 1.9  10  5 5.1

162.0 32.3 8.66  0.0031 1.2  10  5 6.1

162.1 29.9 9.82  0.0046 2.1  10  5 6.2

161.7 16.2 11.88  0.0062 2.8  10  5 6.7

to the pinning of domain walls. To understand the strength of the magnetic coupling in the present system of Pr0.8Sr0.2MnO3 samples, the magnetization data below TC were fitted using the following equation [51]

M (T ) = M (0) − bT

3/2

− cT

5/2

Moment (emu/g)

TC (K) TST (K) M(0) (emu g  1) b (emu K  3/2 g  1) c (emu K  5/2 g  1)

16

12 10 8

Pristine 50kGy 100kGy 200kGy Fit

6 4 2 0 0

30

where M(0) is the magnetization at 0 K and b (∝μB(kB/D) ) and c are constants, and D is the stiffness constant. A typical M-T plot of the Pr0.8Sr0.2MnO3 samples with its fitting curves using Eq. (9) is displayed in Fig. 7 and the best-fit parameters of all the samples in the ZFC modes are listed in Table 3. It is noted from Fig. 2(c) that the value of D is found to increase for low irradiation dosage of the 50 kGy sample. With further increase in EB dosage, D is found to decrease. This finding is correlated with the observed behavior of

90

120

150

T(K)

(9) 3/2

60

Fig. 7. Magnetization fit for the pristine and irradiated Pr0.8Sr0.2MnO3 samples.

the corresponding cell volume. The linear part of the inverse susceptibility data above 200 K is fitted using the Curie-Weiss (CW) law which is given by,

( T − θCW ) 1 H = = M χ C

(10)

126

B. Christopher et al. / Physica B 502 (2016) 119–131

5000

Pristine Fit Curve

4000

H/M (Oe/(emu/g))

H/M (Oe/(emu/g))

5000

3000 2000 1000 0

4000 3000 2000 1000 0

0

50 100 150 200 250 300 Temperature (K)

100kGy Fit Curve

4000

0

H/M (Oe/(emu/g))

H/M (Oe/(emu/g))

50kGy Fit Curve

3000 2000 1000 0

50 100 150 200 250 300 Temperature (K)

200kGy Fit Curve

3000 2000 1000 0

0

50 100 150 200 250 300 Temperature (K)

0

50 100 150 200 250 300 Temperature (K)

Fig. 8. Temperature dependence of inverse magnetic susceptibility measured at H ¼ 250 Oe for the pristine and irradiated Pr0.8Sr0.2MnO3 samples.

where θCW is the CW temperature and C is the Curie constant. Fig. 8 illustrates the behavior of H/M versus T and it is clearly seen that all samples follow the Curie-Weiss law in the paramagnetic state. The effective magnetic moment μeff can be calculated using the equation

μeff μB

=

3kBC NA

(11)

where μB is the Bohr magnetron, NA is the Avogadro's number and kB is the Boltzmann constant. The values obtained from the fit and the values of effective magnetic moment are tabulated in Table 3. The values of fitted parameters for pristine Pr0.8Sr0.2MnO3 sample matches well with the previous reported values [52]. According to the well-known equation [53,54], the theoretical effective paramagnetic moment of Pr0.8Sr0.2MnO3 is given by, theo = μeff

sweeping the magnetic field from þ 70 kOe to 70 kOe and vice versa. It is clearly seen that the magnetization curves of all the samples show a non-saturating behavior even under the application of a high field of 70 kOe. In the high field portion, the nonsaturating magnetization and the small value of susceptibility indicate the contributions from the charge-ordered AFM phase [12].

( (

0.8 μeff Mn3 +

2

))

( (

+ 0.2 μeff Mn4 +

2

))

(12)

where Mn ¼ 4.9μB and Mn ¼3.8μB, respectively. The experimental value of magnetic moment for the pristine Pr0.8Sr0.2MnO3 sample is large as compared to the theoretical value 4.89μB calculated using Eq. (12). This suggests that the itinerant electrons in eg band are much mobile than the holes in narrow t2g band [55] and it can be attributed to the existence of short-range FM interaction above TC. Furthermore, μeff value of the irradiated samples increases with dosage, probably due to the fact that the mobility of electrons in eg band also increases with irradiation. The hysteresis loops of the pristine and the irradiated Pr0.8Sr0.2MnO3 samples measured at 5 K and 300 K are presented in Fig. 9. The magnetization measurements were performed by 3þ



3.4. Seebeck coefficient Temperature dependent Seebeck coefficient S(T) of the Pr0.8Sr0.2MnO3 samples is shown in Fig. 10. It is interesting to note that all samples exhibit only positive S in the entire temperature range of investigation, suggesting that holes are the dominant charge carriers in their thermoelectric transport [56]. The observed S(T) behavior may be attributed to the degree of JT distortion. Under the influence of sufficiently large static JT distortion, the charge carriers normally behave as holes [5,56]. With increasing temperature, the S value smoothly increases as it approaches the characteristic temperature TS and it starts to decrease above TS. There is a slight upturn trend seen in the low temperature region (T o50 K) which is quite similar to the resistivity data at the low temperatures. Such a behavior could be attributed to the Kondo-like scattering process as we discussed in the electrical resistivity section. In this Kondo region, the charge ordered state may coexist with the dynamics FM clusters as deduced from the ZFC magnetization behavior. In order to explain the low temperature behavior, we have used theoretical models similar to electrical resistivity in the FM metallic region which is given by

B. Christopher et al. / Physica B 502 (2016) 119–131

150

Pristine 5K 300K

50

Moment (emu/g)

Moment (emu/g)

100

0 -50 -100 -8 -6 -4 -2

0

2

4

6

100 50

-50 -100

Moment (emu/g)

Moment (emu/g)

150

0 -50 -100 -150

-8 -6 -4 -2 0

2

4

6

0

2

4

6

8

Magnetic Field (T)

5K 300K

50

5K 300K

-150 -8 -6 -4 -2

8

100kGy

100

50kGy

0

Magnetic Field (T) 150

127

8

Magnetic Field (T)

100

200kGy 5K 300K

50 0 -50 -100 -150 -8 -6 -4 -2 0

2

4

6

8

Magnetic Field (T)

Fig. 9. The M-H plots of the pristine and irradiated Pr0.8Sr0.2MnO3 samples at 5 K and 300 K.

75 60

S (μV/K)

where S0 is a constant, S3/2T3/2 is attributed to the magnon drag contribution which strongly influences the low temperature regime and S4T4 is attributed to the spin wave contribution [6,7,11]. For the presently investigated samples, we fitted the experimental S(T) data with Eq. (13) and found that this model alone cannot describe the S(T) data in the low temperature regime. Therefore, it is plausibly to include a term considering Kondo scattering in Eq. (13). For this reason, we have modified the equation which is given by [12,13],

Pristine 50kGy 100kGy 200kGy

45 30

S(T ) = S0 + S3/2T 3/2 + S2T2 + S3T 3 + S4T 4

15 0 0

50

100

150

200

250

300

T (K) Fig. 10. Variation of Seebeck coefficient (S) with temperature for the pristine and irradiated Pr0.8Sr0.2MnO3 samples.

S(T ) = S0 + S3/2T 3/2 + S4T 4

(13)

(14)

where S3T3 is due to the contribution of the phonon drag produced by electron-phonon interaction and S2T2 indicates the contributions due to Kondo-like scattering [12,13]. The S(T) data in the temperature range below TS was fitted to Eq. (14) and is shown in Fig. 11. We observe that by introducing these additional terms, S(T) behavior can be explained using the model represented by Eq. (14). For example at 150 K, the Kondo term S2T2 is almost twice as much as the S4T4 term. In the high temperature region (T4 TS), Seebeck coefficient is mainly governed by polaronic transport since the charge carriers are trapped. As a result, the transport mechanism involves hopping through polarons [12]. Therefore, S(T) in the high temperature region is described by the Mott's polaron hopping model given by [57],

128

B. Christopher et al. / Physica B 502 (2016) 119–131

60

40

S (μ V/K)

S (μ V/K)

60

20

40

20

Pristine Fit

0

50kGy Fit

0 0

50

100

150

200

0

50

60

60

40

40

20 100kGy Fit

0 0

50

100

150

200

T (K)

S (μ V/K)

S (μ V/K)

T (K)

100

150

20 200kGy Fit

0

200

0

50

T (K)

100

150

200

T (K)

Fig. 11. Low temperature fitting of Seebeck coefficient (S) data with inclusion of the Kondo term using the S(T) data of the pristine and irradiated Pr0.8Sr0.2MnO3 samples.

Table 4 Fitting parameters of low temperature and high temperature TEP data of pristine as well as EB irradiated samples.

S0 S1 S2 S3 S4 ES Α TS

1

(μV/K ) (μV/K2) (μV/K3) (μV/K4) (μV/K5) (meV)

Pristine

50 kGy

100 kGy

200 kGy

1.284  0.027 0.0102  1.2  10  4 5.3  10  7 22.06  0.43 154.6

1.091  0.008 0.006  8.5  10  5 3.8  10  7 29.64  0.7 154.7

3.006  0.071 0.018  1.6  10  4 5.9  10  7 35.30  0.89 161.5

1.392  0.006 0.005  7.1  10  5 3.1  10  7 28.47  0.69 160.6

⎤ k ⎡ E S(T ) = B ⎢ S + α⎥ e ⎣ kBT ⎦

is seen to decrease with further increase in EB dosage. A similar trend is also seen in case of activation energy obtained from resistivity data. 3.4.1. Percolation model using Kondo term Since there is a competition between the two mechanisms in the vicinity of TS, Eqs. (14) and (15) cannot explain clearly the S(T) behavior near TS. Hence, Seebeck coefficient behavior near the transition may be described by the percolation model similar to that in analyzing the electrical resistivity data. The percolation model of S(T) for the entire temperature range can be formulated as [14],

S(T ) = SFMM(T )p + ρ PMI (T )( 1 − p) (15)

where ES is the activation energy, e is the electronic charge, and α is a constant of proportionality between heat transfer and kinetic energy of an electron. Here, α o 1 implies the existence of small polarons while for α 4 1 implies the existence of large polarons. From the slope obtained from the linear fit of the 1/T versus S plot as shown in Fig. 11, values of activation energy ES and α were obtained for all the samples and are tabulated in Table 4. The value of α calculated from the fit is less than unity, suggesting that the thermoelectric transport is dominant by small polarons. It is found that ES increases with increase in EB dosage upto 100 kGy, then ES

(16)

where SFMM(T) and SPMI(T) are the contributions to S(T) from the ferromagnetic metallic region and the paramagnetic insulating region, respectively, and p is the metallic volume fraction. The volume fraction of paramagnetic and ferromagnetic domains satisfy the Boltzmann distribution,

p=

1 1 + exp

( ) ΔU kBT

(17)

where ΔU is the energy difference between paramagnetic and ferromagnetic states. Thus, the complete expression for the S(T) in the entire temperature range is rewritten as,

B. Christopher et al. / Physica B 502 (2016) 119–131

50kGy Fitted

60

S (μV/K)

60

S (μV/K)

75

Pristine Fitted

45 30 15

129

45 30 15

0

0 0

50

100

150

200

250

0

300

50

100

100kGy Fitted

250

300

250

300

200kGy Fitted

60

60

S (μV/K)

S (μV/K)

200

T (K)

T (K) 80

150

40 20

45 30 15 0

0 0

50

100

150

200

250

0

300

50

100

150

200

T (K)

T (K)

Fig. 12. Fitting of Seebeck coefficient data using modified percolation model with the inclusion of the Kondo term.

Table 5 Fitting parameters obtained using percolation fitting of TEP data.

TSmod (K)

50 kGy

100 kGy

200 kGy

1.9152  0.094 2.083  3.1 × 10  5 7.1 × 10  7 2.8 × 10  20 173.49

1.8839  0.0015 1.362  9.1 × 10  6 2.8 × 10  7 2.6 × 10  20 190.31

2.7948  0.169 9.438  2.8 × 10  5 9.1 × 10  7 2.5 × 10  20 187.78

1.6597  0.0711 5.202  3.1 × 10  5 5.2 × 10  7 2.9 × 10  20 197.14

16 12 1.28

8

1.20

Pristine 50kGy 100kGy 200kGy

4

(

)

S(T ) = S0 + S3/2T 3/2 + S2T2 + S3T 3 + S4T 4 p ⎤ k ⎡ E + B ⎢ S + α⎥( 1 − p) e ⎣ kBT ⎦

logκ (mW/cmK)

S0 (μV/K ) S1 (μV/K2) S2 (μV/K3) S3 (μV/K4) S4 (μV/K5) U(K/kB)

Pristine

κ (mW/cmK)

1

20

1.12 1.04 160

0 (18)

0

50

100

Pristine 50kGy 100kGy 200kGy Linear Fit

150

200

240

280

T (K)

200

250

300

T (K) By substituting the value of p in Eq. (18), the S(T) data over the entire temperature range can be analyzed. Fig. 12 shows the percolation fitting curves of S(T) for all the samples and the best-fit parameters are summarized in Table 5. The theoretical and the experimental curves are in good agreement, indicative of the percolative nature of the thermoelectric transport in the Pr0.8Sr0.2MnO3 system.

Fig. 13. Temperature dependence of thermal conductivity plots of the pristine and irradiated Pr0.8Sr0.2MnO3 samples. Inset shows the fitting of thermal conductivity data at high temperatures for all the samples.

3.5. Thermal conductivity In order to further elucidate other distinct features of these materials, we have also measured the temperature dependent thermal conductivity κ(T) in the temperature range of 10–300 K

B. Christopher et al. / Physica B 502 (2016) 119–131

κ ( T ) = κ 0exp( T /T ′)

Pristine 50kGy 100kGy 200kGy

140 120 100

0.015

80 60 40 20

Pristine 50kGy 100kGy 200kGy

0.012 0.009 0.006 0.003 0.000 120

135

0 100

150

200

150

165

T (K)

250

180

195

300

T (K) Fig. 14. Temperature dependence of specific heat for the pristine and irradiated Pr0.8Sr0.2MnO3 samples. The CP values for the samples irradiated with 50, 100 and 200 kGy have been offset by 15, 20 and 30 J/mol K, respectively, from the pristine sample for clarity. Inset shows the plot of ΔCp/T versus T for all the samples.

3.6. Specific heat Fig. 14 shows the temperature dependence of specific heat (Cp) for the pristine and irradiated Pr0.8Sr0.2MnO3 compounds in the temperature range of 80–300 K. For each sample, a weak hump around the characteristic temperature denoted by TCp is identified. From the high resolution specific heat measurements, it was revealed that the transition temperature TCp increases slightly with EB irradiation (see inset of Fig. 14). The specific heat jump (ΔCp), near the transition was estimated by subtracting a smooth lattice background fitted far away from the transitions. The change in entropy ΔS associated with the FM transition is calculated in order to separate the lattice contribution and to obtain the excess specific heat due to magnetic ordering. It can be obtained by integrating the area under ΔCp/T versus T curves (inset of Fig. 14). This plot assumes that S¼0 at T ¼0 (known as zero point entropy) [60]. The estimated values of ΔS together with the corresponding TCp are listed in Table 6. It is noted that the present result of pristine sample is in fair agreement with those reported for some of the similar class of materials [6,7,46]. It is noted that a considerable reduction in the value of ΔS is observed with increasing EB dosage, indicating an increase in magnetic inhomogeneity in the EB irradiated samples [7].

(19)

where κ0 and T′ are the fitting parameters and the obtained values for all samples are listed in Table 6. It is found that T′ increases with increasing dosage of EB irradiation, a direct consequence of the degree of local anharmonic lattice distortions associated with small polarons in the high temperature region. Table 6 The parameters obtained from thermal conductivity and specific heat data.

κ0 (W/m K) T ′(K) ΔS (J/mol K) Tcp (K)

160

ΔCP/T (J/mol K2)

and the results are shown in Fig. 13. Since thermal conductivity measurements may provide valuable information about various scattering processes of thermal carriers, the present data would offer an opportunity to probe the interplay between various scattering processes. It should be mentioned here that the measured values of κ(300 K) are small and are comparable to that of other perovskite manganites [6,46,48]. For a crystalline solid, such a low value of thermal conductivity can be originated from various kinds of disorders present in the lattice. Comparing thermal conductivity data of various perovskites manganites [6,46,48], such a scenario can be attributed to the vibronic interactions of Mn3 þ (Jahn-Teller) ions, which critically limit the mean free path of phonons. At low temperatures, κ(T) increases with temperature and a maximum appears around 30 K for all the samples. Such an observation is a typical feature for the reduction of thermal scattering in solids at low temperatures [48]. The small peak value of thermal conductivity is observed for all the samples at characteristic temperature Tκ below 35 K which is an indication of the crossover from Umklapp scattering to defect limited scattering. With further increase in temperature, κ decreases with temperature essentially due to the enhanced phonon-phonon scattering [37,47,48]. It is wellknown that the total thermal conductivity is a sum of the electronic and lattice contributions. It can be expressed as κ(T)¼ κe(T)þ κL(T), where κe is the contribution of electronic thermal conductivity and κL is due to lattice contributions. The electronic thermal conductivity κe can be evaluated using the standard Wiedemann-Franz (WF) law which is given by, κe(T)ρ(T)¼ LT, where ρ(T) and L (¼ 2.45  10  8 W Ω/K2) are the electrical resistivity of samples and the Lorenz number, respectively. For the presently investigated samples the estimated electronic thermal conductivity (κe) contribution from the Wiedemann-Franz law is much smaller as compared to the total thermal conductivity. Consequently, the predominant contribution to the measured κ comes from the lattice thermal conductivity (κL) with a negligibly small contribution of κe. In the high-temperature insulating state, it can be clearly seen from Fig. 13 that κ displays a characteristic of phonon scattering (dκ/ dT40), which is usually observed in amorphous solids. Such an observation is similar and comparable in magnitude to the case of hole-doped manganites [48,58]. Usually the high-T thermal conductivity of the crystalline insulators is mostly a decreasing function of temperature and the observed increasing function of κ(T) cannot be attributed to high-temperature electron or phonon processes. Such an unusual behavior of κ(T) at high temperatures may be attributed to the local anharmonic lattice distortions associated with small polarons [59], in accordance with the present electrical resistivity and the Seebeck coefficient results. Moreover, to have a quantitative view of the small polarons transport, κ(T) can be expressed as the following equation,

CP (J/mol K)

130

Pristine

50 kGy

100 kGy

200 kGy

2.9879 1223.7 0.2246 151.5

2.7563 1365.6 0.1952 153.9

2.6879 1556.6 0.1476 155.8

2.2479 2222.7 0.1459 157.2

4. Conclusions The XRD studies show that pristine as well as EB irradiated Pr0.8Sr0.2MnO3 samples are single phased and crystallize in orthorhombic symmetry with Pbnm space group. The lattice parameters initially decrease for lower EB dosage (up to 50 kGy), however an increase in lattice parameters is observed for dosages beyond 50 kGy. The EB irradiation also causes an increase in bond angle which enhances charge ordering due increase in distortion in the system. The conduction mechanism in the insulating region can satisfactorily explained using SPH model and the metallic region can be explained using a theory based on Kondo-like spin dependent scattering and other electron scattering mechanisms. The electrical transport mechanism in the entire temperature range has been effectively elucidated using the percolation model.

B. Christopher et al. / Physica B 502 (2016) 119–131

All the samples exhibit a FM-PM transition and EB irradiation seems not to have an appreciable effect on TC. Mechanism responsible for Seebeck coefficient at high temperatures was explained using SPH model and the low temperature anomalous S(T) behavior has been described using a theory based on the Kondo effect and electron-electron and electron-phonon interaction. Specific heat measurement clearly indicates that EB irradiation effectively increases the magnetic inhomogeneity of the Pr0.8Sr0.2MnO3 system.

Acknowledgments The authors acknowledge Department of Atomic Energy, Board of Research in Nuclear Sciences (DAE-BRNS), Government of India for financially supporting this work (2011/34/22/BRNS). The authors are grateful to Raja Ramanna Centre for Advanced Technology Indore, Madhya Pradesh, India for providing electron beam irradiation facility. The magnetic and thermal measurements are supported by the Ministry of Science and Technology of Taiwan under Grant no. MOST 103-2112-M-259-008-MY3 (Y.K.K.). One of the authors (B.C.) thanks Dr. Sudha D. Kamath, Ms. Akshatha and Mr. Vinod, Department of Physics, MIT, Manipal for their valuable suggestions.

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