Giant magnetoresistance and correlation between critical behavior and electrical properties in a new compound La0.6Gd0.1Sr0.3Mn0.8Si0.2O3 manganite

Accepted Manuscript Giant magnetoresistance and correlation between critical behavior and electrical properties in a new compound La0.6Gd0.1Sr0.3Mn0.8Si0.2O3 manganite Ah. Dhahri, E. Dhahri, E.K. Hlil PII:

S0925-8388(17)32814-1

DOI:

10.1016/j.jallcom.2017.08.086

Reference:

JALCOM 42843

To appear in:

Journal of Alloys and Compounds

Received Date: 21 April 2017 Revised Date:

12 July 2017

Accepted Date: 10 August 2017

Please cite this article as: A. Dhahri, E. Dhahri, E.K. Hlil, Giant magnetoresistance and correlation between critical behavior and electrical properties in a new compound La0.6Gd0.1Sr0.3Mn0.8Si0.2O3 manganite, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2017.08.086. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Giant magnetoresistance and Correlation between critical behavior and electrical properties in a new compound La0.6Gd0.1Sr0.3Mn0.8Si0.2O3 manganite

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Ah. Dhahria,b*, E. Dhahrib, E.K. Hlilc. b

Laboratoire de Physique Appliquée, Faculté des Sciences de Sfax, BP 1171, Université de Sfax, 3000, Tunisia.

a

c

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Faculté des Sciences, Monastir, Université de Monastir, Avenue de l'environnement 5019. Monastir, Tunisia Institut Néel, CNRS et Université Joseph Fourier, B.P. 166, 38042 Grenoble, France

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Abstract

We investigated the influence of silicone (Si) doping on the structural, magnetic and electrical properties of polycrystalline sample La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 (LGSMSiO), prepared by sol–gel method. The crystallographic study showed that the sample crystallizes in orthorhombic system with Pnma space group. The relationship between the electrical and

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magnetic properties of manganites was traced through analyzing the dependence of LGSMSiO resistivity on temperature. The measurement of resistivity versus the temperature ρ(T) showed a transition change from ferromagnetic (FM) to paramagnetic (PM) at Curie temperature (TC), this usually accompanied by a simultaneous metal-semiconductor (M-

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semiconductor) transition. Resistivity decreased with increasing the applied magnetic field. The values of TM-semiconductor were found to move towards a high temperature side with

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increasing the magnetic field. The critical properties of electron doped manganite LGSMSiO were investigated on the data of static magnetization measurements around the second order ferromagnetic-paramagnetic transition region TC. The magnetic data analyzed in the critical region using Kouvel-Fisher method yield the critical exponents of γ = 1.013 ± 0.02 with TC = 270.69 ± 0.22 K (from the temperature dependence of inverse initial susceptibility above TC) and β = 0.2535 ± 0.0032 with TC = 269.89 ± 0.12 K (from the temperature dependence of spontaneous magnetization below TC). The critical magnetization isotherm M(TC, µ0H) gives

δ =5.01±0.03. The critical exponents found in this study obeyed the Widom scaling relation: δ = 1+γ/β, implying that the obtained values of γ and β are reliable.

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The exponents values obtained from resistivity were quite close to those predicted by the tricritical mean-field model. These results were in good agreement with the analysis of the critical exponents from magnetization measurements. The electrical resistivity was fitted with the phenomenological percolation model, which is based on the phase segregation of the

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ferromagnetic metallic regions and the paramagnetic semiconductor regions. So, we found that the estimated results were in accordance with the experimental data. The magnetocaloric value is 5.35J/kgK, extracted from the M(µ0H) curves.

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Keywords: Manganites, Metal-semiconductor transition, Resistivity, Critical exponents, Percolation model

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Corresponding author Email address: Dhahridhahri14 @gmail.com Tel: (+216) 20 20 45 55 1. Introduction

As far as manganites are concerned, the discovery of a colossal magnetoresistance and

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magnetocaloric (MC) effects in hole-doped perovskite-type manganites of Re1-xMxMnO3 (Re being trivalent rare earth ions, M = Sr, Ca, Ba) has attracted renewed interest in this class of materials, and numerous papers appeared in which the paramagnetic-ferromagnetic phase

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transition was investigated [1-6]. In the study of the critical behavior associated with this transition there is considerable disagreement among the experimental estimates for the exponent β, associated with the temperature dependence of spontaneous magnetization. For

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example, Ghosh et al [7] experimentally determined β=0.37, δ=4.25 and γ= 1.22 for a single crystal of La0.7Sr0.3MnO3. On the other hand, Mohan et al [8] reported significantly different β=0.5, δ=3.13 and γ= 1.08 values for the polycrystalline La0.8Sr0.2MnO3 sample. The values of the critical exponents estimated by Kim et al. [9] for the La0.75Sr0.25MnO3 single crystal lie between those predicted by 3D Ising and mean-field models. Hence, it is not clear from the existing literature whether the differences observed in the values of the critical exponents reports are due to the difference in composition or a manifestation of the crystalline form (single or polycrystalline) of the samples. Moreover, critical exponents in polycrystalline La0.7Ca0.3MnO3 system are more controversial. While Heffner et al. [4] performed muon spin relaxation measurements which points to a second order transition, neutron diffraction [5] and 2

ACCEPTED MANUSCRIPT magnetization studies [6] indicate that the transition is discontinuous and those which cannot be classified into any universality class ever known [9]. Although a lot of work has been conducted to study the Mn-site doping effects, the critical exponents as very important parameters for magnetic transition are less available for the Mn-site doping. In this study, we carried out a systematic and detailed analysis of the magnetization measurement of LGSMSiO

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polycrystalline sample near the ferromagnetic–paramagnetic phase transition temperature. We have also determined the critical temperature TC and the critical parameters β and γ. Then, we have tried to investigate the critical behavior in LGSMSiO at its semiconductor–metallic transition via the measurements of resistivity. The values of these exponents obtained from

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resistivity are very close to those predicted by the tricritical mean-field model. Finally, we intend to study the dependence of the electrical resistivity properties as a function of the LGSMSiO, volume fraction, f , which is analyzed in the framework of the percolation theory.

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A percolation model based on the mixed phase consisting of itinerant electrons and localized magnetic polarons has been proposed to explain the observed results. 2. Experimental details

The microstructure of ceramic materials in general and the colossal magnetic resistance

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(CMR) materials in particular was highly affected by the preparation routes and heat treatments. Sol-gel routes are a recognized methods to produce high quality, homogenous and fine particle materials. This method, based on citric acid as complexing agent, is very effective for the synthesis of our samples. High purity of precursors La(NO3)3,6H2O;

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Sr(NO3)2,6H2O; Mn(NO3)2,4H2O, Gd(OOCCH3)3.xH2O and SiCl4 were used as starting materials. The solution prepared by dissolving stoichiometric amounts of the precursors’

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powder in deionized water was heated to 90°C under constant stirring to eliminate the excess water and to obtain a homogenous solution. Ethylene glycol (EG) (1:1; EG:CA) and citric acid (CA) (CA: Metal ion molar ratios of 1, 2 or 3) were used as polymerization/complexation (PC) agents. After getting a sol-gel by slow evaporation, a gelating reagent, ethylene glycol was added and heated between 140 and 190 °C to get a gel. The gel was dried at 300 °C and sintered at 600 °C for 7h to give a fine powder. Then, the obtained powder was pressed into circular pellets and finally sintered in air at 800°C for 10h. X-Ray diffraction of the powders was carried out at room temperature using a Siemens D5000 X-ray diffractometer with a graphite monochromatized CuKα1 radiation (λCuKα = 1.540598Å). The data were collected in the 2θ range 9-99° with a step size of 0.0167° and a 3

ACCEPTED MANUSCRIPT counting time of 18s per step. This system is able to detect up to a minimum of 3% of impurities according to our measurements. The structural refinement was carried out by Rietveld analysis of the XRD powder diffraction data with a FULLPROF software [10]. The microstructure was observed by a scanning electron microscope (SEM) using a Philips XL30 and semi-quantitative analysis was performed at a 20 kV accelerating voltage using energy

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dispersive X-ray analyses (EDX). Magnetic measurements were performed by using BS1 and BS2 magnetometer developed in Louis Neel Laboratory at Grenoble. In fact, the internal field used for the scaling analysis has been corrected for demagnetization, µ 0 H=µ 0 H appl -Da M , where Da is the demagnetization factor obtained from M vs. µ 0H measurements in the low-

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field linear-response regime at a low temperature. To obtain the metal-insulator transition temperature (TM-semiconductor ) and to study the influence of the magnetic field on resistivity, the electrical resistivity and magnetoresistance measurements were done by standard dc four-

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probe technique using a closed cycle helium refrigerator cryostat in applied fields of 0 T to 5 T. 3. Results and discussion

3.1. Structural analysis and microstructure

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Figure.1.shows the x-ray diffraction patterns of LGSMSiO , at room temperature. The sample is single phase without detectable secondary phase, within the sensitivity limits of the experiment (a few percent). The structure refinement was performed in the orthorhombic setting of Pnma (Z=4) space group (N°62), in which the (La/Gd/Sr) atoms are at 4c(x, 0.25,

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z)position, (Mn/Si) at 4b(0.5,0,0); O(1) at 4c(x,0.25, z) and O(2) at 8d(x, y, z). In contrast, x = 0, 0.10 and 0.15 samples are crystallized in the R3 c rhombohedral structure [11].

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Table 1 summarizes the relevant structural parameters obtained by Rietveld analysis of the powder XRD pattern. This table also reported the residuals for the weighted pattern Rwp, the pattern Rp, the structure factor RF and the goodness of fit χ2. The tolerance factor, which is the geometric measure of size mismatch of perovskites: t = ( r( La /Gd / Sr ) + rO ) / ( r( Mn / Si ) + rO ) 2 is

equal to 0.94, which is in the stable range of the perovskite structure 0.89 < t < 1.02 [12]. From the reflection of 2θ values of XRD profile, we can also calculate the average grain size (SG) from the XRD peaks using Scherer formula: SG =

Kλ , where β is the breadth of the β cos θ

observed diffraction line at its half intensity maximum, K is the so-called shape factor ( = 0.9) 4

ACCEPTED MANUSCRIPT and λ is the X-ray wavelength used. The value of SG is 35 nm. The average size of the particle of this sample is determined using the Scanning Electron Microscope (SEM) images by finding the minimum and maximum dimensions of the large number of particles (seen in the inset of figure. 1). The value is 102 nm. The grain sizes observed by SEM were larger than those calculated by Scherrer’s formula. This can be explained by the fact that each particle

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observed by SEM is formed by several crystallized grains. In order to check the existence of all elements in this sample, energy dispersive X-ray analysis (EDAX) was carried out at room temperature. EDAX spectrum represented inset figure.1 reveals the presence of La, Gd, Sr, Mn, Si and O elements, which confirms that there is no loss of any integrated elements during

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the sintering within experimental errors. The typical cationic composition for this sample is represented in Table 2. This measurement confirmed the cationic composition of this sample

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and the absence of secondary phases in the X-rays. 3.2. Magnetic and magnetocaloric properties Figure. 2

shows temperature dependence of the field-cooled (FC) and zero-field-cooled

(ZFC) magnetizations (M–T curves) for LGSMSiO under an applied field of 0.05 T. The figure exhibts that the magnetization values, which were quite stable at temperatures below

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217 K for x = 0.20, began to decrease rapidly at the phase transition temperature TC. A small separation between the ZFC and FC curves exists at the so-called irreversibility temperature of 205 K. This phenomenon is observed in many magnetic materials [13, 14] and is assigned to the existence of an isotropic field generated from ferromagnetic (FM) clusters [15]. The

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transition temperature TC (defined as the temperature at which the dM/dT versus T curve reaches a minimum which was determined from the M =f( T) curve, insets, figure. 2) is found

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to be 271 K.

In order to clarify the nature of the FM–PM phase transition, we measured the magnetic-field dependence of magnetization at different temperatures (M–µ0H–T), around Curie temperature TC. Figure. 3 shows the evolution of magnetization versus the applied magnetic field obtained at different temperatures (isothermal magnetization). Obviously, the M(µ0H) curves were found to increase with decreasing temperature in the selected temperature range, where thermal fluctuation of spins decreased with decreasing temperature. The M2 versus µ0H/M should appear as straight lines in the high field range in the Arrott plot. The intercept of M2 as a function of µ0H/M on the µ0H/M axis is negative/positive below/above the Curie temperature (TC). The line of M2 versus µ0H/M at TC should cross the origin. According to the 5

ACCEPTED MANUSCRIPT criterion proposed by Banerjee [16], the order of the magnetic transition can be determined from the slope of the straight line: the positive slope corresponding to the second-order transition while the negative slope to the first-order one. Inset of figure. 3 shows the Arrott plot of M2 versus µ0H/M for LGSMSiO around TC. The

phase transition is a second-ordered one.

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positive slope of the M2 vs. µ0H/M relation indicates that the ferromagnetic-paramagnetic

According to a thermodynamic Maxwell’s relation, the isothermal entropy change can be given by means of magnetic measurements: µ0 H max

0

 ∂M    d ( µ0 H )  ∂T  µ0 H '

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∆S M ( T , µ0 H ) = S M (T , µ0 H ) − S (T , 0 ) = ∫

(1)

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Where M denotes magnetization. The magnetic entropy changes, ∆SM, are calculated from Mµ0H isotherms using Eq.(1). Figure.4 illustrates the magnetic entropy change of LGSMSiO as a function of temperature and the external field change. The maximum ∆SM of LGSMSiO is 1.11, 2.15, 3.21, 4.27, 5.35 J/kg.K for external field change from 1, 2, 3, 4, 5T respectively. The large magnetocaloric effect in perovskite manganites could originate from the spin-lattice

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coupling in the magnetic ordering process [17].The strong coupling between spin and lattice was shown by the observed lattice changes accompanying magnetic transitions in these manganites [18]. The lattice structure changes in the dMn/Gd/Sr-O bond distance as well as in the θMn/Gd/Sr-O-Mn/Gd/Sr bond angle, would in turn favor the spin ordering. Then, a more abrupt

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variation of magnetization near the magnetic transition occurs and results in a large magnetic entropy change. On the other hand, magnetic refrigerants are desired to have not only a large

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∆SM but also a large refrigerant relative cooling power(RCP) determined as a product of the peak value of the entropy change ∆SM and the full width at half maximum of ∆SM(T) and is written as[19]: RCP = − ∆S Mmax δ TFWHM , where ∆S Mmax and δ TFWHM are the maximum of the entropy variation and the full-width at half-maximum in the temperature dependence of the magnetic entropy change ∆SM. The RCP(s) value being about 180J/kg for a sample studied, may be compared with 176J/kg at 293K as reported for La0.7Ca0.1Pb0.2Mn0.85Al0.075Sn0.075O3[20].

4. Critical parameters determined from magnetization data According to the scaling hypothesis, the critical behavior of a magnetic system showing a second-order magnetic phase transition near the Curie point is characterized by a set of 6

ACCEPTED MANUSCRIPT critical exponents, β (the spontaneous magnetization exponent), γ ( the isothermal magnetic susceptibility exponent) and δ ( the critical isotherm exponent). Mathematically, the scaling hypothesis suggests the following powder-law relation near the critical region defined by [21]:

M s (T ) = lim( M ) = M 0 ε , ε < 0, T < TC β

(1)

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µ0 H → 0

 h0  γ  ε , ε > 0, T > TC  M0 

χ 0−1 (T ) = lim( µ0 H / M 0 ) =  µ0 H → 0

M = D ( µ0 H )

1/ δ

(2)

, ε = 0, T = TC

(3)

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Where M0, h0 and D are the critical amplitudes, and ε = (T − TC)/TC is the reduced temperature. Ms (T), χ0-1 (T) and H are the spontaneous magnetization, the inverse initial susceptibility and the demagnetization adjusted applied magnetic field, respectively.

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Another independent way to determine the exponent β and γ is available as well. It uses the scaling theory, which predicts the existence of a reduced equation of state given by: M ( µ 0 H , ε ) = ε β f ± ( µ0 H / ε γ + β )

(4)

Where f + for T > TC and f − for T < TC are regular analytical functions and ε is the reduced TC

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temperature ε = T − TC [22]. This equation implies that for the scaling relations and right β

choice of β, γ and δ values, the scaled M / ε plotted as a function of the scaled H / ε

β+ γ

will

fall in tow universal curve, one above TC and the other below TC.

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We determined the values of the critical exponents of LGSMSiO sample from the magnetization data versus temperature and magnetic field M (µ0H, T), to understand their

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magnetic and magnetocaloric properties. Experimental results revealed that this sample exhibits a continuous (second-order) paramagnetic (PM) to ferromagnetic (FM) phase transition. In mean field theory at near TC, M2 versus µ0H/M at various T should form a progression of parallel straight lines. The line for T = TC passes through the origin on this plot. Moreover, the intersections of these curves for T > TC with the µ0 H / M axis gave the values of 1/ χ0 (T ) at µ0H = 0T. In the present case, all curves in the Arrott plot are nonlinear, and show an upward curvature even in the high-field region, which indicates that the meanfield theory ( β = 0.5, γ = 1 and δ = 3) (inset figure. 3) characteristics of systems with longrange interactions is not valid for the present phase transition. In order to evaluate the critical behavior of the present sample in the vicinity of both the TC’s, the initial isothermal M-µ0H 7

ACCEPTED MANUSCRIPT data (figure. 3) were recorded as functions of the increasing magnetic field and temperature at close (3K) temperature intervals. These data show that the magnitude of magnetization decreased with increasing temperature. Therefore, the values of M S (T ) and χ 0−1 (T ) were determined using a modified Arrott plot (MAP). In this technique, the M=f(µ0H) data are

relationship [23]: 1/ γ

 µ0 H     M 

1/ β

T − TC  M  = +  T'  M '

( 5)

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converted into series of isotherms( M 1/ β = f ( µ0 H / M )1/γ ) depending on the following

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In the high-field region, the effects of charge, lattice and orbital degrees of freedom are

suppressed in a ferromagnet, and the order parameter can be identified with the macroscopic

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magnetization [24]. Three kinds of trial exponents of the 3D- Heisenberg model

( β = 0.365, γ =1.336 and δ = 4.80 ) , the tricritical mean- field model ( β = 0.25, γ =1and δ = 5) and 3D-Ising model ( β = 0.325, γ = 1.241 and δ = 4.82 ) are used to make a modified Arrott plot, as shown in figure.5(a)-(c). All the three models yield quasi-straight lines in the high-field region. It is difficult to determine which one is better between the three models. Thus, the S (T ) in order to distinguish which model is S (TC = 271K )

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relative slope (RS) is defined as RS =

better to describe this system. The RS of the most satisfactory model should be the one close to 1 mostly for the reason that the modified Arrott plots are a series of parallel lines. As

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shown in figure.5(d), the RS of 3D- Heisenberg and 3D-Ising model deviate from the straight line of RS = 1 but RS of tricritical mean- field model is close to it. The critical properties of

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LGSMSiO sample can be described with tricritical mean- field model. Thus, in figure 5(b), the linear extrapolation from high field region to the intercepts with the axes ( M )

1/ β

and

1/ γ

 µ0 H    yield the reliable values of spontaneous magnetization Ms(T,0) and inverse  M  susceptibility χ 0−1 (T , 0 ) , respectively. These values as function of temperatures Ms(T,0) versus T and χ 0−1 (T , 0 ) versus T, are plotted in figure.6(a). According to Eqs.(1) and (2), the experimental data(solid circles) can be fitted to two new values of β = 0.257 ± 0.003 with

TC = 269.89 ± 0.12 K and γ = 1.013 ± 0.02 with TC = 270.69 ± 0.22 K . These results are very

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ACCEPTED MANUSCRIPT close to the critical exponent of tricritical mean-field model. Alternately, these critical exponents and TC can be obtained more accurately from the Kouvel-Fisher(KF) method[25] M s (T ) T − TC = dM s / dT β −1 0

(T ) / dT

=

T − TC

(7)

γ

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dχ

χ 0−1 (T )

(6)

According to this method, Ms(dMs/dT)-1 versus temperature and χ 0−1 ( d χ 0−1 / dT )

−1

with slopes

1/β and 1/γ, respectively. When these straight lines are extrapolated to the ordinate equal to zero, the intercepts on T axis just correspond to TC (figure.6(b)). The fitting results with

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Kouvel-Fisher method give the exponents and TC to be of β = 0.2535 ± 0.0032 with

TC = 269.89 ± 0.12 K and γ = 1.013 ± 0.02 with TC = 270.69 ± 0.22 K . Obviously, the obtained

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values of the critical exponents and TC using the Kouvel-Fisher method are in agreement with those using the modified Arrott plot of tricritical mean-field model. The values of another critical exponent, δ can be determined according to Eq.(3). The isotherm magnetization at TC = 271K is given in figure.6(c), and the inset of figure.6(c) plots the log-log scale. The ln(M)-ln(µ0H) relation yields a straight line in the higher-field

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range(µ0H > 1T), and the slope is 1/δ. Thereby, the third exponent δ = 5.01 ± 0.12 is obtained. These three critical exponents obey the Widom scaling relation [26]: δ = 1 +

γ . Thus, we β

have δ = 4.99 from figure.5(a) and δ = 4.97 from figure.5(b), They are both close to the one

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obtained from isothermal magnetization at TC. This proves that the obtained critical exponents are reliable.

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Next we compare our data with the prediction of the scaling theory. In the critical region, the magnetic equation of state is given by: M ( µ0 H , ε ) = ε β f ± ( µ0 H / ε γ + β ) . This equation implies

that the M ε

−β

, as a function of µ0 H ε

−( β + γ )

, produces two universal curves: one for

temperature above TC and the other for temperature below TC. Using the value of γ and β obtained by the Kouver-Fisher method, the scaled data for our sample is plotted in figure.6(d). All the points fall on two curves, one for TTC. This suggests that the value of the exponents and TC are reasonably accurate. On the other hand, the universality class of the magnetic phase transition depends on the range of the exchange interaction J(r) in homogeneous magnets [3, 27]. Fisher et al [27] have 9

ACCEPTED MANUSCRIPT performed a renormalization group analysis of systems with an exchange interaction of the form J ( r ) =1 / r

−( d + σ )

, where d is the spatial dimension, σ > 0 is the range of the interaction.

For the three-dimensional material (d = 3), there holds the relation J ( r ) =1 / r −( 3 + σ ) with 3/2 ≤ σ ≤ 2. When σ = 2, the Heisenberg exponents ( β = 0.365, γ = 1.336 and δ = 4.80 ) are valid for

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the three-dimensional isotopic ferromagnet, i.e., J(r) decreases faster than r-5. When σ = 3/2, the mean- field exponents ( β = 0.5, γ = 1 and δ=3.0) are valid, which indicates that J(r)

decreases slower than r-4.5. In the intermediate range of 3/2 ≤ σ≤ 2, the FM behavior belongs to different universality classes depending on σ.

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5. Electrical properties

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5. a. Magnetoresistance property

Figure. 6(a) shows resistivity measurements as a function of temperature at different magnetic fields of 1 to 5 T for the LGSMSiO sample. The value of TM-semiconductor for the sample varies with the applied field, suggesting that transport properties can be tuned by the external magnetic field. The results in Figure. 6(a) show that TM-semiconductor increases with the increase of applied filed. Still there is another significant result that we are interested in the

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magnetoresistance properties in our sample which are related to the reduction of the electrical resistivity of the material by applying a magnetic field. The percentage of the resistivity reduction (MR%) is calculated by using the formula

MR % =

∆ρ

ρ

=

ρ ( µ0 H = 0 ) − ρ ( µ0 H ) × 100 ρ ( µ0 H = 0 )

where

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ρ(µ0H = 0) is the zero field resistivity and ρ(µ0H) is the resistivity under external magnetic field of 5 T. The MR dependence of the temperature is shown inset Figure. 7(b) under the

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magnetic fields of 5 T. These curves show the presence of peaks around the semiconductor– metal transition temperature. The value of MR% is around 89.9%, which is higher than that found in other manganite oxides [28, 29]. The strong increase of the MR (%) value at the temperatures much lower than TC, T<
ACCEPTED MANUSCRIPT metal-semiconductor transition, and assigning of one of these models to second order systems have been extremely useful for better understanding the nature of phase transition. Depending on Fisher-Langer theory [30], specific heat at a constant pressure (Cp) and at the phase transition temperature is proportional to the temperature derivative of the resistivity at

 dρ   dρ  CP ∝   = η −α  =  η dT d     where α is

the

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T= TM −Semiconductor. . The thermal derivative of the resistivity is given by Fisher-Langer as:

(8)

specific

heat

critical

exponent,

Cp

is

the

specific

heat

and

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η = [T − TM −Sc / TM −Sc ] is the reduced temperature. The two power law forms of equation (4) below and above TM-semiconductor given by Geldert et al [31] are:

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 1 dρ  A + C (T ) =  [(−η ) −α − 1] + B + for T < TM − Semiconductor . =  ρ (TC ) dT  α

 1 dρ  A − −α ' − C (T ) =   = ' [(−η ) − 1] + B for T > TM − Semiconductor .  ρ (TC ) dT  α

(9)

(10)

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where A and B are constants, α and α’ are specific heat critical exponents below and above TM-semiconductor .The temperature derivative of resistivity normalized with respect to its value at TM-semiconductor [(1 / ρ (T C )(dρ / dT )] against η is shown in figure. 8 (b) for LGSMSiO sample and the equations (5) and (6) are fitted below and above TM-semiconductor at the same figure. The

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solid lines passing through the data are the best fits in the two regions. The values of constants A, B and the specific heat critical exponents below and above TM-semiconductor (α and α’) are

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obtained from the fitting analysis for the sample (present work) and the values of other manganites are listed in table 3 for comparison. It is clear from Table 3 that the specific heat critical exponents for LGSMSiO sample (α and α’) are found to be 0.454 which agrees well with that obtained using tri-critical mean-field model [32]. The specific heat critical exponents for Co doped sample (α and α’) are found to be -0.115 and this value is consistent with that obtained using 3D-Heisenberg model. For the Cr doped samples, the plots below and above TM-semiconductor are agreement with the values of 0.001 close to the mean field theory, suggesting long range ferromagnetic order [33].

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ACCEPTED MANUSCRIPT In addition, other critical exponents β and γ are calculated from the Suezaki-Mori model [34] which relates the temperature derivative of the electrical resistivity to the reduced temperature ( η ) magnetic ordering as follows: for T > TM − semiconductor

dρ  − (α + λ ) / 2 − α + γ −1) + B− η (  dt  = − Bg η

(11)

for T < TM − semiconductor

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dρ  − (α +γ −1)  dt  = B+ η

(12)

where the constants B+ and B- incorporate the term involving the zone boundary energy gap

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Bg and [(T − TM − semiconductor ) / TM − semiconductor ] is the reduced temperature, as already denoted.

Ln(

dρ ) = (α + γ − 1) Ln(η ) dt

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Taking natural logarithm on both sides, equation (7) can be rewritten as: for T > TM − semiconductor

(13)

The slope of ln(dρ/dT) versus ln(η ) plot gives the value of ( α + γ − 1 ). As α is obtained from the fit with Fisher-Langer method, we can obtain the value of γ .

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Figure 8 (c) shows ln(dρ/dT) vs ln(η ) above TM −semiconductor and gives the value of α + γ − 1 for LGSMSiO sample. The slope is estimated to be 0.504 ± 0.001. Substituting the value of α (derived from the figure in this relation), the critical exponent γ was obtained with a value equal to 1.041 ± 0.003.The first term in equation (8) involving Bg will be dominant at

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temperatures less than TM-semiconductor because the scaling law gives (α + γ ) / 2 − (α + γ − 1) = β . As done earlier, the equation (8) can also be rewritten by taking natural logarithm on both

Ln(

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sides as:

dρ ) = ((α + γ ) / 2) − (α + γ − 1)) Ln(η ) dt

for T < TM − semiconductor

(14)

Using the scaling relation, ( ([α + γ ] / 2) − (α + γ − 1) ) is equal to the value of the critical exponent β . Hence, the direct slope of the plot ln(dρ/dT) versus ln( η ) below TM-semiconductor will give β value. Figure 8(d) presents ln(dρ/dT) versus ln(η ) below TM-semiconductor for LGSMSiO sample and the value of slope is obtained as β = 0.2525±0.0018. The critical exponents are determined for LGSMIO (present work) and theoretical models are listed in Table 4. 12

ACCEPTED MANUSCRIPT Finally, one can note that Rushbrooke scaling relation α + 2 β + γ = 2 (theory) which gives 2.006 for LGSMSiO sample is also satisfied [35]. Generally, for LGSMSiO, the exponents’ values obtained from the resistivity are very close to the ones predicted from the tri-critical mean-field model. These results are in agreement with the analysis of critical exponents from the magnetization measurements. This study shows a descriptive report of the correlation

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between magnetic and electrical transport properties. In light of this qualitative agreement, a strong correlation between electrical and magnetic properties in manganite of LGSMSiO type near the phase transition temperature is proved.

In order to understand the transport mechanism in our sample, we will use the theoretical

SC

model describing it. Many scattering mechanisms such as electron-magnon, electron-electron, magnon-magnon, and electron-magnon scattering processes were proposed to explain the low

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temperature electrical behavior (T< TM-semiconductor). In the high temperature (T> TM-semiconductor) region, thermal activation process, hopping motion of small polaron (SPH) and variable range hopping mechanism, ect, were fitted. In the metallic conducting temperature region (T< TM-semiconductor), the metallic resistivity can be represented as [36]:

ρ (T ) = ρ 0 + ρ 2T 2 + ρ 4.5T 4.5

where ρ0 arises from grain or domain boundaries, grains boundary, ρ2T2 term represents the

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electrical resistivity due to the electron-electron scattering process and is generally dominant up to 100K[37], ρ4.5T4.5 is a combination of electron-magnon, electron-electron and electron phonon scattering processes[38]. Meanwhile, the conductivity in the high temperatures

EP

(T > TM-semiconductor), paramagnetic phase insulating phase can be described by the adiabatic small polarons hopping mechanism (ASPH), according to the following formula:[39]:

Ea ) k BT

(15)

AC C

ρ (T ) = ρα T exp(

where Ea is the activation energy and kB is the Boltzmann constant.

6. Percolation model None of the mentioned models can explain the prominent change of the ρ-T curves near

TM-semiconductor , which is based upon an approach that the system consists in phase separation between ferromagnetic metallic and paramagnetic insulating regions. Li et al. [40] proposed that in CMR materials, a metallic conductivity exists in the ferromagnetic regions and that a 13

ACCEPTED MANUSCRIPT semiconductor-like conductivity above TC exists in the paramagnetic regions. In such a phase–foliated system, the metal-insulator transition is a percolation phase transition and the behavior of ρ (T ) can be explained on the basis of the percolation theory In order to elucidate the transport mechanism in the entire temperature region, we attempt to fit the experimental ρ-T data according to phenomenological percolation approach. Under this

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scenario, the resistivity for the entire temperature range can be expressed as [40]:

ρ (T ) = f ρ FM + (1 − f ) ρ PM

where ƒ and (1- ƒ) are the volume fractions of ferromagnetic domains and paramagnetic regions, respectively and are given as: 1  ∆U  1 + exp    k BT 

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(16 )

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f=

and

(17)

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 ∆U  exp   k BT   1− f = 1  ∆U  1 + exp    k BT 

Where ∆U is the difference in energy between the FM and PM states. It may be expressed as   . In this expression U0 is taken as the energy difference for temperature well  

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 T ∆U ≈ U 0 1 − mod  T C 

below TCmod ( TCmod is a FM-PM transition temperature used in the model and near/equal to TC). The total ρ(T) can be represented as:

AC C

ρ (T ) = f ( ρ 0 + ρ 2T 2 + ρ 4.5T 4.5 ) + (1 − f ) ρα T exp(

Ea ) k BT

(18)

The total (ρ ) can be represented as: ρ (T ) = f ( ρ 0 + ρ 2T 2 + ρ 4.5T 4.5 ) + (1 − f ) ρα T exp(

14

Ea ) k BT

ACCEPTED MANUSCRIPT

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   T     −U 0 1 − mod     TC     exp      k BT     Ea  1    2 4.5 ρ (T ) = ( ρ0 + ρ 2T + ρ4.5T ) . + ρα T exp( )  k BT     T  T   U 1 U 1 − − − −  0  0    TCmod   TCmod        1 + exp 1 + exp     k BT k BT            

This equation (18) can be used to examine our data over the whole temperature range both

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above and below TC. The solid line in figure.9 shows the fitting results for the ρ-T curves obtained at 0, 2 and 5T for the sample. The best fit parameters for all samples are given in

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table 5. Goodness of fit between the experimental and calculated data is evaluated by calculating the χ2 value for each fit. It can be found 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 for all samples. As a result, TCmod is close to the TM-semiconductor. These agreements confirm that FM domains and PM regions coexist near TM-semiconductor. It is clear from the table that the activation energies Ea are found to decrease with increasing

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magnetic field and the observed behavior may be attributed to the decrease in the values of charge localization under the influence of magnetic field [41]. It is seen that the volume fraction ƒ is equal to one (FM phase) well below the Curie temperature and slowly

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approaches to zero (PM phase) as the temperature increases. The transition from FM to PM state takes place slowly over a wide temperature range. This observation confirms the validity of the percolation model in the presently studied system. The temperature dependence on the

AC C

volume concentration of the ferromagnetic phase f is shown in figure 10. It is clear that f (T) remains equal to 1 below the metal– semiconductor transition temperature, which confirms the strong dominance of the FM fraction in this range. Then, the FM volume fraction begins to decrease to 0 from the ferromagnetic metallic state to a paramagnetic-semiconductor state, confirming the validity of the percolation approach which assumes a conversion from ferromagnetic to paramagnetic regions. 7. Conclusion To conclude, we have investigated many physical properties of La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 (LGSMSiO) manganite. We have found a large magnetocaloric effect, the maximum ∆SM is 15

ACCEPTED MANUSCRIPT arround 5.35 J/kg.K for 5T and a giant magnetoresistance of 89.9% at 5T field, which is higher than that found in other manganite oxides. We have examined the critical behavior of resistivity in LGSMSiO sample under different applied magnetic fields. The estimated critical exponents are ( β = 0.2535±0.0032; γ = 1.013±0.002 and α =0.454). The estimation of critical exponents suggests the short-range ferromagnetic order by having the tricritical mean-field

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model in agreement with the analysis of critical exponents from magnetization measurements. The conduction mechanism was explained by a small polaron hopping in the insulating region, and by electron scattering mechanisms in the metallic region. Then, to understand the transport mechanism in the entire temperature range, we have used the phenomenological

SC

percolation model, which is based on the phase segregation of ferromagnetic metallic clusters

AC C

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M AN U

and paramagnetic semiconductor regions.

16

ACCEPTED MANUSCRIPT References [1] Salamon M.B and Jaime M 2001 Rev. Mod. Phys.73(2001) 583. [2]S.E. Lofland, V. Ray, P.H. Kim, S.M. Bhagat, M.A. Manheimer, and S.D. Tyagi, Phys. Rev. B 55 (1997) 2749. [3] K. Ghosh, C.J. Lobb, R.L. Greene, S.G. Karabashev, D.A. Shulyatev, A.A. Arsenov, and

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Y.M. Mukovskiy, Phys. Rev. Lett. 81 (1998) 4740. [4] R.H. Heffner, L.P. Le, M.F. Hundley, J.J. Neumeier, G.M. Luke, K. Kojima, B. Nachumi, Y.J. Uemura, D.E. MacLaughlin, and S-W. Cheong, Phys. Rev. Lett. 77 (1996) 1869. 3

[5] J.W. Lynn, R.W. Erwin, J.A. Borchers, Q. Huang, A. Santoro, J-L. Peng, and Z.Y. Li,

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Phys. Rev. Lett. 76 (1996) 4046.

[6] J. Mira, J. Rivas, F. Rivadulla, C. Vázquez-Vázquez, and M.A. López-Quintela, Phys. Rev. B 60 (1999) 2929.

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[7] K. Ghosh, C.J. Lobb, R.L. Greene, S.G. Karabashev, D.A. Shulyatev, A.A. Arsenov, and Y.M. Mukovskiy, Phys. Rev. Lett. 81(1998) 4740. [8] Mohan Ch. V, Seeger M, Kronmuller H, Murugaraj P and Maier J, J. Magn. and Magn. Mater. 183(1998) 348. [9] D. Kim, B.L. Zink, F. Hellman, J.M.D. Coey, Phys. Rev. B 65 (2002) 214424.

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[10] H.M. Rietveld, J. ppl. Crystallogr. 2 (1969) 65-71.

[11] Ah.dhahri, E.Dhahri, E.K.Hlil, J. Alloys and Compnds, 700, ( 2017)169-174. [12] Xiaming Liu, Xiaojun Xu, and Yuheng Zhang, Phys. Rev. B 62(2000)15112 s.

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[13] D.N.H. Nam, R. Mathieu, P. Nordblad, N.V. Khiem, N.X. Phuc, Phys. Rev. B62 (2000) 1027.

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[14] D.N.H. Nam, K. Jonason, P. Nordblad, N.V. Khiem, N.X. Phuc, Phys. Rev. B59 (1999) 4189. [15] M.S. Kim, J.B. Yang, Q. Cai, X.D. Zhou, W.J. James, W.B. Yelon, P.E. Parris, D. Buddhikot, S.K. M alik, Phys. Rev. B 71 (2005) 014433. [16] S.K. Banerjee, Phys. Lett. 12 (1964) 16. [17] M.-H. Phan, S.-C. Yu, N. H. Hur, and Y.-H. Yeong, J. Appl. Phys. 96 (2004) 1154. [18] P. G. Radaelli, D. E. Cox, M. Marezio, S.-W. Cheong, P. E. Schiffer, and A. P. Ramirez, Phys. Rev. Lett. 75(1995) 4488. [19] Ah. Dhahri, M. Jemmali, E. Dhahri, M.A. Valente, J. Alloys and Compds, 638( 2015)221-227.

17

ACCEPTED MANUSCRIPT [20] Khadija. Dhahri, N.Dhahri, J.Dhahri, K. Taibi and E.K. Hlil, J.Alloys and Compds, 699(2017)619-626. [21] M.E. Fisher. Rep Prog Phys 30, (1967), 615. A.K. Pramanik, A. Banerjee Physical Review B 79, (2009), 214426.

[23] Arrott A. and Noakes J. E., Phys. Rev. Lett., 19(1967) 786.

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[22] S. N. Kaul, J. Magn. Magn. Mater. 53(1985)5.

[24] Fan J., Ling L., Hong B., Zhang L., Pi L. and Zhang Y., Phys. Rev. B, 81 (2010) 144426. [25] J. S. Kouvel and M. E. Fisher, Phys. Rev. 136, (1964) A1626.

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[26] Kadanoff L. P., Physics, 2 (1966) 263.

[27] Fisher M. E., Shang-Keng M. and Nickel B. G.,Phys. Rev. Lett., 29 (1972) 917.

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[28] N. Zaidi, S. Mnefgui, A. Dhahri, J. Dhahri, E.K. Hlil, J. Alloys. Compds 616 (2014) 378–384. [29] K. Cherif, Arwa. Belkahla, J. Dhahri, E.K. Hlil, Ceramics International 42 (2016) 10537–10546. [30] M. E. Fisher and J. S. Langer, Phys. Rev. Lett. 20 (1968) 665. [31] D J W Geldart and T G Richard, Phys. Rev. B 12 (1975) 5175.

Lett. 89 (2002) 227202.

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[32] D. Kim, B. Revaz, B. L. Zink, F. Hellman, J. J. Rhyne and J. F. Mitchell, Phys. Rev.

[33] R. Thiyagarajan, S. Esakki Muthu, G. Kalaiselvan, R. MahendiranArumugam, J. Alloys. Comp 618 (2015) 159-166

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[34] Y. Suezaki and Y. Mori, J.Prog.Theoret.Phys. 41 (1969) 1177

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[35] Igor Herbut, Cambridge University Press Science (2007) [36] E. Tka, K. Cherif, J. Dhahr, E. Dhahri, J.Alloys and Compds 509 (2011) 8047–8055. [37] P.T. Phong, N.V. Khiem, N.V. Dai, D.H. Manh, L.V. Hong, N.X. Phuc,J. Magn. Magn. Mater. 321 (2009) 3330-3334. [38] G.J. Synder, R. Hiskes, S. DiCarolis, M.R. Beasley, T.H. Geballe, Phys. Rev. B 53 (1996) 14434-14444. [39] Y.Moritomo, H.Kuwahara, Y.Tomioka, Y.Tokura, Phys.Rev.B.55(1997)7549. [40] G. Li, H.D. Zhou, S.L. Feng, X.-J. Fan, X.G. Li, J. Appl. Phys., 92 (2002) 1406 [41] S.Bhattacharya, R.K.Mukherjee, B.K.Chaudhuri, H.D.Yang, Appl.Phys.Lett.82 (2003)4101. 18

ACCEPTED MANUSCRIPT [42] H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena _Oxford University Press, London, 1971, Chap. 12.4, p. 200.

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[43] K. Huang, Statistical Mechanics, 2nd ed. Wiley, New York, 1987, Chap.17.6, p. 432.

19

ACCEPTED MANUSCRIPT Table legend Table 1:Room-temperature structural parameters(x-ray Rietveld refinement) for orthorhombic Pnma manganite. The numbers in parentheses are estimated standard deviations to the last significant digit. Biso: the isotropic Debye-Waller factor. Agreement factors of profile Rp and weighted profile Rwp. χ2: the goodness of fit.

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Table 2: Results of EDAX analysis of La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 sample.

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Table 3: Values of different parameters used to fit the experimental data to equations (9) and (10). Table 4: Estimated critical exponents for La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 and theoretical models

Table 5: Obtained parameters from the best fit to the Eq. (18) of the experimental data of

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M AN U

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 sample at 0, 2 and 5 T.

20

ACCEPTED MANUSCRIPT Figures captions: Figure. 1. X-ray diffraction pattern (solid curve) and Rietveld refinement result (open symbols) for

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 at room temperature. The difference between the data and the calculation is shown at the bottom. Inset EDAX spectrum for La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 and the typical SEM.

Shows

temperature

dependences

of

ZFC

and

FC

magnetization

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Figure.2.

for

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 compounds under a magnetic field of 0.05 T. Inset shows the differential of field-cooling M-T curve. The inset indicates the plot of dM/dT curve for

Figure.3.

Magnetic

isotherms

measured

at

SC

determining TC.

different

temperatures

for

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 sample close to the Curie temperature (TC = 271 K). Isothermal

M AN U

magnetization in the temperature range under a magnetic field up to 5 T. Inset shows the Arrot plot (M2 vs. µ0H/M) of La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 compound. Figure.4. Temperature dependence of magnetic entropy change under different external fields

for La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 compound. Figure.5.

Modified Arrott plots: isotherms of M1/βvs.(µ 0H/M)1/γ with (a) 3D-Heisenberg

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model ( β = 0.365, γ = 1.336 and δ = 4.80 ) , model ( β = 0.25, γ = 1 and δ = 5 ) ,

tricritical

mean-field

(c) 3D-Ising model ( β = 0.325, γ = 1.241 and δ = 4.82 ) , and

S (T ) . S (TC = 271K )

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(d) RS vs. temperatures: RS =

(b)

Figure.6. (a) The spontaneous magnetization MS(T, 0) and the inverse initial susceptibility

AC C

1 / χ 0 as a function of a temperature, respectively for the LGSMSiO sample. (b) Kouvel– Fisher plots for the spontaneous magnetization MS(T, 0) and the inverse initial susceptibility

1 / χ 0 (T ) . The solid lines are the linear fits. (c) Isothermal M vs µ 0H plot of LGSMSiO at TC = 271 K; the inset shows the same plot in log-log scale and the solid line is the linear fit. (d) Scaling plots M|ε|−βvs. µ 0H|ε|−(β+γ), indicating two universal curves below and above TC for LGSMSiO sample. Inset shows the same plots on a log–log scale.

Figure.7. Variation of resistivity as function of temperature of the LGSMSiO under 0 to 5 T. Inset the magnetoresistance percentage MR% under 5T.

21

ACCEPTED MANUSCRIPT Figure. 8(a): The thermal derivative of resistivity normalized with respect to resistivity value

at TC for LGSMSiO.(b): The thermal derivative of resistivity normalized with respect to resistivity

value

at

TM-semiconductor,

as

a

function

of

reduced

temperature

[η= (T-TM-semiconductor)/TM-semiconductor] LGSMSiO. (c):ln(dρ/dT) versus ln [(T- TM-semiconductor)/ TM-semiconductor] below TM-semiconductor for LGSMSiO under 5 T. (d):ln(dρ/dT) versus ln [(T- TMTM-semiconductor] above TM-semiconductor for LGSMSiO under 5 T.

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semiconductor)/

Figure. 9: The temperature dependence of electrical resistivity of the LGSMSiO sample under

different magnetic fields applied. Symbols are the experimental results and solid lines are the

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graphs fitted by Eq. (18).

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Figure. 10: Variation of the volume fraction of the FM phase f versus. T.

22

ACCEPTED MANUSCRIPT Tableau.1 Pnma

a(Å)

5.4412 (1)

b(Å)

7.6702 (4)

c(Å)

5.4612 (3)

V(Å3)

227.92

La/Gd/Sr

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Cell parameters

Space group

0.0028(3)

x

0.0041(1)

z Biso(Å2) Mn/Si

Biso(Å2)

(O1)

0.19(1)

x

0.4733(2)

y

0.976(1)

Biso(Å2)

1.56(3)

x

0.28(1)

y

0.0021(4)

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(O2)

z

0.771(2)

Biso(Å2)

1.86(6)

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dMn-O1 (Å)

Structural parameters

Agreement factors

0.29(5)

M AN U

Atoms

SC

LGSMSiO

1.965(4)

θMn-O1-Mn (°)

159.21(3)

dMn-O2 (Å)

1.963(1)

θMn-O2-Mn (°)

167.70(1)

(Å)

1.964(1)

<θ θMn-O-Mn>(Å)

163.45(3)

Rp (%)

4.55

Rwp (%)

1.98

RF (%)

3.78

χ2

1.77

23

ACCEPTED MANUSCRIPT Table 2

Element

Typical cationic composition

Wt.%

At.%

Nominal

composition

0.568

33.876

11.361

Gd

0.101

6.886

2.021

Sr

0.332

12.452

6.640

Mn

0.801

18.205

16.022

Si

0.202

8.979

4.043

AC C

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M AN U

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La

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from EDX

24

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3

ACCEPTED MANUSCRIPT Table 3 Samples

Region

A

B

α

Ref.

T< TM-semiconductor

-0.00226±6.8E-5

-0.0058±1.41E-5

0.454

This work

T> TM-semiconductor

0.0098±0.0003

0.0031±8.4E-4

T< TM-semiconductor

0.00238 ±0.001

1.02438 ±0.012

T> TM-semiconductor

- 0.00572±0.000597

T< TM-semiconductor

-0.00219±1.52451E-4

SC

-0.01109±3.69503E-4

25

0.463

This work

-0.115

[38]

0.941 ±0.00471

-0.115

[38]

3.20123 ±0.15264

0.001

[38]

-0.00493 ±4.72716E-4

0.001

[38]

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T> TM-semiconductor

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PCMCrO

AC C

PCMCoO

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LGSMSiO

ACCEPTED MANUSCRIPT Table 4

γ

β

δ

Ref.

-

This work

Materials

α and α '

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3

0.454(T< TM-

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3

0.463(T> TM-semiconductor)

Pr0.6Ca0.4Mn0.96Co0.04O3

-0.115

0.336±0.04

Pr0.6Ca0.4Mn0.96Cr0.04O3

0.001

0.502±0.03

3D-Heisenberg model

-0.115

0.365±0.003

1.336±0.004

4.8±0.04

[42]

Mean field model

0

0.5

1.0

3.0

[42]

Ising model

0

0.325±0.002

1.241±0.002

4.82±0.02

[42]

Tricritical mean-field theory

0

0.25

1.0

5.0

[43]

0.2525±0.0032

1.041±0.003

-

This work

1.304±0.02

-

[38]

1.192±0.01

-

[38]

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M AN U

SC

-

-

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semiconductor)

26

ACCEPTED MANUSCRIPT

Table 5

ρ 0 (Ω.cm)

ρ 2 (Ω.cm/K2) ρ4.5(Ω.cm/K2)

ρα (Ω.cm)

Ea k B (K )

0T

0.0016

9.26E-6

5.56E-13

4.89 E-7

2879

2T

0.0013

8.22E-6

4.71E-13

2.41 E-7

1529

5T

0.0057

7.21E-6

3.64E-13

2.21 E-7

1197

273

0.9997

5521

270

0.9995

5337

269

0.9998

SC

5637

M AN U TE D EP AC C 27

2 ∆U / k B ( K ) TCmod ( K ) R

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µ0H (T)

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ACCEPTED MANUSCRIPT

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Figure.1

28

ACCEPTED MANUSCRIPT

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35

ZFC FC

25

20 0,1

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0,0

15

-0,1

10

-0,2

-0,3

-0,4

-0,5

5

TC=271K

-0,6 0

50

100

150

200

T(K)

0 0

M AN U

dM/dT(emu/gK)

Magnetization(emu/g)

30

50

100

250

300

150

350

400

200

250

TE D

Temperature(K)

AC C

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Figure 2

29

300

350

400

ACCEPTED MANUSCRIPT

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50

Tc=271K

30

1800

T=243K

1600

20

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1400

2

1200

M2(emu/g)

Magnetization(emu/g)

40

10

TC=271K

1000 800 600

T=298K

M AN U

400 200

0 0,00

0

0,05

0,10

0,15

0,20

0,25

µ0H/M(T.g/emu)

0

1

2

3

4

5

6

TE D

µ0H(T)

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EP

Figure.3

30

7

8

9

10

ACCEPTED MANUSCRIPT

6

µ0H=1T

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5

µ0H=2T

µ0H=3T µ0H=4T µ0H=5T

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3

2

1

0 200

225

M AN U

−∆ SM(J/kg.K)

4

250

275

TE D

T(K)

AC C

EP

Figure.4

31

300

325

ACCEPTED MANUSCRIPT

3D-Heisenberg β=0.365

a

2500000

1/β (emu/g)

15000

1/β

TC=271K

1500000

TC=271K

1000000

M

10000

500000

5000 0 0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

3D-Ising β=0.325 γ=1.24

90000

c

80000

0,25

1,10

TE D

50000

TC=271K

40000 30000 20000

0,05

0,10

EP

10000

0,15

0,20

0,25

0,30

0,35

1,00 0,95 0,90 0,85 0,80

1/δ 1/δ (T,g/emu)

µ H/M) 0

RS

1,05

60000

AC C

1/β (emu/g)

0,20

1/δ 1/δ µ H/M) (T,g/emu) 0

Mean-field Tricritical mean-field 3D-Heisenberg 3D-Ising

d

1,15

70000

1/β

0,15

1,20

100000

M

0,10

M AN U

1/δ 1/δ (µ0H/M) (T,g/emu)

0 0,00

0,05

SC

0 0,00

Tricritical mean field β =0.25 γ=1

2000000

20000 1 /β 1/β M (emu/g)

b

γ=1.336

RI PT

25000

300

310

320

330

T(K)

Figure.5

32

340

350

360

0,30

0,35

ACCEPTED MANUSCRIPT

TC = (268.47±0.12) K

30

TC = (270.69 ± 0.22) K γ = (1.0126 ± 0.02)

β = (0.2535±0.0032)

10 250

260

270

280

290

-80

T (K)

230

240

250

TE D

3,6

20 3,4

15 10

3,2

3,0

0

δ = 5,01

2,8 -1

260

270

0

1

-5 1

2

3

4

AC C

0

280

T>T c

0

T>Tc

10

1 1

0

µ0H (T)

1000

10

33

100

µ0H/εβ+γ (T)

2000

µ0H/εβ+γ (T)

Figure. 6

300

T
50

5

290

d

100

2

4

TC = 271 K

T
100

Ln (µ0H)

6

γ = (1.013± 0.001)

150

EP

5

M/ε β(emu/g)

25

Ln (M)

Magnetization (emu/g)

200

c

12

T(K)

M/ε β (emu/g)

TC=271K

3000

1000

4000

−1 −1 −1

14

8

β = (0.255±0.03)

d

30

16

TC = (270.45±0.005) K

250

35

18

10

TC = (269.88±0.02) K

-120

0,00 310

300

20

b

-60

-100

0,02

240

-40

M AN U

20

0,04

-20

χ0 (dχ0 /dT ) (K)

0,06

−1

40

−1

0,08

Ms (dMs/dT ) (K)

Ms(T, 0) (emu/g)

a

50

22

Experimental data Fitting data

0

0,10

χ0 (T.g/emu)

60

RI PT

0,12

Experimental data Fitting data

SC

70

ACCEPTED MANUSCRIPT

1,6

RI PT

a 90

1,4

µ0H=2T

80

µ0H=5T

70 60

MR(%)

1,2

50 40

20

b

SC

1,0

10

0

0

µ0H = 0T

0,8

100

200

300

400

500

T(K)

0,6

M AN U

ρ (Ω. .cm)

30

µ0H = 5T

0,4 0

100

200

300

400

Figure.7

AC C

EP

TE D

T (K)

34

500

600

700

0,006

0,006

a

b µ0H=5T

0,004

0,004

0,000

Linear Fit

-0,002

M AN U

-0,002

SC

1/ρ (T=Tc).dρ /dT

0,000

-0,004

-0,004

-0,006

-0,006 100

200

300

-6,95

-7,25 -7,30 -7,35

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

η

γ=1.041±0.003

-4,0

β = 0,2525±0,0032

-4,5 Ln(dρ/ dT)

TE D

-7,20

EP

-7,15

Above TM-Sc

-5,0 Below TM-Sc

-5,5 -6,0

c

-6,5

AC C

-7,10

-0,4

-3,5

-7,00 -7,05

-0,6

400

T(K)

Ln(dρ /dT)

1/ρ (T=Tc).dρ /dT

µ0H=5T

0,002

0,002

RI PT

ACCEPTED MANUSCRIPT

-1,85 -1,80 -1,75 -1,70 -1,65 -1,60 -1,55 -1,50 -1,45 Ln(η )

d

-7,0 -4,0

-3,5

-3,0

-2,5

Ln( η )

Figure.8

35

-2,0

-1,5

RI PT

ACCEPTED MANUSCRIPT

1,4

SC

µ0H = 5T µ0H = 2T

1,2 1,0

Fit

0,8

0,4

100

200

300 T(K)

Fig.9

AC C

EP

0

TE D

0,6

M AN U

ρ (Ω, cm)

µ0H = 0T

Figure.9

36

400

500

1,0 µ0H=2T

SC

0,8

µ0H=5T

0,6 0,4 0,2 0,0 150

200

250

T(K)

Figure.10

AC C

EP

TE D

100

M AN U

volume fraction ( f )

µ0H=0T

RI PT

ACCEPTED MANUSCRIPT

37

300

ACCEPTED MANUSCRIPT

EP

TE D

M AN U

SC

RI PT

La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 sample are prepared using sol-gel technique. The compound crystallizes in the orthorhombic system with Pnma space group. The sample exhibit PM–FM phase transition. La0.6 Gd0.1 Sr0.3 Mn0.8 Si0.2 O3 exhibit a large MR value.

AC C

• • • •