Pr3+ doping at the A-site of La0.67Ba0.33MnO3 nanocrystalline material: assessment of the relationship between structural and physical properties and Bean–Rodbell model simulation of disorder effects

Bulk nanocrystalline samples of (La1−xPrx)0.67Ba0.33MnO3 (0.075 ≤ x ≤ 0.30) manganites with a fixed carrier concentration are prepared by the sol–gel based Pechini method. Rietveld refinement of the X-ray diffraction patterns, shows the formation of single-phase compositions with rhombohedral symmetry. Upon Pr3+ doping at the A-site, the unit cell volume and the B–O–B bond angles are reduced. FTIR spectra present a prominent absorption peak of the in-phase stretching mode (B2g mode) rising from the vibration of the Mn–O bond. Raman spectra at room temperature reveal a gradual shift toward lower frequencies in (Eg) phonon mode with increasing Pr3+ concentration. The M(T) measurements shows a clear ferromagnetic (FM)–paramagnetic (PM) phase transition with increasing temperature. An increase in resistivity and activation energy and a decrease in the metal–semiconductor transition (TM–SC) and Curie temperatures (TC) was observed as a consequence of Pr3+ doping. The results are discussed according to the change of A-site-disorder effect caused by the systematic variations of the A-site average ionic radius 〈rA〉 and A-site-cation mismatch σ2, resulting in the narrowing of the bandwidth and the decrease of the mobility of eg electrons. The magneto-transport behavior in the whole measured temperature and a magnetic field can be described by a percolation model, which is in agreement with the limited experimental data of the samples for x = 0.075, 0.15 and 0.30. The experimental results confirm that A-site substitution with Pr3+ destroys the Mn3+–O2−–Mn4+ bridges and weakens the double exchange (DE) interaction between the Mn3+ (t32ge1g, S = 2) and Mn4+ (t32ge0g, S = 3/2) ions. On the other hand, the Bean and Rodbell model has been successfully used to simulate the magnetization data of the samples with x = 0.15 and x = 0.22. The random replacement of La3+ by Pr3+ is shown to induce more disorder in the system, which is reflected in the increase of the fitted disorder parameter and spin value fluctuation. At a temperature close to room temperature, the maximum magnetic entropy change (ΔSMax) and the relative cooling power (RCP) of La0.52Pr0.15Ba0.33MnO2.98 are found to be, respectively, 1.34 J kg−1 K−1 and 71 J kg−1 for a 1.5 T field change.


Introduction
The doped perovskite manganites with the general formula R 1Àx A x MnO 3 (where R and A are trivalent rare earth and divalent alkaline earth ions, respectively) stimulate great scientic research because of their rich physical properties. In particular, these materials exhibit a remarkably rich variety of structural, magnetic, and transport properties because of couplings between spin and orbital moments. [1][2][3][4] Doped lanthanum based manganites have been used in an enormous number of technological applications, including magnetic recording, high-density data storage, hard disks, magnetic sensors, spin-electronic devices, and magnetic refrigerants. [5][6][7] These materials are of particular interest because of their chemical stability, the tunability of their Curie temperatures (T C ) through doping, and their low synthesis cost. Barium-substituted lanthanum manganite (La 1Àx Ba x MnO 3 ) is among the existing colossal magnetoresistance (CMR) manganites displaying ferromagnetic behavior in a wide concentration range x with a maximum T C well above room temperature for x ¼ 0.33. 8 Hence, the structure of La 1Àx Ba x MnO 3 can be derived from the cubic perovskite by tilting all oxygen octahedra about the [111] pseudo-cubic axes (a-a-a-tilt system). This system can be strongly modied by replacing a fraction x of the La 3+ ions by the larger Ba 2+ ions, resulting in a reduction of the Mn-O bond length (d Mn-O ) and an increase of the Mn-O-Mn bond angle (q Mn-O-Mn ) towards 180 . Due to charge neutrality, replacing La by Ba causes the conversion of Mn 3+ (t 3 2g e 1 g , S ¼ 2) into Mn 4+ (t 3 2g e 0 g , S ¼ 3/2), which in turn introduces mobile e g electrons in the manganite oxides. The mobile electrons are closely related to the ferromagnetic (FM) interactions between Mn 3+ and Mn 4+ (i.e., the formation of Mn 3+ -O 2À -Mn 4+ networks) according to the double exchange (DE) interaction model, [9][10][11] which is one of the mechanisms used to explain the magnetic and transport properties of these compounds. The signicant changes in structure, magnetic and magnetoresistive (MR) properties of manganites can be achieved by varying particle size, [12][13][14] oxygen stoichiometry 15 and substituting cations at the A-or the B-sites. 4,16,17 There are various methods to synthesize the manganites compounds involving solid state reaction, hydrothermal synthesis and Pechini sol-gel method. Pechini method has been used successfully to produce high-quality specimens due to these potential advantages such as better homogeneities, lower processing temperatures, short annealing times, high purity of materials and improved material properties. 18 La 0.67 Ba 0.33 MnO 3 (LBMO) has been one of the most appealing manganites, and in its bulk form, it has been found to exhibit by Mn-site substitution (B-site) in perovskite oxides, with other transition metal ions, 8,17,18 a second order of magnetic phase transition. Besides, past studies on substituting praseodymium at the A-site of manganite are focused on polycrystalline ceramics. 19,20 The objective of this work was to synthesize nanocrystalline samples of (La 1Àx Pr x ) 0.67 Ba 0.33 MnO 3 with an extended doping levels up to x ¼ 0.30 and study the inuence of praseodymium substitution at A-site on the crystal structural, magnetic, magneto-transport properties and magnetocaloric effect. Also, we aim to emphasize the interplay between experimental results and theoretical aspects of magnetization using Bean-Rodbell model and electrical resistivity adopting the percolation model.

Synthesis of samples
Nanocrystalline samples of (La 1Àx Pr x ) 0.67 Ba 0.33 MnO 3 (0.075 # x # 0.30) were synthesized using the Pechini sol-gel technique using highly pure metal nitrates as starting materials (>99.99% purity): The initial solution was prepared by mixing distilled water, nitrates (properly weighed according to the specic composition), citric acid (CA) (99.5% purity) and ethylene glycol (EG) (99.5% purity) in the following molar proportion 1 : 5 : 4 : 3. The resulting solution was heated by constant stirring at temperatures of 80 C. Aer the evaporation of water at 80-100 C, the viscosity of the solution increased and further heating led to the formation of polymeric resin. The resin was pre-calcined (673 K for 3 h) to eliminate the organic material, ground and calcined again (1073 K for 4 h) to eliminate the residual organic material. The obtained black powder was cold-pressed into pellets with a diameter of 13 mm and thickness of about 2-3 mm under a pressure of 5 tons per cm 2 . Subsequently, the powder was sintered at 1323 K for 12 hours in air.

Characterizations
2.2.1. X-ray diffraction (XRD). The samples were characterized using X-ray diffraction (XRD) to conrm the crystallinity, purity and single-phase formation of the samples of present investigation. The XRD patterns were further analyzed by employing Rietveld renement technique (using Fullprof program), to estimate the lattice parameters, space groups, type of crystal system, Bragg reections and other related statistics of the samples. Structural characterization using a ''Panalytical X pert Pro'' diffractometer with Cu K a radiation (k ¼ 1.5406Å). Data for Rietveld renement were collected in the range of 2q from 10 to 120 with a step size of 0.017 and a counting time of 18 s per step.
2.2.2. Iodometric titration. The Iodometric titration method was performed to estimate the Mn 4+ /Mn 3+ ratio and oxygen stoichiometry of samples. Powders were weighed (about 100 mg) and dissolved in a mixture of 10 ml of 10 mass% potassium iodide aqueous solution and 2.5 ml of 2 M hydrochloric acid. Liberated iodine was titrated against standard sodium thiosulfate (0.04 N) solution using starch as an indicator.
2.2.3. Surface morphology (FE-SEM). The morphological properties of the samples were investigated by scanning electron microscopy (SEM) on a JSM-6400 apparatus working at 20 kV.
2.2.4. DC electrical resistivity. Electrical resistivity measurements were carried out by standard four-probe method in the temperature range 5-300 K up to 5.0 T. The measurements were performed using the DC resistivity option in a Quantum Design physical property measurement system (PPMS).
2.2.5. Magnetic measurement. The magnetization was measured in a eld-cooled (FC) mode between 5 K and 400 K, under a magnetic eld of 500 Oe, using a Quantum Design SQUID susceptometer, model MPMS-XL5. The isothermals M versus H at various temperatures around T C have been measured in applied elds up to 5 T. These isothermals are corrected by a demagnetization factor D that has been determined by a standard procedure from low-eld dc magnetization measurement at low temperatures (H ¼ H app À DM). The isothermal magnetization was performed aer the sample was heated well above T C for a long enough time, then cooled under zero eld to the objective temperature.

Structure and morphology studies
The XRD patterns at room temperature for the (La 1Àx Pr x ) 0.67 -Ba 0.33 MnO 3 (x ¼ 0.075, x ¼ 0.15 and x ¼ 0.22) samples are shown in Fig. 1(a). It is evidence that all samples show typical reections of the perovskite structure with rhombohedral symmetry and R 3c (Z ¼ 2) as a space group, no. 167. Hence, sharp peaks are clearly seen in all XRD patterns, indicating the studied samples to be highly crystalline. No traces of secondary phases were detectable, within the sensitivity limits of the experiment. The diffraction data were rened using the FullProf program by employing Rietveld powder diffraction technique. 21 Background Rietveld renements were tted with a polynomial function; a pseudo-Voigt function was employed to model the peak shape. As a representative of the series, the renement data of x ¼ 0.15 composition is depicted in Fig. 1(b). The calculated results are shown in Table 1. Very good agreement between the calculated and the observed data is obtained. It may be seen that for all samples the residual factor is R p # 3.02, the weight residual factor is R wp # 3.71 and the goodness-of-t factor is c 2 # 2.85. These parameters conrm that the renements are acceptable and the samples compositions are the same as their nominal compositions, including that the oxygen content was close to 3 for all the samples. 22 The three equivalent positions (6a (0, 0, 1/4), 6b (0, 0, 0), and 18e (x, 0, 1/4)) in the rhombohedral unit cell are occupied by 6a (La 3+ , Pr 3+ , Ba 2+ ), 6b (Mn 3+ , Mn 4+ ), and 18e O 2À respectively.  Table 1, where a and c are the hexagonal cell parameters, V is the unit cell volume, B iso is the isotropic thermal parameter, q (Mn-O-Mn) is the bond angle, d MnÀO is the bond length and x is the oxygen position. It is clearly noticeable that the average A-site radius and the cell parameters of the rhombohedral compounds are found to decrease with increase Pr doping concentration on the A-site as shown in Table 1. The average A-site ionic radius has been calculated using nine coordinated ionic radii given by Shannon. 23 The observed behavior might be attributed to the fact that the substitution of a smaller Pr 3+ ion (1.179Å) at site La 3+ ion (1.216Å) compresses the unit cell in all the three directions, thus decreasing its volume. These lattice effects are similar to those observed in previous studies on the same A-site substitution with praseodymium. 19,24 It should also be pointed out that a strong correlation exists between hr A i and the Goldschmidt's tolerance factor t g dened as: where hr A i, hr B i and hr O i are respectively the average ionic radii of A and B perovskite sites and of the oxygen anions. When hr A i decreases, t g also decreases and gives a lower symmetry arrangement by the tilting of the MnO 6 octahedra. It is wellknown that an orthorhombic structure is realized for t g < 0.96, rhombohedral for 0.96 < t g < 1, and cubic as t g moves close to 1.
In present study, it is found that t g decreases from 0.9985 to nearly 0.9591 with increasing x, consistent with the experimental observation that the crystal structure of studied compounds is rhomobohedral. The decrease of q (Mn-O-Mn) bond angles (Table 1) increases the distortion of MnO 6 octahedra that diminishes the strength of magnetic exchange interaction between the Mn 3+ and Mn 4+ ions. This could disfavor the longrange ferromagnetic order that results in shi of Curie temperature (T C ) to lower temperature, which is comprehensively discussed in the next section. As a representation, the eld emission scanning electron microscopy (FE-SEM) morphology for x ¼ 0.22 is displayed in the inset of Fig. 1 The average grain size (GS) 25,26 estimated is approximately 100 nm (AE10 nm). From the iodometric titration method, the average ratio of Mn 3+ /Mn 4+ is found to be xed with an accuracy of AE0.03, while the oxygen content is close to stoichiometry (see Table 1). X-ray line prole analysis is a powerful and simple tool to identify the presence of dopant ion in the host lattice and quantify the microstructural parameters like size and lattice strain. Williamson-Hall (W-H) had proposed that the crystallite size and strain contributions to line broadening are independent to each other and it can be deduce in the following mathematical expression: 27 where b hkl is the integral breadth (in radians). The b parameter was corrected for instrumental broadening. l is the wavelength of the X-rays (Cu K a radiation, l ¼ 1.5406Å), q is Bragg diffraction angle, 3 is the lattice strain and k is the shape factor (k ¼ 0.9). A plot is drawn by taking 4 sin q along X-axis and b hkl cos q along Y-axis (not shown). The strain present in the material and the crystallite size are, respectively, extracted from the slope and the intercept of the linear t made to the plot. The estimated values of the strain (3) and the crystallite size (D W-H ) are given in Table 1. It is clear from the table that the average crystallite size values are found to be in the range of 75-93 nm.

Fourier transform infrared spectroscopy (FTIR)
FTIR spectra of (La 1Àx Pr x ) 0.67 Ba 0.33 MnO 3 (where, x ¼ 0.075, 0.15, and 0.30) samples recorded in the wavenumber range 400-1000 cm À1 are presented in Fig. 2. These metal oxygen bonds are subsequently organized into a MnO 6 octahedral structure, as evidenced by the appearance of well-dened peaks. The higher frequency band at 610 cm À1 (for x ¼ 0.30) corresponds to the in-phase stretching mode (B 2g mode) of Mn ion against the oxygen octahedron, which involves the internal motion of a change in Mn-O bond length. 28,29 Since the increase in the concentration of Pr 3+ ion with less ionic radii produces the shiing of wavenumbers (587 cm À1 for pristine sample 20 ) to higher frequency, which is determined by a decrease of symmetry of the lattice. The increase in B-O vibration frequency for ABO 3 structure indicates a strong coupling constant and hence the shorter bond lengths/decrease in lattice volume, supporting the XRD results discussed above. The band at 410 cm À1 corresponds to the E g -symmetry mode associated to an internal bending mode of the MnO 6 octahedra. These two bands are related to the environment surrounding the MnO 6 octahedra in the ABO 3 perovskite and conrms the formation of perovskite structure, 30,31 which is in agreement with the XRD results.

Raman spectroscopy
Raman spectroscopy is a powerful and sensitive tool for understanding crystal symmetry, the local structural distortion and its dependence on doping. Our samples crystallize in rhombohedral structure, space group R 3c (D 6 3d ), Z ¼ 2. This structure can be obtained from the simple cubic perovskite by the rotation of the adjacent MnO 6 octahedra in the opposite directions around the [111] cubic direction. According to the group theory, for this structure, thirty vibrational degrees of freedom at the G point are distributed among the irreducible representation as: The rhombohedral distortion gives rise to ve Raman active modes.
Room temperature Raman spectrum of (La 1Àx Pr x ) 0.67 -Ba 0.33 MnO 3 (where, x ¼ 0, 0.075, 0.15, and 0.22) samples in the frequency range of 100-700 cm À1 is shown in Fig. 3. Five vibration modes have been identied, one (A 1g ) and four (E g ). These broad bands are located at 125 (A 1g ), 190 (E g ), 289 (E g ), 436 (E g ) and 547 (E g ) cm À1 , which are associated with rotational-, bending-, and stretching-like vibrations of the MnO 6 octahedra, respectively. 32,33 In this work, we underline the (E g ) mode (approx. 547 cm À1 ) allowed for the symmetric stretching vibration of oxygen in MnO 6 octahedra. This mode shows

Magnetic properties
To investigate the magnetic properties of (La 1Àx Pr x ) 0.67 -Ba 0.33 MnO 3 (0 # x # 0.30) nanocrystalline, we performed temperature dependent eld cooled magnetization measurements (M-T) from 400 K to 5 K at 500 Oe magnetic eld (Fig. 4). A transition from a low-temperature ferromagnetic phase to a high temperature paramagnetic phase is evident. The Curie temperature T C is the temperature at which the absolute value of dM/dT is maximum (see the le inset of Fig. 4), are summarized in Table 2. The $337 K transition for the pristine compound is shied toward room temperature with increasing Pr concentration, until in the x ¼ 0.30 composition occurs at T C ¼ 309 K. The effective e g bandwidth W, 35 determined by the overlapping of Mn 3d and O 2p orbitals, strongly depends on ionic radii and the structural distortion. In this work, both Pr 3+ and La 3+ are trivalent positive ions, the substitution of La 3+ by Pr 3+ does not change the charge carrier density. As we know, the smaller average ionic radius hr A i decreases the Mn-O-Mn bond angles and increases the Mn-O bond lengths, 36,37 which weakens the hopping integral of e g electrons and attenuates the DE interaction. The initial decrease of T C (see Table 2) is related to the reduce of the bandwidth. On the one hand, we can see in Fig. 4 that the magnitude of magnetization in the ferromagnetic region is decreased (i.e., when Pr 3+ content increases, as discussed above), which is consistent with results reported earlier. [38][39][40] Moreover, other studies of A-site doped manganites 41,42 also reveal that the mismatch in the size of the A-cation (s 2 ) inuences the T C . Thus, we have to consider s 2 , which is dened by the relations: is the fractional occupancy and r A is calculated as: Â r Ba 2+. The substitution of smaller Pr 3+ for larger La 3+ cations causes a decrease in the average A-site cationic radius, while s 2 increases (the intrinsic size disorder) (see Table 1). This enhancement in the mismatch in the crystal structure induces a lattice strain by causing a random displacement of oxygen atoms from their average crystallographic positions, thereby resulting in a distortion of the MnO 6 octahedra, and hence the e g electrons are localized. So, these changes lead to decrease in T C value of the compounds by weakening double-exchange interaction. To get a clear knowledge about the magnetic interaction for (La 1Àx Pr x0.67 Ba 0.33 MnO 3 series, the inverse susceptibility (1/c) versus temperature (T) curves are plotted as shown in Fig. 4. A typical Curie-Weiss behaviour is observed above the T C where 1/c is changing almost linearly with the temperature which can be tted by the Curie constant and q p is the paramagnetic Curie-Weiss temperature. By tting the linear region, the Curie-Weiss temperatures q p , which are an indication of the nature and strength of coupling in the structure, and C were obtained. It is evident that q p is always positive for all three samples, indicating the existence of FM exchange interaction between spins. Next, the experimental effective paramagnetic moments m exp eff , are derived for each sample using the following equation: where k B ¼ 1.38016 Â 10 À23 J K À1 is the Boltzmann constant, N A ¼ 6.023 Â 10 23 mol À1 is Avogadro's number, M m is the molecular weight and m B ¼ 9.274 Â 10 À21 emu is the Bohr magnetron. These values, together with the Curie-Weiss temperature, are listed in Table 2. The theoretical effective paramagnetic moment is calculated based on the chemical formula of (La 1Àx Pr x ) 3+ 0.67 Ba 2+ 0.33 Mn 3+ 0.67 Mn 4+ 0.33 O 2À 3 , using the following expression: The spin-only magnetic moments for free Mn 3+ , Mn 4+ and Pr 3+ are 4.89m B , 3.87m B , 3.58m B , respectively. Thus, both the experimental m exp eff and theoretical m th eff values of the effective moment are given in Table 2. As it can be seen from the Table 2, the experimental (m exp eff ) values are in the range of $6.03-6.72m B , and thus are little larger than the theoretical values. Such a difference in (m eff ) values may be ascribed to the appearance of short-range FM interactions in the paramagnetic state (above T C ), which is commonly observed in manganites. 18,20,43

The Bean-Rodbell model
In order to study the nature of the magnetic transition, we have applied the Bean-Rodbell model to our magnetization data for (La 1Àx Pr x ) 0.67 Ba 0.33 MnO 3 (x ¼ 0.15, and 0.22). Manganite materials 18,44 with second-and rst-order phase transition have been adequately interpreted using this model, which describes in particular the magnetovolume interactions. 45 The model considers the dependence of the exchange interaction on the interatomic distance. This dependence is phenomenologically described by considering the dependence of the critical magnetic phase-transition temperature on the volume change in the following way: where n is the volume and n 0 is the equilibrium volume obtained in the absence of magnetic interaction. T 0 is the magnetic ordering temperature in the absence of deformations. The parameter b represents the slope of the dependence of the Curie temperature (T C ) on the cell deformation.  Considering a material with compressibility K, spin J and spin density N, one denes the h parameter: where k b is the Boltzmann constant. Bean and Rodbell proved that in this model this parameter governs the nature of the magnetic phase transition. In the absence of external pressure, for 0 # h < 1 the transition is second order type while for h > 1 the transition is purely rst order type, 45 with coupled volume and magnetization discontinuities at specic eld and temperature values. Note that, the model is a modied form of the Bean-Rodbell model extended to include spin clustering via the parameter J. We see a good match especially at high eld and high magnetization between measurements and simulated data. As the model assumes a homogeneous and isotropic system, effects such as magnetic domains, anisotropy, and demagnetization are not taken into account, justifying the higher deviation between experimental data and simulations at lower elds. 46 Table 3 shows the parameters obtained from these simulations. The second-order transition of our samples is conrmed by their h parameter value (h < 1). 45 The partial substitution of La 3+ by magnetic ions Pr 3+ does not alter the ratio of Mn 3+ /Mn 4+ ions but results in a more distorted structure. These changes lead to suppression of the ferromagnetism which affect the long-range ferromagnetic order. To our knowledge, the relationship between the Pr 3+ doping at A-site of lanthanum manganite and disorder effects has not been reported before in manganites. From Table 3, it can be observed that Pr 3+ doping induces more disorder in the system, as it can be seen from the evolution of the disorder parameter and spin value uctuation.

Prediction of the magneto-transport properties using percolation model
To investigate the effect of substitution with magnetic ions (i.e., case of Pr 3+ ) at A-site on the electronic transport properties of the samples, the temperature dependence of electrical resistivity measured both in presence and in absence of magnetic eld (up to 5.0 T) on (La 1Àx Pr x ) 0.67 Ba 0.33 MnO 3 (x ¼ 0.075, 0.15 and 0.30) samples are shown in Fig. 6(a-c). All the studied samples exhibit metallic behavior below the metal-semiconductor transition temperature (T M-SC ) and semiconductor-like features above T M-SC . For the pristine sample, the metal-semiconductor transition is observed at the temperature (T M-SC ) of about 340 K. 18 The values of T M-SC are found to decrease by 50% with increasing Pr 3+ concentration (with x up to x ¼ 0.30), supporting the XRD and magnetic results discussed above. Resistivity in the entire temperature range increases with increase in Pr 3+ concentration, which can be attributed to the weakening of the DE interaction between the Mn 3+ (t 3 2g e 1 g , S ¼ 2) and Mn 4+ (t 3 2g e 0 g , S ¼ 3/2) via the intervening oxygen. On the other hand, the resistivity at a given temperature is found to decrease with increasing eld and that T M-SC values (see Table 4) are found to move towards high temperature side with increasing magnetic eld. Praseodymium substitution at A-site may favor the charge carrier delocalization induced by the magnetic eld, which suppresses the resistivity and consequently leads to the local ordering of the electron spins. Due to this ordering, the ferromagnetic metallic (FM-M) state may suppress the paramagnetic semiconducting (P-SC) regime resulting in complete polarization of conduction electrons (e 1 g ) inside the magnetic domains and, thus are easily transferred between the pairs Mn 3+ and Mn 4+ via oxygen. To elucidate the carrier transport behavior in the whole measured temperature and a magnetic eld, we attempted to t the magnetoresistance of (La 1Àx Pr x ) 0.67 Ba 0.33 MnO 3 (x ¼ 0.075, 0.15 and 0.30) samples according to the percolation model. 47 This model assumes the materials to be composed of ferromagnetic and paramagnetic regions and semiconductor-like transport properties are exhibited in the paramagnetic region, whereas metallic transport always show up in the ferromagnetic region. The relationship applied in the prediction of the magneto-transport can be expressed as follows  10 22 where T mod C (adjustable parameter) means a temperature in the vicinity of what the resistivity has a maximum value. 47 All other parameters, viz., r 0 , r 2 , r 4.5 , and E a are kept xed to their respective values obtained independently for the metallicferromagnetic (T < T M-SC ) and semiconductor-paramagnetic (T > T M-SC ) regions (see Table 4). The experimental data in Fig. 6 were tted using eqn (9). Fitting lines are shown in Fig. 6 and the results are presented in Table 4. The results calculated from eqn (9) agree well with the experimental data. However, the activation energy (E a ) in the absence of an external magnetic eld of the samples is extracted in the semiconductor-like conducting temperature region (well above T M-SC ) in terms of a magnetic polaron picture 48 (see Fig. 7). It was further observed that E a in the transport process of the carriers increases with decreasing hr A i and/or t g , implying the decrease of the localization length and the reduction of the carrier mobility, which is intimately related to the localization of carriers and the destruction of DE interaction arising from Pr-doping at A-site. Thus, are in accordance with the structural and magnetic properties discussed in the previous sections. MCE is an intrinsic property of magnetic materials. It is the response of the material toward the application or removal of a magnetic eld. This response is maximized when the material is near its magnetic ordering temperature. The magnetization M as a function of the applied magnetic eld, at various temperatures, is shown in Fig. 8(a). At the lowest temperatures, the magnetization saturates rapidly due to an easy orientation of the spins under the action of the applied eld. No magnetic hysteresis is found around the transition temperature, suggesting that the material is a so ferromagnetic. To assess the nature of magnetic phase transitions, Arrott plots 49 (m 0 H/M versus M 2 ) were constructed based on the M-H data (Inset of Fig. 8(a)). All of the M 2 vs. m 0 H/M curves show positive slopes without inexion points, which is characteristic of second order transitions according to the Banerjee criterion. 50 This feature is in agreement with Bean-Rodbell model analysis. The magnetic entropy changes, DS M , of La 0.52 Pr 0.15 Ba 0.33 MnO 2.98 has been calculated using the Maxwell relation 51 and is plotted in Fig. 8(b) as a function of temperature and eld. The maximum value of magnetic entropy change DS Max is found to be around T C and it increases with increasing the magnetic applied eld due to the enhancement of FM interactions.  At a DS M of 5 T, the maximum value of the magnetic entropy change DS M is found to be about 3.39 J kg À1 K À1 (1.34 J kg À1 K À1 for 1.5 T) and the estimated relative cooling power (RCP), which is considered as the efficiency of magnetocaloric materials based on the magnetic entropy change, is found to be 251 J kg À1 (71 J kg À1 for 1.5 T). The RCP value is calculated from the product of the peak entropy change times the full width at half maximum. These values are about 61% of those of pure Gd, the prototype magnetic refrigerant material (RCP ¼ 410 J kg À1 ). 52 For comparison, the obtained values are higher than the observed in manganite polycrystalline, La 0. 40 53 From these results, we can estimate that our material is potential candidates to magnetic refrigeration applications around room temperature.

Conclusion
The inuence of praseodymium substituting at La-site in (La 1Àx Pr x ) 0.67 Ba 0.33 MnO 3 (0.075 # x # 0.30) has been investigated, in structural, magnetic and electrical transport properties. The samples were synthesized using the Pechini sol-gel method. Rietveld renement of XRD patterns shows that all samples crystallized in a rhombohedral structure with R 3c space group. FTIR and Raman measurements conrms the perovskite structure of all the samples. The substitution of Pr 3+ changes A-site average cationic radius and decreases the lattice parameters, Curie temperatures (T C ), metal-semiconductor transition (T M-SC ), and the magnitude of magnetization in the ferromagnetic region. It is observed that doping of Pr induces an increase in polaron activation energy. This fact indicates that Pr doping enhances electronic localization. Numerical simulations, in the framework of the molecular mean eld model incorporating the Bean-Rodbell magnetovolume coupling were performed. We have found that Pr 3+ doping on A-site leads to more chemical/structural disorder in second-order magnetic system. On the other hand, the behavior of r (T,H) of these samples in a wide range of temperatures and magnetic elds can be explained using the phenomenological model based on the phase segregation mechanism (percolation model).
Around room temperature, the La 0.52 Pr 0.15 Ba 0.33 MnO 2.98 sample exhibit a sizable magnetic entropy change of 1.34 J kg À1 K À1 and a RCP of 71 J kg À1 under a magnetic eld change of 1.5 T, making this compound a suitable candidate for active magnetic refrigeration.

Conflicts of interest
There are no conicts to declare.