Structural, magnetocaloric, electrical properties and theoretical investigations in manganite La0.67Sr0.1Ca0.23MnO3 type perovskite

Accepted Manuscript Structural, magnetocaloric, electrical properties and theoretical investigations in manganite La0.67Sr0.1Ca0.23MnO3 type perovskite Za. Mohamed, Mounira Abassi, E. Tka, J. Dhahri, E.K. Hlil PII: DOI: Reference:

S0925-8388(15)01426-7 http://dx.doi.org/10.1016/j.jallcom.2015.05.122 JALCOM 34238

To appear in:

Journal of Alloys and Compounds

Received Date: Revised Date: Accepted Date:

28 March 2015 12 May 2015 14 May 2015

Please cite this article as: Za. Mohamed, M. Abassi, E. Tka, J. Dhahri, E.K. Hlil, Structural, magnetocaloric, electrical properties and theoretical investigations in manganite La0.67Sr0.1Ca0.23MnO3 type perovskite, Journal of Alloys and Compounds (2015), doi: http://dx.doi.org/10.1016/j.jallcom.2015.05.122

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Structural, magnetocaloric, electrical properties and

in

manganite La0.67Sr0.1Ca0.23MnO3 type perovskite

Za. Mohameda, Mounira Abassia, E. Tkaa, J. Dhahria, E.K. Hlilb a

Laboratoire de Physique de la matière condensée et des nanosciences, Faculté des Sciences,

5019, Université de Monastir, Tunisia. b

Institut Néel, CNRS et Université Joseph Fourrier, B.P. 166, B.P.W-38042 Grenoble Cedex

9, France. *Corresponding author E-Mail: [email protected] Tel.:+216 73 500 278

Abstract The structural, magnetocaloric and electrical properties of La0.67Sr0.1Ca0.23MnO3 (LSCMO) perovskite have been studied. The sample was prepared by conventional solid-state ceramics route. X-ray diffraction revealed that the compound is in the rhombohedral phase with an

R3 c space group. Magnetization as a function of temperature under 1, 2, 3, 4 and 5 T magnetic fields showed that the sample exhibits a transition from a ferromagnetic (FM) to paramagnetic (PM) phase with increasing temperature. Magnetic entropy change, relative cooling power and specific heat for magnetic field variation were predicted with the help of the phenomenological model. The maximum of the magnetic entropy change SMmax and large relative cooling power (RCP) values in a magnetic field change of 5 T are found to be 5.971 Jkg-1K-1 and 278.547 Jkg-1, respectively at 294 K. It is suggested that LSCMO sample is a suitable candidate as a refrigerant at near room temperature region. Moreover, the dependence of electrical resistivity on temperature shows a metal–semiconductor transition at TM-Sc for LSCMO. The electrical resistivity is fitted with the phenomenological percolation model which is based on the phase segregation of ferromagnetic metallic clusters and paramagnetic insulating regions. Hence, we found that the estimated values of resistivity are in good agreement with experimental data.

Keywords: Phenomenological model; Magnetocaloric effect; Entropy change; Percolation model.

1

1. Introduction Manganites Re1-xAxMnO3 (Re = La, Pr, Nd and A = Ca, Sr, Ba) are the focus of contemporary research activity in order to understand their complex phase diagram, metal insulator transition and most importantly colossal magnetoresistance (CMR) [1-3]. The magnetocaloric effect (MCE, i.e. the magnetic entropy change) is another important physical diagram. It results from the spin-ordering (i.e. ferromagnetic ordering) and is induced by the variation of the applied magnetic field. MCE is crucial for the technology of magnetic refrigeration. It has some advantages over gas refrigeration such as, low noise, softer vibration, longer usage time, absence of Freon, etc. Perovskite manganites with the same CMR and MCE are often observed around the ferromagnetic ordering transition temperature (TC) [4-6]. Among these compounds, La1-xSrxMnO3 compounds are given particular attention. This is thanks to their interesting

magnetic

properties

such

as

colossal

magnetoresistance

(CMR)

and

magnetocaloric effect [7, 8]. In addition to this, the strontium-substituted manganites show their ferromagnetic (FM)-paramagnetic (PM) transition (TC) well above room temperature compared to their Ca counterpart [9]. When the Re site is doped with a divalent ion, a proportional number of Mn3+ ions are converted into Mn4+ ions and mobile eg electrons are introduced, which led to mediating the ferromagnetic interaction according to a double





4 3 1 exchange between Mn3+ and Mn4+ with electronic configuration 3d , t 2g  e g , S  2 and

3d , t 3

3 2g



 e0g , S  3 / 2 respectively. The magnetic properties of the perovskite manganite

phase are strongly affected by the Mn–O bond length and Mn–O–Mn bond angle controlled by the ionic radii of A and B sites and Mn3+/Mn4+ ratio which modifies the double exchange and super exchange interactions [10]. Generally, manganese oxides exhibit a metal– semiconductor transition accompanied by a FM–PM transition near the Curie temperature TC. The metallic behavior is usually described in terms of electron scattering process and electron–phonon interaction [11]. But in the semi-conductor state, the carriers are localized as small polarons due to the strong Jahn Teller distortion. Some models can explain the transport mechanism in manganites. However, most of them are only applied to fit the prominent change of the ρ-T curves in a finite temperature region (above or below TC). In order to explain the transport mechanism in the whole temperature range, Li et al. [12] developed a new model based on the mechanism of phase segregation [4]. Such a model supposes that the materials are composed of paramagnetic and ferromagnetic regions. Following this mechanism, the electrical resistivity at any temperature is determined by the change of the volume fractions of both regions. In the present study, we investigate the structure, the magnetic properties and magnetocaloric effect of La0.67Sr0.1Ca0.23MnO3 compound, which can be a suitable candidate as a working 2

substance in magnetic refrigeration at near room temperature.

In addition, the analyses of resistivity based on the percolation theory were successfully used to explain the transport mechanism in the whole temperature range.

2. Experimental details In this paper, La0.67Sr0.1Ca0.23MnO3 is denoted as LSCMO. The sample was prepared using a conventional solid state reaction method. Pure (≥ 99.99%) raw powders with appropriate amounts of La2O3, SrCO3, CaCO3 and MnO2 were thoroughly ground and mixed, then pressed into pellets. These were calcined at several processing steps with increasing temperatures from 900°C to 1200°C and with intermediate grindings and pelletizations. The product was then sintered at 1400°C for 12 h in ambient atmosphere. The obtained sample was characterized by X-ray diffraction patterns (measured by a Siemens D5000 with CuKα radiation). The phase analysis was carried out using FULLPROF software based on Rietveld method [13]. Magnetization as a function of temperature M(T) and isothermal magnetization M(µ0H, T) were performed using an extraction magnetometer. The magnetocaloric effect was estimated in terms of isothermal magnetic entropy change ( S M ) using M-µ0H-T data and Maxwell’s relation [14]: S M (T , 0 H)  

0 H max

0

 M (T , 0 H)    d ( 0 H ) T   0 H

(1)

where S, M, µ0H and T are the magnetic entropy, magnetization of the material, the applied magnetic field and the temperature of the system, respectively. The relative cooling power (RCP) was calculated using the relation [15]: RCP   ΔSM  T  dT T2

T1

(2)

where T1 and T2 are the temperatures of hot and cold sinks which correspond to the full width at half maximum (FWHM) points. The material with a larger RCP value usually represents a better magnetocaloric substance due to its high cooling efficiency.

3

To obtain the metal-semiconductor transition temperature (TM-Sc), measurements of the electrical resistivity were done by a standard dc four-probe technique using a closed cycle helium refrigerator cryostat over a temperature range 5-400K. 3. Results and discussions 3.1. Structural properties The powder X-ray diffraction patterns of the polycrystalline LSCMO collected at room temperature is shown in Fig.1. From this figure, we can see that the sample is single phased without any detectable secondary phase, within the sensitivity limits of the experiment. The structure refinement was performed in the hexagon of the rhombohedral structure with a space group R3 c , in which La/Ca/Sr atoms are at 6a (0,0,1/4) position, Mn at 6b (0,0,0) and O at 18e (x,0,1/4) position. The structural parameters are refined by a standard Rietveld technique [13] and the fitting between the experimental spectra and the calculated values is relatively good, taking into consideration the low values of 2. Detailed results of the refinement are listed in Table 1. In order to quantitatively discuss the ionic match between A and B sites in perovskite compounds, a geometrical quantity, Goldschmidt tolerance factor (tG), is usually introduced and tG is defined as [16]: tG 

 2



rA rB

 rO



 rO



where  r A  ,  rB  and  rO  are the average ionic radii of A, B and oxygen, respectively in the perovskite ABO3 structure. Oxide-based manganite compounds have a perovskite structure if their tolerance factor lies in the limits of 0.75 < t < 1 and in an ideal case the value must be equal to unity. The value of tG was estimated at 0.965 which is within the range of stable perovskite structure. The value of average crystallite size was estimated from the full width at half maximum of Xray diffraction peaks. The effects of synthesis, instruments and processing conditions were taken into consideration while making the calculation of crystallite size. The broadening of Bragg reflections due to micro strains was considered to have an angular dependence. This is given by:  strain  4 tan  here  strain is the peak shift due to strain,

 d   is a coefficient related to strain and  is Bragg angle. The micro strains include the  d 



effects of structural defects such as dislocations, stacking faults, twin boundaries and inter 4

growths. The dependence of the size effect is given by Scherer’s formula [17]:  size 

k D cos 

where λ is the wavelength of Cu Kα radiation (λ = 1.5406 Å), k is grain shape factor (for a spherical grain k = 0.89) and D is the thickness of the crystal. In the present investigation, only the prominent peaks were considered. The instrument broadening effect was eliminated by subtracting the values of full width at half maximum (  Si ) from  size at respective Bragg peaks of a standard sample such as silicon. Finally, the complete expression for the full-width at half maximum (FWHM) of the X-ray diffraction peaks is given by [18]:

 hkl 

k  4 tan  D cos 

After plotting βhkl cos θ vs. sin θ (Fig.2), lattice strain was calculated from the slope of the line and the particle size D was calculated from the intersection with the vertical axis. The values of average crystallite size and micro-strain of LSCMO sample are tabulated in Table 1. The particle size, calculated in the present system using Williamson–Hall technique, is larger than the particle size obtained from Debye–Scherer method because the broadening effect due to strain is completely excluded in Debye–Scherer technique [19]. 3.2. Magnetic properties Figure 3 shows magnetization as a function of temperature (M vs. T) measured in an applied field µ0H = 0.05 T. The sample exhibits a paramagnetic (PM) to a ferromagnetic (FM) transition at Curie temperature TC. The latter was identified from the inflection points in the dM/dT vs. T plots (the inset of Fig.3). Fig.4 shows the temperature dependence of the inverse magnetic susceptibility χ-1 of LSCMO at 0.05 T. As for ferromagnetic system, the relation between χ and temperature T should follow Curie-Weiss law in the paramagnetic (PM) region;  

C where χ is the T   CW 

magnetic susceptibility,  CW is Curie-Weiss temperature and C is Curie constant. According to La0.67Sr0.1Ca0.23MnO3 sample, the calculated effective paramagnetic moment should be:

effcal  0.67  eff  Mn3  2  0.33  eff  Mn4  2 where eff Mn3   4.9 B , eff Mn 4   3.87 B [20]. The percentage of Mn3+ and Mn4+ ions in our sample is checked by the conventional chemical technique. First, we dissolve our powder in oxalic acid dihydrate (H2C2O4, 2H2O) and concentrated sulfuric acid (H2SO4). Then, the resulting solutions are titrated by potassium permanganate (KMnO4). The result shows that the experimental values of manganese ions’ concentration (Mn3+ (%) = 67.6 and Mn4+ (%) = 32.4) are close to the theoretical ones. The red line in Fig.4 is the fitting curve deduced from Curie-Weiss equation. The parameters C and θCW were obtained. The value of θCW is higher than that of TC. Generally, the difference 5

between θCW and TC (θCW > TC) depends on the substance and is associated with the presence of short-range ordered slightly above TC, which may be related to the presence of a magnetic inhomogeneity. The positive value of θCW indicates the ferromagnetic (FM) interaction between spins. The degree of magnetic frustration can be measured through the divergence between TC and θCW, while the effective paramagnetic moment µeff could be derived from the exp fitting line. The experimental effective paramagnetic moments  eff  was determined from

C

exp 2 N A  eff

3k B M m

 B2 ; where Mm is the molecular weight, N A  6.023  1023 atoms/mol is

Avogadro’s number, kB 1.38 1016 erg / K is Boltzmann’s constant and  B  9.274 10 21 emu exp  and effcal  are listed in Table 2. is Bohr’s magneton. The temperature range of fit, θCW,  eff

Fig.5 shows the isothermal magnetization M versus applied magnetic field µ0H measured at different temperatures, from 0 to 5 T, for this compound. Below TC, magnetization increases sharply with the applied magnetic field for µ0H < 0.05 T. The saturation of magnetization shifts to a higher value of magnetic field with the decreasing temperature, which confirms the FM behavior of our sample at low temperature. However for T > TC, a drastic decrease of M(µ0H, T) is observed with an almost linear behavior reflecting a paramagnetic behavior. This decrease is mainly due to the thermal agitation which tends to disorder the magnetic moments [21]. For further evidence of the first order magnetic phase transition, we also generated the Arrott plots i.e. M2 versus µ0H/M isotherms around TC as shown in the a-inset of Fig.5 M being experimentally determined magnetization and µ0H the applied magnetic field. According to Banerjee criterion [22], a negative or a positive sign of the slope of Arrott curves corresponds to the first or the second-order magnetic phase transition. In the present investigation the observed positive slope of Arrott plot around TC is the clear indication of second-order metamagnetic transition. The M(µ0H) curves can be simulated by the law-approach to saturation (b-inset of Fig.5) in the term [23]. M  M s (1 

a

 0 H 

n

)

(3)

where 0  n  1, Ms is the saturation of magnetization, the a /  0 H n term indicates the deviation of magnetization from saturation and the factor n changes with respect to the origin of deviation. The a-factor is correlated with the ferromagnetic correlation length. The a, n and Ms values are given in Table 2. The large n factor and the small a factor for the compound should be associated with the long-range spin order of magnetic moment.

6

4. Theoretical considerations The magnetocaloric effect (MCE) which is intrinsic to all magnetic materials is induced by the coupling of the magnetic sublattice with the magnetic field. In order to determine the (MCE) effect especially in these materials, both the experimental and theoretical approaches were adopted. For the experimental evaluation, heat capacity and/or magnetization data are required. Change in entropy (∆SM), full width at half maximum (δTFWHM), change in specific heat (∆CP,H) and relative cooling power (RCP) etc., are important parameters in the investigation of MCE. Therefore, in the present investigation, a simple approach was adopted for the evaluation of all these parameters. From the fundamentals of thermodynamics, the entropy of a magnetic material ΔS M can be written as: S M  

0 H max

0

 S    d  0 H     0 H  T

(4)

The magnetic entropy is related to magnetization M, to the strength of the magnetic field µ0H and to the absolute temperature T through Maxwell relation [24]:  S   M     =  T  H   ( 0 H ) T

(5)

After integration yields, one may write as from (4) and (5): S M  

0 H max

0

 M    d  0 H   T  0 H

(6)

Based on the phenomenological model [25], the dependence of magnetization on the variation of temperature and Curie temperature TC may be written as:  M -M  M =  i f  tanh[A(TC -T)]  2 

(7)

To reach a full agreement between the experimental and the theoretical results for the variation of magnetization versus temperature at different magnetic fields (µ0H) under adiabatic conditions, we made several attempts and analyses in the context of phenomenological modeling dependence of magnetization on temperature variation. Two more terms B T and C are added to explain the variation of magnetization of several types of magnetic materials. So, the dependence of magnetization versus temperature and Tc (Curie temperature) is presented by:  M -M M = i f  2

  tanh [A(TC -T)] + BT + C 

(8) 7

where Mi and Mf are initial and final values of magnetization at ferromagnetic (FM)– paramagnetic (PM) transition (as shown in Fig.6) and

A=

2(B-Sc ) Mi -M f

B is magnetization sensitivity dM/dT in the ferromagnetic state before transition, S c is magnetization sensitivity dM/dT at Curie temperature TC and  M i +M f  C    BTC 2  

Differentiating equation (8) gives:

 Mi  M f  dM 2   A  sec h  A TC  T    B dT 2   where sech(x) =

(9)

1 cosh( x)

The magnetic entropy change (ΔSM) can be obtained through adiabatic change of temperature due to the application of magnetic field. The variation of ΔSM with temperature, when the magnetic field is varied from 0 to µ0Hmax, is given by:

  M -M ΔSM = - A  i f   2

  2  sech [A(TC -T)]+B  0 H max  

(10)

At T = TC, entropy change ΔSM becomes maximum so that (10) may be written as,

  Mi -Mf ΔSmax M = 0 H max - A    2

   +B   

(11)

The determination of full-width at half-maximum TFWHM can be carried out as follows:

δTFWHM =

 2A(Mi -M f )  2 sech   A  A(Mi -M f )+2B 

(12)

Relative cooling power (RCP) is a useful parameter, which decides the efficiency of magnetocaloric materials based on the magnetic entropy change [26]. The RCP is defined as the product of the maximum magnetic entropy change sMmax and full width at half maximum (δTFWHM) in ΔSM(T) curve. max RCP = - δTFWHM  ΔSM (T, μ 0 H max )

= (M i -M f -2

 2A(M i -M f )  B )μ 0 H max  sech   A  A (M i -M f )+2B 

(13)

The heat capacity ΔCP,H, can be calculated from the magnetic contribution to the entropy change induced in the material, by the following expression [27]: 8

ΔCp,H =T

δΔSM δT

From Eq. (10)

(14)

δΔSM can be inferred as follows: δT

δΔSM   M -M  2 A2  i f δT  2 

  2  sech [A(TC -T)]tanh(A(TC -T))  0 H max  

(15)

From Eqs. (14) and (15), Cp,H can be rewritten as:

ΔCp,H = -TA2 (Mi -Mf )sech 2  A(TC -T)]tanh[A(TC -T) 0Hmax

(16)

From this phenomenological model, SM, TFWHM, RCP and Cp,H can be simply evaluated for LSCMO under magnetic field variation. 5. Model application Numerical calculation was made with parameters as displayed in Table 3. These parameters were determined from experimental data. Fig.7 shows magnetization vs. temperature in different applied magnetic fields for the sample. The symbols represent experimental data, while the solid line represents modeled data using parameters given in Table 3. The results of calculations and experimental data of magnetization are in good agreement for the sample. We can report that magnetization exhibits a continuous change around TC in different magnetic fields, and that TC significantly increases with the increase in magnetic field [28]. Fig.8 shows the dependence of the magnetic entropy change on temperature for different applied magnetic fields for La0.67Sr0.1Ca0.23MnO3 sample. The solid lines are modeled results and symbols represent experimental data. It is seen that the results of calculations are in a good agreement with the experimental results. It is interesting to note that the maximum of the magnetic entropy change is obtained near Curie temperature (TC = 294 K) of the sample. One can also see that the magnitude of ΔSM increases with an increasing strength of µ0H and reaches a maximum value of 5.97J/kgK for µ0H = 5 T. These results clearly suggest that this compound could be a suitable candidate as a working material in refrigeration devices near room temperature. To explain a large magnetic entropy change in perovskite manganites, Zener’s double–exchange model is strongly recommended [29]. The effect of the double– exchange interaction between Mn3+ and Mn4+ ions would be closely related to the change in Mn3+/Mn4+ ratio, under the doping process. Furthermore, the large magnetic entropy change in perovskite manganites could be originating from the spin-lattice coupling in the magnetic ordering process [6]. Strong coupling between spin and lattice is corroborated by the observed significant lattice changes accompanying magnetic transition in perovskite manganites [30]. The lattice structural change in the Mn-O bond length and Mn-O-Mn bond angle would in 9

turn favor the spin ordering. Thus, a more abrupt variation of magnetization at near TC occurs, resulting in a large magnetic entropy change as a large MCE. In magnetic refrigeration, it is important to consider not only the maximum value of (ΔSM), but also the relative cooling power RCP defined as [26]: RCP  SMmax TFWHM

(17)

where  TFWHM represents the full width at half maximum of the magnetic entropy change curve. RCP gives an estimate of the quantity of heat transfer between the hot (Thot) and cold (Tcold) ends during one refrigeration cycle. It is also the area under the (ΔSM) vs. T curve between two temperatures (  TFWHM  Thot  Tcold ) of the full width at half maximum (FWHM) of the curve. Since the RCP factor represents a good way for comparing magnetocaloric materials, our compound, LSCMO can be considered as a potential candidate for magnetic refrigeration thanks to its high RCP value comparing with conventional refrigerant materials (Table 4). The values of maximum magnetic entropy change, full width at half maximum (

 TFWHM ) and relative cooling power (RCP) at different magnetic fields for LSCMO are calculated by using Eqs. (11), (12) and (13) respectively. They are summarized in Table 4. Fig.9 shows the dependence of Cp on temperature under different field variations for the sample

calculated

from

ΔCp = Cp  T,μ 0 H  - Cp  T,0  =T Since M / T

ΔSM–T

curves

of

Fig.8

by

using

relation

SM  T,μ 0 H  and the predicted values. T

0 , therefore SM

magnetization. Furthermore at T

0 , and consequently the total entropy decreases upon

T C , CP

0 , and at T

T C , CP

0 [31]. The ΔCP

undergoes a sudden change from positive to negative around TC with a positive value above TC and a negative value below TC and rapidly decreases with decreasing temperature. The positive or negative values of CP closely above or below TC may strongly alter the total specific heat. Furthermore, the maximum and minimum values of specific heat change for this sample are estimated and summarized in Table 4. Finally, in this model, a few necessary parameters are required and the processing time for the simulation is limited. The used procedure does not add any supplementary computational effort to the numerical simulation and it is suitable to be coupled with field computation. 6. Percolation model The dependence of resistivity on temperature  (T ) in LSCMO polycrystalline sample was measured in the 5-400 K temperature range in zero magnetic field. This is shown in Fig.10. At low temperatures, the sample is magnetically ordered and resistivity has a metallic character due to the strong ferromagnetic coupling. At higher temperatures, we have a semi10

conducting behavior. The value of temperature T , obtained from the inflexion point of d  / dT plot is found to be 272 K, which is close to its Curie temperature TC (TC = 294 K),

indicating strong correlations between the magnetic and electrical properties in LSCMO sample. We can, therefore, define the ferromagnetic-metallic-like and the paramagneticsemiconductor-like behaviors as a function of temperature. In order to determine the dependence of percolation threshold on a concentration of doping elements, we carried out a quantitative analysis for the explored sample’s dependence of resistivity on temperature. The electrical resistivity in the low temperature of the metallic phase below TM-Sc is fitted to the following equation.

  0  2T 2  9/2T 9/2

(18)

where  0 is the residual resistivity arising from the temperature independent processes such as domain wall, grain boundary and vacancies, 2T 2 indicates electron-electron scattering, whereas 9/2T 9/2 is attributed to a two magnon scattering process in the FM state. However, as this model is not in a position to explain the low temperature upturn in resistivity, it has been concluded that along with the above mentioned phenomena some other factors might have also contributed to the low temperature behavior. Based on the strong correlated effect in manganites, one has to consider the electron-electron interaction, which causes a T 1/2 dependence of resistivity in a disordered system [32]. Therefore, in order to explain the origin of the low temperature resistivity upturn, the experimental data were analyzed by taking into account the Kondo-like scattering, electron-electron interaction and electron-phonon interaction etc. To represent these phenomena, three more terms were included in Eq. (18) and the new equation is,

 (T )  0  eT 1/2  s ln T  PT 5  2T 2  9/2T 9/2

(19)

where the term eT 1/2 takes into account the contributions from correlated electron-electron interactions, while  s ln T represents the contributions due to Kondo-like spin dependent scattering and  PT 5 term is due to electron-phonon interactions. Kondo effect was originally observed in diluted magnetic alloys and was attributed to the interaction between localized spins of magnetic impurities and the conduction electrons. In order to explain the variation of electrical resistivity with temperature in the high temperature region, T

   T exp( EA / kBT )

T adiabatic small polaron model [33] given by an equation, (20)

11

was used. Here E A represents the activation energy, while   2kB / 3ne2 a 2 is the residual resistivity here k B is Boltzmann’s constant, e is electronic charge, n is the number of density of charge carriers, a is site-to-site hopping distance and  is the longitudinal optical phonon frequency. Taking into account that metal-semiconductor transition (M-Sc) has a percolation character and assuming that a competition between ferromagnetic and paramagnetic regions is of great importance in the formation of the CMR effect, a complete expression for resistivity can be written in the following way [12]

 (T)  FM f  PM 1  f 

(21)

where f and 1  f  are the volume concentrations of the (FM) domains and (PM) regions, respectively. The volume concentrations of FM and PM phases satisfy Boltzman’s distribution:

f 

1 1  exp  U / k BT 

(22a)

and

f '  1 f 

exp(U / k BT ) 1  exp(U / k BT )

(22b)

where

 T  U  U 0 1  mod   TC 

(23)

U implies an energy difference between FM and PM states, TCmod means a temperature in

the vicinity of which the resistivity reaches a maximum value [12]. U 0 is taken as the energy difference for temperatures well below TCmod [12]. From Eqs.(22) and (23), one can find that,

(i) f  0 for T >> TCmod , f = 1 for T << TCmod and f  fC 

1 at T  TCmod [34] 2

(ii)1  f  1 for T >> TCmod , 1  f  0 for T << TCmod and 1  f  fC 

1 at T  TCmod [34] 2

where f C is the percolation threshold.

12

To conclude, when f

is less than f C (respectively 1  f

fC ) the sample remains

semiconducting and when f is larger than f C (respectively 1  f

fC ) it becomes metallic.

Then a complete expression describing the resistivity dependence as the temperature function is of the form:

 (T )  ( 0  eT 1/2   s ln T   pT 5   2T 2  9/2T 9/2 ). f   T exp(

 (T )  ( 0  eT 1/2   s ln T   pT 5   2T 2  9/2T 9/2 ).

  T   U 0 1  mod    TC   exp    k BT   EA     T exp( ). k BT   T   U 0 1  mod    TC   1  exp    k BT    

EA ).(1  f ) kBT

(24a)

1   T  U 0 1  mod  TC 1  exp   k BT  

      (24b)

Fig.10 displays the simulated (red line) and experimental results for the  (T ) curve obtained for zero field and with magnetic field (2 and 5 Tesla ) for LSCMO. The best fit parameters are given in Table 5. It is worth mentioning that this percolation model is suitable to explain the electrical transport of LSCMO. Their excellent agreement confirms that FM domains and PM regions coexist at near TC. In the presently studied LSCMO system, we have noticed a minimum of resistivity in the lowest temperatures around 30 K. The resistivity upturn below Tmin is also found to be suppressed with increasing the magnetic field (µ0H) as shown in the Fig.10. In view of these observations, the origin of this resistivity minimum at low temperature could be associated with the competition between the weak localization effect, electron–electron scattering and electron–phonon scattering processes [35-37]. It is mentioned, from Table 5, that the value of 0 is higher at 0 T than those at 2 and 5 T. The reduction in  2 and 9/2 could be attributed to the decrease in electron spin fluctuations in the presence of magnetic field. As for  p , it is found that the electron-phonon (e-p) interaction seems insensitive to the applied fields, because it is smaller than the other coefficients by several orders. The terms  s and  e appear be the higher than the others parameters. 13

Therefore, we concluded that the resistivity minimum in the ferromagnetic region may be attributed to both the electron–electron interaction and Kondo-like spin-dependant scattering. The temperature dependence on the volume concentration of the ferromagnetic phase f for zero field for example is shown in Figure 11. When temperature is considerably below TC, f is close to 1 (hence complete ferromagnetic state), but when temperature increases, at T

TC ,

the concentration of the ferromagnetic phase approaches zero (hence, paramagnetic state).

Conclusion A detailed investigation of structural, magnetic, magnetocaloric and electrical properties of polycrystalline La0.67Sr0.1Ca0.23MnO3 compound synthesized using the solid state reaction method was carried out. It was observed that the magnetic phase transition from ferromagnetic to paramagnetic is of a second order. The maximum value of magnetic entropy change increases with the applied magnetic field. A large magnetocaloric effect is observed, under an applied magnetic field of 5T, and the maximum of the magnetic entropy change

SMmax and the large relative cooling power (RCP) are found to be 5.971 J/kg.K and 278.547 J/kg, respectively. The large MCE, relatively high RCP, high magnetization, and low cost jointly make the present compound a promising candidate for magnetic refrigeration near room temperature. The dependence of magnetization on temperature variation for LSCMO upon different magnetic fields was simulated. The prediction of the magnetocaloric properties of LSCMO such as magnetic entropy change, full width at half maximum, relative cooling power and magnetic specific heat change upon different magnetic fields was done. The dependence of resistivity on temperature shows a transition from metal to semiconductor phase. Finally, to study the transport mechanism in the whole range of temperature, we used the theoretical percolation model, including the ferromagnetic-metallic and paramagneticsemiconductor states.

Acknowledgments This work is supported by the Tunisian National Ministry of Higher Education, Scientific Research, and the French Ministry of Higher Education and Research of CMCU 10G1117 collaboration.

14

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[19] K.S. Rao, B. Tilak, K.Ch.V. Rajulu, A. Swathi, H. Workineh, J. Alloys Compd. 509 (2011) 7121–7129. [20] B.D. Cullity, C.D. Graham, IEEE Press, ISBN 978-0-471-47741-9, 2009. [21] B. Arayedh, S. Kallel, N. Kallel, O. Peña, J. Magn. Magn. Mater. 361 (2014) 68–73. [22] S.K. Banerjee, Phys. Lett. 12 (1964) 16–17. [23] Y.S. Su, T.A. Kaplan, S.D. Mahanti, Phys. Rev. B. 61 (2000) 1324–1329. [24] A.H Morrish, The Physical Principles of Magnetism, Wiley, New York, 1965. p. 360. [25] M.A. Hamad, Phase Transitions 85 (2012) 106–112. [26] K.A. Gschneidner Jr, V.K. Pecharsky, A.O. Tsokol, Rep. Prog. Phys. 68 (2005) 1479– 1539. [27] T. Samanta, I. Das, S. Banerjee, Appl. Phys. Lett. 91 (2007) 082511 1–082511 3. [28] J. Shen, B. Gao, Q.Y. Dong, Y.X. Li, F.X. Hu, J.R. Sun, B.G. Shen, J. Phys. D: Appl. Phys. 41 (2008) 245005 1–245005 8. [29] Z.M. Wang, G. Ni, Q.Y. Xu, H. Sang, Y.W. Du, J. Appl. Phys. 90 (2001) 5689–5691. [30] P.G. Radaelli, D.E. Cox, M. Marezio, S.W. Cheong, P.E. Schiffer, A.P. Ramirez, Phys. Rev. Lett. 75 (1995) 4488–4491. [31] H. Yang, Y.H. Zhu, T. Xian, J.L. Jiang, J. Alloys Compd. 555 (2013) 150–155. [32] M. Ziese, Phys. Rev. B 68 (2003) 132411 1–132411 4. [33] D. Emin, T. Holstein, Ann. Phys. 53 (1969) 439–520. [34] M. Pattabiraman, G. Rangarajan, P. Murugaraj, Solid State Commun, 132 (2004) 7–11. [35] D. Varshney, I. Mansuri, M.W. Shaikh, Y.K. Kuo, Mater. Res. Bull. 48 (2013) 4606– 4613. [36] V. Sen, N. Panwar, G.L. Bhalla, S.K. Aguarwall, J. Phys. Chem. Solids 68 (2007) 1685– 1691. [37] L. Li, K. Nishimura, M. Fujii, K. Mori, Solid State Commun.144 (2007)10–14. [38] M. Pekala, V. Drozd, J.F. Fagnard, P. Vanderbemden, M. Ausloos, Appl. Phys. A 90 (2008) 237–241. [39] M.H. Phan, S.B. Tian, D.Q. Hoang, S.C. Yu, C. Nguyen, A.N. Ulyanov, J. Magn. Magn. Mater. 258 (2003) 309–311. [40] Y. Sun, X. Xu, Y. Zhang, J. Magn. Magn. Mater. 219 (2000) 183–185.

16

[41] S.K. Barik, C. Krishnamoorthi, R. Mahendiran, J. Magn. Magn. Mater. 323 (2011) 1015– 1021. [42] A. Rostamnejadi, M. Venkatesan, P. Kameli, H. Salamati, J.M.D. Coey, J. Magn. Magn. Mater. 323 (2011) 2214–2218.

17

Table captions

Table 1: Results of Rietveld refinements, determined from XRD patterns measured at room temperature for La0.67Sr0.1Ca0.23MnO3. Table 2: Experimental effexp and calculated effcal effective paramagnetic moments, CurieWeiss temperature CW , fitted saturation magnetization M sfit , a and n factors for LSCMO sample. Table 3: Model parameters for La0.67Sr0.1Ca0.23MnO3 sample in different applied magnetic fields. Table 4: Comparison of maximum entropy change, specific heat change, and RCP for La0.67Sr0.1Ca0.23MnO3 sample and several materials. Table 5: Obtained parameters corresponding to the best fit to Eq.24 of the experimental data of LSCMO at µ0H = 0 T, 2 T and 5 T.

18

Figures captions

Fig.1: X-ray diffraction pattern (solid curve) and Rietveld refinement result (open symbols) for La0.67Sr0.1Ca0.23MnO3 at room temperature. The vertical lines show the Bragg peak positions. The difference between the data and the calculation is shown at the bottom. Fig.2: The Williamson-Hall analysis plots of La0.67Sr0.1Ca0.23MnO3 sample. Fig.3: Variation of the magnetization M vs. temperature for LSCMO sample at µ0H = 0.05T. The inset shows the plot of dM/dT curve as a function of temperature. Fig.4: Inverse susceptibility vs. temperature for LSCMO obtained from magnetization measurement in a field 0.05 T. The line is the calculated curve according to the Curie–Weiss law. Fig. 5: Isothermal magnetization versus magnetic field for LSCMO measured at different temperatures, by steps of 5 K. The a-inset show the Arrot plots M2 versus µ0H/M and the binset represents the modeled of the curve M (µ0H) at 5 K for LSCMO sample. Fig. 6: Temperature dependence of magnetization under constant applied field.

Fig. 7: Magnetization vs. Temperature for LSCMO sample at several magnetic fields. The solid lines are modeled results and symbols represent experimental data. Fig.8: Magnetic entropy change, (-SM), versus temperature for LSCMO sample at several magnetic fields. The solid lines are predicted results, and symbols represent experimental data. Fig.9: Heat capacity changes (CP) as function of temperature for LSCMO in different applied magnetic field variations. Fig. 10: Resistivity versus temperature plot of La0.67Sr0.1Ca0.23MnO3 without and with magnetic field (2 and 5 Tesla). Symbols are the experimental data and solid line is the calculated resistivity using Eq.24 corresponding to the parameters indicated in Table 5. Fig. 11: The temperature dependence of ferromagnetic phase volume fraction f (T) for LSCMO at µ0H = 0.05T.

19

La0.67Sr0.1Ca0.23MnO3 R3 c phase

a = b(Å)

5.3940(3)

c(Å)

13.4212(6)

V(Å3)

350.21(3)

Biso(La/Sr/Ca)(Å2)

0.37(2)

Biso(Mn) (Å2)

0.25(1)

x(O)

0.4539(5)

Biso(O) (Å2)

1.37(5)

Discrepancy factors Rwp(%)

6.25

Rp(%)

4.24

RF(%)

5.32

 2 (%)

3.16

Debye-Scherrer technique (DSC)(nm)

41

Williamson-Hall technique (D)(nm)

48

Strain (  ) %

0.56

Table. 1

20

La0.67Sr0.1Ca0.23MnO3 exp ( B ) eff

4.74

cal ( B ) eff

4.58

θCW (K)

297 K

M Sfit (emu/g)

68.48

a

0.043

n

0.887

Table. 2

21

µ0H(T)

Mi (emu/g)

Mf (emu/g)

TC (K)

B (emu/gK)

SC (emu/gK)

1

66.21

14.55

295

-0.516

-1.771

2

69.80

21.68

296

-0.487

-1.764

3

74.65

23.73

297

-0.465

-1.451

4

78.37

28.29

300

-0.302

-1.423

5

83.09

31.86

301

-0.273

-1.311

Table. 3

22

TFWHM

RCP

Cp,Hmax

Cp,Hmin

(J/kgK)

(K)

(J/kg)

(J/kgK)

(J/kgK)

1

2.431

42.37

103.001

25.41

-23.90

Present

2

3.721

40.16

149.435

27.02

-24.90

Present

3

4.736

40.75

192.992

28.02

-24.23

Present

4

5.742

42.32

243.001

28.19

-23.88

Present

5

5.971

46.65

278.547

28.70

-24.39

Present

Gd

5

10.2

–

410

–

–

[5]

La0.7Ca0.3MnO3

2

2.2

–

55

–

–

[38]

La0.6Sr0.2Ba0.2MnO3

1

2.26

–

67

–

–

[39]

La0.60Y0.07Ca0.33MnO3

3

1.46

–

140

–

–

[40]

La0.7Sr0.3Mn0.93Fe0.07O3

5

4

–

255

–

–

[41]

La0.67Sr0.33MnO3

2

2.68

–

85

–

–

[42]

Materials

La0.67Sr0.1Ca0.23MnO3

µ0H (T) -SM

Ref

Table. 4

23

La0.67Sr0.1Ca0.23MnO3 µ0H(T)

0T

2T

5T

0 (.cm)

0.02425

0.01566

e (.cm / K 1/2 )

0.00412

0.00221

0.00178

s (.cm)

0.46114

0.5011

0.31397

P (1013 .cm / K 5 )

3.5641

2.4165

2.1616

2 (106 .cm / K 2 )

13.1842

8.7815

1.0534

9/2 (1012 .cm / K9/2 )

5.4637

3.4399

3.2668

U 0 / kB ( K )

2367

2411

2425

T modC ( K )

298

299

301

 (106 .cm)

35.74

25.91

26.39

EA / k B ( K )

692.77

428.36

237.26

R 2 (%)

99.92

99.98

99.99

0.01066

Table. 5

24

La0.67Sr0.1Ca0.23MnO3

Fig.1

25

Fig.2

26

Fig.3

27

Fig.4

28

Fig.5

29

Fig.6

30

Fig.7

31

Fig.8

32

Fig.9

33

Fig.10

34

Fig.11

35

Highlights 

LSCMO is crystallized in the rhombohedral structure with the R3 c space group.

  

The variation of (M) versus (T) reveals a (FM) to (PM) phase transition around TC. Application of phenomenological model was performed. The results of calculation are in a good agreement with the experimental results.