Magnetocaloric effect and critical behavior near the first to second-order phase transition of La0.7Ca0.3−xSnxMnO3 compounds

The magnetocaloric effect and the critical behavior near the first to second-order phase transition of La0.7Ca0.3-xSnxMnO3 compounds (with x = 0–0.04), which were prepared by a conventional solid state reaction method, have been investigated. With increasing Sn-doping, a systematic decrease in the Curie temperature (TC) and the magnetic entropy change (ΔSm) are observed. We also pointed out that the width and the order of the magnetic phase transition in La0.7Ca0.3-xSnxMnO3 compounds can be easily modified by changing Sn concentration. The Banerjee criterion suggests that the Sn-undoped sample (x = 0) undergoes a first-order phase transition (FOPT). Meanwhile, Sn-doped samples (x = 0.02 and 0.04) undergo a second-order phase transition (SOPT). Based on the Kouvel-Fisher method and the critical isotherm analyses, we have determined the values of the critical exponents (β, γ, and δ) and TC for two SOPT samples. The results obtained for x = 0.02 sample are β = 0.218, γ = 0.858, and δ = 4.717, which are close to those expected for the tricritical mean field theory. Whereas, β = 0.468, γ = 1.095 and δ = 3.315 obtained for x = 0.04 sample are close to those expected for the mean field theory. This suggests that the presence of Sn favors establishing the ferromagnetic long-range interactions in the sample.


Introduction
It is known that the hole doped perovskite manganite La 0.7 Ca 0.3 MnO 3 is a typical material exhibiting a colossal magnetoresistance (CMR) and a magnetocaloric effect (MCE) with high values magnetoresistance (MR) and magnetic entropy change (ΔS m ), respectively. These values are almost larger than those obtained on the other manganites [1][2][3][4][5][6][7]. Nevertheless, La 0.7 Ca 0.3 MnO 3 polycrystalline or single crystal bulk sample is a first-order phase transition (FOPT) material [8][9][10][11]. There are two important drawbacks in the FOPT materials, namely the narrowness of the FM-PM phase transition region and the presence of the thermal and magnetic hysteresis, which limit their applicability [12]. To improve these drawbacks, it is necessary to modify the order of phase transition in La 0.7 Ca 0.3 MnO 3 compound from FOPT to SOPT.
Recent studies have shown that there are some ways to modify the order of phase transition in La 0.7 Ca 0.3 MnO 3 compound, including reduced dimensionality [11], reduced crystalline or particle size [9,13], and doped suitable elements into the La/Ca [14][15][16][17][18] and/or Mn sites [19,20]. Depending on crystalline size, dopant types, and doping content, modifying the FOPT to SOPT results would be different. To distinguish whether a material is the FOPT or SOPT, we can use the criteria proposed by Banerjee [21]. According to these criteria, H/M is plotted versus M 2 in the vicinity of T C . A material is a FOPT if there is a negative slope on some H/M versus M 2 curves, while a positive slope corresponds to a SOPT [21]. Besides, it is known that the β, γ, and δ Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. critical exponents which featured for the SOPT around T C are corresponded with the M S spontaneous magnetization, the χ 0 −1 magnetic susceptibility at the beginning, the critical isotherm at T C [22,23].
To further understand the MCE and the critical behaviors near the first to second-order phase transition, we prepared three samples of La 0.7 Ca 0.3-x Sn x MnO 3 (with x=0.0, 0.02, and 0.04) and studied their magnetic characters. The dependences of magnetic entropy change on temperature and applied magnetic field were determined by using the Maxwell relation and a phenomenological model [24,25]. Besides, we applied the Banerjee's criteria [21], the Kouvel-Fisher method [23], and the critical isotherm analyses [22] to investigate the critical behaviors for samples. We pointed out that the presence of Sn favors establishing the SOPT and the FM long-range interactions in La 0.7 Ca 0.3-x Sn x MnO 3 compounds.

Experimental details
With the solid-state reaction procedure, we synthesized three bulk samples of La 0.7 Ca 0.3-x Sn x MnO 3 (x=0, 0.02, and 0.04). The precursors are highly immaculate powders (99.9%) of Sigma-Aldrich included La 2 O 3 , CaCO 3 , SnO 2 , and Mn 3 O 4 . The mass of these precursors were calculated and weighed according to the nominal composition (La 0.7 Ca 0.3-x Sn x MnO 3 ), then were crushed, blended, and calcinated at 1200°C in about 24 h in the air. Thereafter, the mixed products were crushed again, pressed tablets under a pressure of 4000 kg cm −2 and sintered at 1400°C within 28 h in the air. X-ray diffraction (XRD) patterns at room temperature of final products were recorded on an x-ray diffractometer (Equinox 5000, Thermo Scientific) using a Cu-K α radiation source (λ=1.5406 Å). The grain size and the component of samples were estimated through the scanning electronic microscopy (SEM) image and the energy dispersive x-ray (EDX) spectroscopy on a Fe-SEM (S4800, Hitachi). The magnetization depends on temperature and magnetic field was measured on a vibrating sample magnetometer system.

Results and discussion
These XRD patterns for samples are presented in figure 1. All XRD peaks in each pattern correspond to the Miller indexes of an orthorhombic structure, Pnma space group, and suitable for a PDF card No. 01-089-8075 [26] in the international centre for diffraction data. This confirms that all samples are single phase of La 0.7 Ca 0.3-x Sn x MnO 3 , without any secondary phase. The lattice parameters for samples were estimated and showed in table 1. Clearly, the presence of Sn does not change the orthorhombic structure but modifies the value of the lattice parameters. A slight decrease in these parameters with increasing Sn concentration was observed. This could be related to the average ionic radius of A-site (〈r A 〉) in perovskite structure ABO 3 [27,28]. Our result is completely opposite when Sn substituted into Mn-site (B-site) in similar manganites [28,29]. An increase of the unit cell parameters was observed when Sn substituted into Mn-site in La 0.67 Ba 0.33 Mn 1-x Sn x O 3 [30] and La 0.57 Nd 0.1 Sr 0.33 Mn 1-x Sn x O 3 [29] compounds. This result has been explained by the substitution of Sn 4+ with a larger ionic radius (r Sn4+ =0.69 Å) for Mn 4+ with a smaller radius (r Mn4+ =0.53 Å). Therefore, in our work, the substitution of Sn into Mn-site would not have happened.
In order to explain the increase of the lattice parameters of La 0.7 Ca 0.3-x Sn x MnO 3 compounds when increasing the amount of Sn, we have assumed that the valence of Sn ion is 2+ and it could be substituted into A-site because r Sn2+ =1.18 Å, which is quite close to that of Ca 2+ (1.34 Å) or La 3+ (1.36 Å). Therefore, the average ionic radius of A-site could be deduced as 〈r A 〉 = 0.7r La3+ +(0.3-x)r Ca2+ +xr Sn2+ . Using the ionic radii r La3+ =1.36 Å, r Ca2+ =1.34 Å, and r Sn2+ =1.18 Å [31], the value of 〈r A 〉 is found to be 1.354 Å, 1.350 Å, and 1.347 Å for x=0, 0.02, and 0.04, respectively (table 1). It shows that the 〈r A 〉 value monotonously decreases with increasing Sn concentration. Thus we believe the slight decrease of the unit-cell volume of La 0.7 Ca 0.3-x Sn x MnO 3 is closely related to the substitution of Sn 2+ with a smaller ionic radius (1.18 Å) for La 3+ /Ca 2+ ions (1.36 Å/1.34 Å). Figure 2 show SEM images and EDX spectra of two samples with x=0 and 0.04. We can see that their grain size reaches about micrometers with sharp grain boundary, figures 2(a) and (c). The EDX spectra show peaks corresponding to lanthanum, calcium, manganese, oxygen, and tin, figures 2(b) and (d). These elements are included in the samples, without any strange elements. The values of atomic percentage obtained are quite close to those expected of compounds. It means that starting materials have fully reacted to create La 0.7 Ca 0.3-x Sn x MnO 3 phase, no element is neither lost nor added during the fabrication process.  x  (7) 230.29 (8) The temperature dependence of the magnetization, M(T), at H=100 Oe for samples are show in figure 3(a). With increasing temperature, samples exhibit a FM-PM transition. T C values determined from the flexion points in M(T) curves are about 256, 198, and 166 K for x=0, 0.02, and 0.04, respectively. Clearly, T C value decreased monotonically with increasing Sn concentration. The decrease of T C could be associated to a reduction of 〈r A 〉 value, which is a consequence of the replacing Sn with smaller radius into La/Ca-site. On the other hand, T C value decreases because of the effect of the average ionic radius of A-site. Due to different ion sizes occupy at A-site (La/Ca/Sn-site) in perovskite structure, there is a size disorder between the ions. This disorder created a strong local stress in MnO 6 octahedral and also varying the Mn-O-Mn angles leading to the change in structural parameters and magnetic characters [28,32]. Figure 3(b) shows M(T) curves for samples measured at H=10 kOe, where the solid lines are fitting curves of experimental data to a phenomenological model, which was suggested by Hamad [24,25]. Detailed descriptions for this phenomenological model can be found elsewhere [24,25,32]. According to Hamad [24,25], the temperature dependence of magnetization can be presented by:       [37]). Therefore, this compound could be useful for the magnetic cooling technology. According to [24,25,32], the magnetic entropy change (ΔS m ) and the adiabatic temperature change (ΔT ad ) of a magnetic system under adiabatic magnetic field change from 0 to H max can be determined by using the equations where C p is the heat capacity. In this work, C p =605 J·kg −1 ·K −1 has been used from [32]. To learn about the nature of FM interactions in two SOPT samples (x=0.02 and 0.04), we have investigated their critical behaviors. Firstly, we used four different models for trial exponents, including the mean field theory (β=0.5 and γ=1.0) [22], the 3D-Heisenberg model (β=0.365 and γ=1.336) [22], the 3D-Ising model (β=0.325 and γ=1.241) [22], and the tricritical mean field theory (β=0.25 and γ=1.0) [8] to build the M 1/ β versus (H/M) 1/γ curves based on the M(H) data in the vicinity of T C for each sample (not shown). To select the best model, we have calculated the relative slope S(T)/S(T C ), with S(T) and S(T C ) are slopes at temperatures T and T C , respectively. It is known that if the values of β and γ are suitable, the M 1/ β versus (H/M) 1/γ curves show a series of parallel lines, the relative slope should be kept to 1 independently of temperatures [39]. From figure 6(a) we can see that the values of β and γ with x=0.02 can be best determined by the tricritical mean field theory. While, the critical properties for x=0.04 can be described by the mean field theory. The set of β=0.25, γ=1.0 and β=0.5, γ=1.0 are thus selected as the trial values for our investigations into the critical behaviors of x=0.02 and 0.04, respectively.
According to the Kouvel-Fisher method [23], the values of β, γ, and T C could be determined from the relations:  (6), we get the new values of β, γ, and T C, respectively. They are unbrokenly used for the next steps until achieving the durable β, γ, and T C values. The Kouvel-Fisher plots for x=0.02 and 0.04 with β and γ obtained from the final step are shown in figures 6(b) and (c), respectively. One can see that the value of T C obtained for each sample from the Kouvel-Fisher method (T C ≈197.3 and 166.3 K for x=0.02 and 0.04, respectively) is very close to that obtained from the M(T) curve at figure 3(a). The critical exponent of δ can be got by fitting the critical isotherm  (7). This proves that critical parameters β, γ, δ, and T C obtained above are reliable. However, in the other way, checking the reliability of the obtained critical exponents and T C values can be based on the scaling hypothesis [22] e where ε=(T-T C )/T C is the reduced temperature, f ± are regular analytic functions for temperatures above and below T C , respectively [22]. It insinuates that M/|ε| β as a function of H/|ε| β+γ falls into two universal curves, corresponding to T>T C and T<T C if determined values of critical exponents are correct. In this work, using the critical exponents and T C values obtained above, the M/|ε| β versus H/|ε| β+γ data of x=0.02 and 0.04 samples are plotted in the log-log scale as showed in figure 7. Interestingly, all experimental data of M(H, T) fall on two universal branches for upper and lower T C attesting that the values of β, γ and T C determined above are trustworthy. However, the M(H, T) data little deviates from the universal curves at the low fields (H<2 kOe). It is attributed to the redistribution of magnetic domains where they are not entire in a straight line with the field. Comparing our critical exponents determined and those of theoretical models (table 3) [8,22], it can be clearly seen that β=0.218, γ=0.858, and δ=4.717 for x=0.02 are quite near to those expected for the tricritical mean field theory (β=0.25, γ=1.0, δ=5.0) [8]. It is suggested that x=0.02 exhibiting tricriticality associated with the crossover of FOPT and SOPT, which is similar with that previous reported in La 0

Conclusion
In summary, a detailed study on MCE and the critical behaviors of La 0.