Study of Solid-State Synthesized Pr0.55Sr0.45Mn1-xCrxO3 Perovskites with x=0.0, 0.05, 0.1 and 0.15: Rietveld analysis, Magnetic and Magnetocaloric Properties for Magnetic Refrigeration Applications

Study of Solid-State Synthesized Pr0.55Sr0.45Mn1-xCrxO3 Perovskites with x=0.0, 0.05, 0.1 and 0.15: Rietveld analysis, Magnetic and Magnetocaloric Properties for Magnetic Refrigeration Applications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Study of Solid-State Synthesized Pr0.55Sr0.45Mn1-xCrxO3 Perovskites with x=0.0, 0.05, 0.1 and 0.15: Rietveld analysis, Magnetic and Magnetocaloric Properties for Magnetic Refrigeration Applications Ahmed Selmi, A. Hela, Malek Gassoumi, E. K. Hlil, Abdelaziz Bouazizi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8638249/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In the current study, the structural (X-ray diffraction XRD), magnetic, critical behavior and magnetocaloric properties of the polycrystalline Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 Manganites with (x = 0.0, 0.05, 0.1 and 0.15) samples were examined. All our samples have been elaborated by means of the solid-state reaction from stoichiometric powder mixtures of binary oxides at high temperatures. The compounds crystallize in the orthorhombic structure with Pnma space group, according to Rietveld refinement of the XRD pattern. All of the samples exhibit a second-order FM to PM phase transition, according to temperature and field-dependent magnetization measurements; however, the Curie temperature T C value decreases from 300 K to 275 K as the Cr (% x) content increases from 0.00 to 0.15. Using Maxwell thermodynamic relations, the magnetocaloric effect MCE in terms of maximum entropy change \(\:{-\varDelta\:S}_{M}^{max}\) , and relative cooling power RCP has been calculated using isothermal magnetization data around T C . In a magnetic field shift of 5 T, the highest values of the magnetic entropy change \(\:{-\varDelta\:S}_{M}^{max}\) have been determined to be 3.8 J/kg.K, 3.63 J/kg.K, 3.87 J/kg.K, and 2.55 J/kg.K for x = 0.0, x = 0.05, x = 0.1, and x = 0.15, respectively. For x = 0.0, x = 0.05, x = 0.1, and x = 0.15 at 5 T, the highest value of the relative cooling power RCP is found to be 247 J/kg, 254.1 J/kg, 205.1 J/kg, and 201 J/kg, respectively. The RCP value of 254.1 J/kg (5% of chromium) is equivalent to 58% of the RCP value of gadolinium metal. Technically, the developed material is highly promising for magnetic refrigeration because of these significant values. Manganite XRD diffraction magnetocaloric critical behavior paramagnetic PM and ferromagnetic FM magnetic refrigeration APPLICATION Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The perovskite manganite with a general formula RE 1 − x AE x MnO 3 RE = Rare Earth (La 3+ , Pr 3+ , Nd 3+ , Sm 3+ , etc…, & AE = alkaline earth (Sr 2+ , Ba 2+ , Bi 2+ …) have drawn a lot of interest in three recent decades because to their unique physical characteristics, including as phase separation, charge and orbital ordering, metal-to-insulator transition, and Magnetocaloric effect [ 1 ]. We are interested in a family of perovskite compounds in this paper. Recently, perovskite manganite compounds have been employed in a variety of applications, such as magnetic refrigeration systems [ 2 ], magnetoresistance [ 3 , 4 ], and high-efficiency photovoltaic solar cells [ 5 ] ... showed manganite-family perovskites with different doping atoms have extremely high Relative Cooling Powers (RCP), making them suitable for use as clean refrigeration sources [ 2 ]. The magneto-caloric effects (MCE), which Warburg discovered in 1881 [ 6 ] and have since been extensively studied, are the foundation of the so-called "magnetic refrigeration". Numerous researches have examined the crucial character of manganites close to a PM-FM phase transition [ 7 – 33 ]. Several methods of changing the physical characteristics of perovskite manganite RE 1 − x AE x MnO 3 , for example replace the trivalent rare earth ions (RE 3+ ) in the perovskite structure with a divalent element (AE 2+ ). A mixed valence of manganese Mn 3+ and Mn 4+ appears as a result of the partial substitution of RE 3+ . This valence state is at the base of the changes in the physical properties of these perovskites’ manganites, in particular the appearance of a ferromagnetic FM order of the spins of the Mn ions, following which the electron e g becomes itinerant and can hop from a Mn cation, via the oxygen anion, to another manganese having a completely empty e g band. The strong relationship between structural, electrical, and magnetic properties is one of the essential features of manganites. The double exchange (DE) mechanism, first proposed by Zener in 1951, provides an explanation for this association [ 34 ]. The replacement of rare earths has an indirect effect on the conduction mechanism, affecting the bandwith and angle of the conncetion between rearby manganese ions, according to a number of recent scientific studies [ 35 – 37 ] on manganites. Other way is studying the impacts of Mn doping by other elements is interesting since it is undeniable that Mn ions play a significant part in the double exchange interaction. Over the last few years, a number of research papers and project [ 38 – 49 ] have been conducted to comprehend the impact of replacing manganese at the B-Site with a transition element. It has been demonstrated that the addition of a transition metal with an electronic configuration distinct from Mn should result an important change to both Mn and the substituent elements configurations. So, the conduction mechanism is directly impacted by the replacement of Mn, making it possible to more effectively modify the manganite system physical characteristics. Additionally, the replacement of trivalent and tetravalent elements for Mn results in an increase in resistivity and a drop in transition temperature T C and magnetism. However, the type of the replacement elements mostly determines the precise effect. Chromium is one of these elements that affects manganites structural and magnetic characteristics. Doping of Mn by magnetic Cr have been cited in the studies like [ 50 – 55 ] both investigations show that the inclusion of Chromium in both systems has comparable outcomes, specifically a drop in the temperature of the magnetic transition from the FM state to the PM state as the rate of substitution x rises. Additionally, the Mn-O-Mn networks are impacted by the substitution of Mn sites by other elements. [ 56 , 57 ] the strong electron–phonon interaction known as the Jahn–Teller effect [ 58 ] and the double-exchange interaction (DE) linked Mn 3+ /Mn 4+ ions [ 59 ]. The characteristics of the magnetocaloric effect have been explained by these considerations. One of the manganites that has been investigated the most is Pr 1 − x Sr x MnO3, which exhibits a \(\:-{\varDelta\:s}_{M}^{max}\) arround 3 J/kg.K under applied magnetic field 5 T and passes through a paramagnetic metal to ferromagnetic metal transition around T C \(\:\approx\:\) 301 K [ 60 ]. This combination may undergo a ferromagnetic transition at ambient temperature with \(\:{-\varDelta\:S}_{M}^{max}\) greater than 4 J/kg.K, either by partially substituting Mn ions with other transition metal ions, such as M = Cr (Chromium). The structural, magnetic, and magnetocaloric characteristics of the series of manganites compounds Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 with (x = 0.0, 0.05, 0.1 and 0.15) are thoroughly examined in this paper. Rietveld's method of analysing rayon diffraction diagrams allowed for the precise determination of the structural characteristics of samples. In order to do this, we thoroughly examined the magnetocaloric effect and calculated the relative refroidissement power RCP, a crucial performance indicator. 2. Experimental details Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 with (x = 0.0, 0.05, 0.1 and 0.15) were synthesized using the standard solid-state reaction method at high temperature, by mixing Pr 6 O 11 , SrCO 3 , MnO 2 and Cr 2 O 3 . up to 99.9% purity in the desired proportions. In an agate mortar, the initial components were well combined. The obtained powders were then pressed into pellets (of about 1 mm thickness) and sintered at 900, 1100°C for 24h and 1200, 1300°C for 12h for each cycle to ensure a better crystallization with intermediate regrinding and repelling [ 61 , 62 ]. Phase purity, homogeneity and cell dimensions were determined by powder X-ray diffraction XRD at room temperature using a ‘Panalytical-X-pert-Pro‘ diffractometer with Cu-Kα radiation with λ = 1.5406 Å. Structural analysis was carried out by the standard Rielveld method [ 63 – 65 ] using Fullprof software. A vibrating sample magnetometer (VSM) was used to detect magnetization against temperature in the range of 20–400K and against applied magnetic field up to 5 T. Magnetization measurements against applied magnetic fields up to 5 T at several temperatures were used to deduce MCE findings. 3. Results and discussion 3.1 Structural analysis The x-ray diffraction pattern of Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 with (x = 0.0, 0.05, 0.1 and 0.15) at room temperature is shown in Fig. 1 . The XRD patterns sharp, well-defined peaks reveal a completely crystalline phase of Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 with a distinct orthorhombic phase with Pnma space group. The excellent quality and single phase of the elaborated samples was demonstrated by the absence of secondary phase-corresponding peaks (without impurity). We used Fullprof software to do Rietveld refinement [ 63 , 64 , 66 ] in order to gain a improved understanding of the structural characteristics of the orthorhombic phase. The two reliability factors, R p and R wp (weighted discrepancies between measured and calculated values), and the goodness of fit, χ 2 , which must tend to 1 and 2, were used to assess the quality of the fitting of the experimental data. Using Rietveld refinement, the values of several structural parameters, lattice parameters (a, b and c), unit volume, Bond lengths, Bond angles and the goodness of fit χ 2 etc…are showed in Table 1 . Table 1 Structural properties of compounds Pr 0.55 Sr 0.45 Mn 1-x Cr x O 3 with (x = 0.0, 0.05, 0.1, and 0.15) at room temperature as determined by the Rietveld method. x 0 0.05 0.10 0.15 a (Å) 5.4409(3) 5.4372(2) 5.43928(20) 5.4455(5) b (Å) 7.6558(3) 7.6502(3) 7.6548(3) 7.6514(6) c (Å) 5.4807(2) 5.48076(19) 5.48331(17) 5.4739(5) V (Å 3 ) 228.296(0.018) 227.976(0.015) 228.305(0.013) 228.073(0.035) Bragg R-factor 3.79 5.55 5.86 4.69 Rf-factor 7.52 10.1 10.3 6.18 () (Å) 2.06232 1.91294 1.96855 1.90844 (Mn1) -( O2) -( Mn1) 173.244 168.219 168.224 154.745 () (Å) 1.80577 1.96766 1.91368 2.04774 (Mn2) -( O2) -( Mn2) 173.244 168.219 168.224 154.745 () (Å) 1.94945 1.93545 1.93661 1.93427 (Mn1) -( O1) -( Mn1) 158.099 162.355 162.357 162.932 R e 16.4 16.5 17.0 17.6 R p (%) 30.5 31.7 33.6 33.1 R wp (%) 20.5 20.7 21.8 22.4 c² (%) 1.56 1.57 1.64 1.63 Table 2 Summary of \(\:-\varDelta\:{S}_{M}^{max}\) , T C and RCP values for Pr 0.55 Sr 0.45 Mn 1-x Cr x O 3 with (x = 0.0, 0.05, 0.1, and 0.15). x 0 0.05 0.10 0.15 T C (K) 300 292 286 275 - \(\:{\varDelta\:S}_{M}^{max}\) (J/kg.K) 3,80 3.63 3.87 2.55 δT FWHM 65 70 53 79 RCP(J/kg) 247 254.1 205.1 201 A thorough comprehension of the structural and functional characteristics intrinsic to our Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 compound series (where x = 0.0, 0.05, 0.1, and 0.15) requires a careful examination of the crystallographic parameters, especially the Manganese-Oxygen distances bond and the inter-octahedral angles. The size and degree of deformation of the MnO 6 octahedra are directly indicated by the interatomic distances. In the Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 structure, the substitution of Mn by chromium Cr significantly changes the average oxidation state of the manganese ions, resulting in the introduction of certain structural stresses. The Jahn-Teller effect, which is usually connected to the presence of Mn 3+ cations, is likewise very sensitive to these ensuing variations in bond lengths. These ions electrical asymmetry forces the octahedra to elongate or compress, which is crucial in establishing the local structural environment. At the same time, the connectivity and coupling effectiveness between neighboring MnO 6 octahedra are determined by the bond angles. The amount of octahedral inclination is directly influenced by the degree of chromium substitution. The double-exchange DE process (Mn 3+ -O-Mn 4+ ) that drives the observed ferromagnetism in these manganites is crucially mediated by this tilting, making it extremely significant. In particular, the orbital overlap is maximized when the angle gets closer to the optimal 180 degrees, which improves charge carrier mobility and fortifies the magnetic interactions. In conclusion, examining the simultaneous changes in distances controlled by the Jahn-Teller effect and substitution and the angles which determine the effectiveness of the double-exchange pathway is crucial to understanding the magnetic properties seen in Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 . 3.2 Magnetic properties The temperature dependence of the magnetization, M(T), under an applied magnetic field µ 0 H = 0.05 T, for all our samples are displayed in Fig. 2 (a) . We plotted in Fig. 2 (b) the magnetization as a function of temperature under a weak applied field of 0.05 T, with the dM/dT curve used to determine the minimum temperature Tc of the parent compound curve, clearly demonstrating the paramagnetic-ferromagnetic transition. For the Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 series (x = 0.0, 0.05, 0.1, and 0.15), the magnetization versus temperature M(T) curves provide important information on their magnetic behavior. These compounds show a change from the paramagnetic PM to a ferromagnetic FM state as the temperature decreases. The key parameter known as the Curie temperature T C indicates the temperature at which a material changes from a paramagnetic to a ferromagnetic state. The Curie temperatures T C have determined from the minimum value of the dM/dT versus T curves (refer to the inset of Fig. 2 ) The T C values for the Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 series are shown to decrease as the Cr concentration increases: for x = 0.0, 0.05, 0.10, and 0.15, T C (K) = 300 K, 292 K, 286 K and 275 K. This pattern implies that the ferromagnetic interactions are weakened when Mn is replaced with Cr in the lattice, which lowers the Tc, similarly in the literature, that is confirmed in the work of A.K. Saw and all [ 67 ] and other work [ 68 ]. Furthermore, when Cr is substituted in Cr-doped manganites, the magnetism in the FM region also decreases. A qualitative explanation for the decline in T C and magnetization with increased chromium concentration is the decrease in the Mn 3+ /Mn 4+ ratio. This action increases the SE Super exchange antiferromagnetic state by reducing the Mn 3+ -Mn 4+ couples that cause DE Double exchange ferromagnetism and introducing a small amount of Mn 3+ -Mn 3+ , Mn 4+ -Mn 4+ , Cr 3+ -Cr 3+ , and Mn 3+ -Cr 3+ couples [ 69 ]. The magnetization isotherms M(H) recorded for all compounds in magnetic fields equal to 5 T over a broad temperature range of 240–320 K demonstrate that, below Curie temperature, magnetization increases significantly in weak applied fields until approaching saturation for applied fields \(\:{\mu\:}_{0}H\) =1 T. Figure 3 (a), (b), (c), and (d) display the usual magnetization isotherm shape for x = 0.0, 0.05, 0.1, and x = 0.15. As the temperature decrease, the saturation magnetization increase. The purely ferromagnetic behavior of the samples at low temperatures is confirmed by this result. Important information on the magnetic characteristics and phase transitions of manganites is provided by the magnetization versus magnetic field M(H) measurements. The nature of the magnetic ordering and the transitions between various magnetic phases are revealed by these observations. For example, the M(H) curves in Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 (x = 0.00, 0.05, 0.1, and 0.15) show a second-order ferromagnetic FM to paramagnetic PM phase transition, where the Curie temperature T C decreases with increasing Cr-doped concentration. Similarly, the M(H) measurements reveal a second-order PM-FM transition in the studie of A. Dhahri & all Pr 0.67 Sr 0.33 Mn 1−x M x O 3 (0.0 < x ≤ 0.09) [ 70 ]. These findings are also essential for comprehending the magnetic interactions and the materials possible uses in magnetic refrigeration and other technologies. 3.3 Critical behavior The analysis of the Arrott curve makes it possible to understand the critical behavior at the critical point. The magnetic equation of state for a system that adheres to the theory of the average field (MFT) is as follows: $$\:\frac{\text{H}}{\text{M}}=\text{A}+\text{B}{\text{M}}^{2}\:$$ 1 The order of the magnetic phase transition is revealed by a thorough analysis of M(H) isotherms. From M(H) isotherms near T C , we inferred the Arrott plots ((M 1/β vs µoH/M) 1/g ), which are shown in Fig. 4 (a), (b), (c), and (d) Banerjee's criterion [ 71 ] states that a first-order or second-order magnetic phase transition is indicated by a negative or positive slope of Arrott curves. The results of M 2 against µ 0 H/M graphs for Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 reveal the second-order FM to PM phase transition, with a positive slope in all cases throughout the entire M 2 range, the values of exponents β and γ are taken 0.5 and 1, respectively, as expected from mean field theory). Curie temperatures T C determined from Arrott plots coincide with those obtained from the low field magnetization curves M(T) for All compounds. Figure 5 show the temperature dependence of the spontaneous magnetization (M sp ) deduced from the M(H) curves and the inverse of the susceptibility (1/χ) as a function of temperature for Pr 0.55 Sr 0.45 MnO 3 sample. In the paramagnetic phase (T > T C ), this sample exhibit linear inverse susceptibility behavior. \(\:{\chi\:}=C/(\text{T}-{{\theta\:}}_{P})\) , where \(\:{{\theta\:}}_{P}\) is the Curie constant and C is the Curie-Weiss temperature. For x = 0.0, the \(\:{{\theta\:}}_{P}\) value is determined to be 303 K. The presence of a ferromagnetic exchange interaction between the closest neighbors is indicated by the positive value of q P . The resultant value is marginally above the Curie temperatures. We can deduce that this difference depends on the substance and is related to the presence of short-range ordered slightly above the Curie temperature, which is related to the presence of a magnetic inhomogeneity [ 72 ]. For x = 0.0, the critical exponent β is determined to be 0.362, indicating that all of our samples exhibit ferromagnetic activity at low temperatures. The ferromagnetic condition described for manganites [ 63 , 72 , 73 ] is in good agreement with this value. 3.4 Magnetocaloric measurements The thermodynamic theory states that the magnetic entropy change brought about by the magnetic fields variation from 0 to \(\:{\text{H}}_{max}\) is as follows [ 74 ]: $$\:{{\Delta\:}\text{S}}_{M}\:(\text{T},\text{H})=\:{\text{S}}_{M}\:(\text{T},\text{H})\:-\:{\text{S}}_{M}\:(\text{T},0)=\int\:\frac{{dM}(T,H)}{dT}dH$$ 2 Using Maxwell’s relation $$\:(\frac{\partial\:M}{\partial\:T}{)}_{H}=(\frac{\partial\:S}{\partial\:H}{)}_{T}$$ 3 The following expression can be obtained: $$\:{{\Delta\:}\text{S}}_{M}\:(\text{T},\text{H})={\int\:}_{0}^{{H}_{max}}{\left(\frac{\partial\:M}{\partial\:T}\right)}_{H}dH$$ 4 Equation ( 4 ) states that the magnetic entropy change reaches its highest during the magnetic transition phase. The magnetic entropy change can be it was calculated approximately using the numerical formula employing isothermal magnetization data in small discrete fields and temperature intervals [ 75 ]: $$\:{{\Delta\:}\text{S}}_{\text{M}}\:\left(\text{T},\:\text{H}\right)=\sum\:\left(\frac{{M}_{i}-{M}_{i+1}}{{T}_{i+1}-{T}_{i}}\right){{\Delta\:}\text{H}}_{\text{i}}$$ 5 where M i and M i+1 are the experimental magnetization values obtained at the temperatures T i and T i+1 , respectively, in an applied magnetic field H i . The magnetic entropy changes \(\:\left|{\Delta\:}{\text{S}}_{\text{M}}\right|\) of Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 samples as a function of temperature under various magnetic applied field variations is plotted in Fig. 6 (a, b, c, and d) . We find that rises and peaks around the magnetic-transition temperature. The \(\:-{\Delta\:}{\text{S}}_{\text{M}}\) exhibits a broad positive peak around T c (normal MCE) for all samples. The maximum values of the magnetic entropy change, \(\:\left|\varDelta\:{S}_{M}^{max}\right|\) are 3.8 J/kg.K, 3.63 J/kg.K, 3.87 J/kg.K and 2.55 J/kg.K in a magnetic field change of 5 T for x = 0.0, x = 0.05, x = 0.1 and x = 0.15 respectively. The relative cooling power (RCP) [ 76 – 78 ] is evaluated as: $$\:RCP=-\varDelta\:{S}_{M}(T,H)\times\:{\delta\:T}_{FWHM}$$ 6 Where \(\:{\delta\:T}_{FWHM}\) is the full-width at half-maximum of \(\:-{\Delta\:}{\text{S}}_{\text{M}}\) versus temperature [ 79 – 81 ]. For our samples, the RCP values are respectively 247 J/kg, 254.1 J/kg, 205.1 J/kg and 201 J/kg at 5 T for x = 0.0, x = 0.05, x = 0.1 and x = 0.15. Despite having the lowest \(\:\left|\varDelta\:{S}_{M}^{max}\right|\) , the composition of 5% of chromium doping manganese seems to be the most promising for magnetic refrigeration applications because of its high RCP value. For cooling cycles to be effective, entropy change and temperature range must be balanced. As seen in Fig. 7 , the delta \(\:\left|\varDelta\:{S}_{M}^{max}\right|\) values obtained and the RCP values computed using Eq. ( 6 ) are plotted versus µ 0 H. It was evident that at T C , the relative cooling power RCP and maximum entropy change \(\:\left|\varDelta\:{S}_{M}^{max}\right|\) are both proportional to µ 0 H. RCP is a field-dependent variable, as evidenced by its trend with µ 0 H. Our sample RCP (5% of chromium) value of 254.1 J/kg is 58% of Gd RCP value, which is the industry standard for refrigeration [ 75 ] materials with high \(\:{\delta\:T}_{FWHM}\) and RCP values can operate over a wide temperature range and have a large cooling capacity. Magnetic refrigeration works well with these materials [ 82 , 83 ]. Numerous methods for figuring out the order of magnetic phase transitions have been proposed in the literature [ 71 , 84 ]. One of these is to use the relation \(\:{\varDelta\:\text{S}}_{\text{M}}(\text{H},\text{T})\approx\:{aH}^{n}\) , where a is a constant and n is an exponent related to magnetic order, to examine the field dependence of the samples MCE [ 85 – 87 ]. Important details regarding the type of magnetic phase transition in the investigated materials can be found by calculating the exponent values at specific temperatures. The logarithmic derivative of experimental data can be used to determine the exponent n at a specific temperature and magnetic field \(\:{\varDelta\:\text{S}}_{\text{M}}(\text{H},\text{T})\) [ 85 ] : $$\:n\left(T,\:H\right)=\frac{dln\:(\varDelta\:{S}_{M}\left(T,\:H\right))}{dln\:\left(H\right)}\:\:\:\:\:\left(7\right)$$ The Curie-Weiss rule causes the n values to approach n = 2 at high temperatures in the paramagnetic phase (over the T C ) [ 86 ]. In the ferromagnetic phase, n typically has a value that tends to be n = 1 at temperatures well below the transition point. The value of n changes according to the kind of phase transition (first or second-order) of the material within a crucial temperature range surrounding the Curie temperature. Previous investigation has demonstrated that a quantitative criterion of n > 2 close to the transition temperature \(\:T={T}_{C}\) could be interpreted as a first-order magnetic phase transition of the material. It has also been demonstrated that this criterion could be successfully applied to a variety of magnetocaloric materials in order to identify the type of magnetic phase transition [ 87 ]. Figure 8 illustrate the Pr 0.55 Sr 0.45 MnO 3 compound temperature dependency of exponent n under various magnetic fields n(T). The sample exponent n tends to approach 1 at temperatures significantly below the Curie temperature (ferromagnetic region). The exponent n tends to 2 for temperatures greater than Tc (paramagnetic zone). This behavior for exponent n is typically explained by a second-order phase transition. As the temperature drops near the transition temperature, a fall in n is seen, with a minimum value at the Curie temperature. Other magnetic materials with first and second-order transitions have been reported to exhibit similar behavior. [ 41 , 71 , 84 – 86 , 88 ]. 4. Conclusions In summary, this study concentrated on the structural, magnetic and magnetocaloric characterisation of the Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 Manganites compounds with (x = 0.0, 0.05, 0.1 and 0.15), which were successfully elaborated using a solid-state reaction method. The crystalline structure was found to be orthorhombic, corresponding to the Pnma space group, and X-ray diffraction investigations verified the production of a single phase over the compositional range without impurity phase. For all produced compounds, magnetization measurements as a function of temperature and applied field consistently showed a magnetic phase transition from the ferromagnetic (FM) to the paramagnetic (PM) state. It is remarkable that this transition was found to be of second order. It was discovered that the Curie temperature \(\:{T}_{C}\) , which decreased from 300 K to 275 K over the examined substitution period, could be efficiently modulated by gradually adding chromium in place of manganese. The crucial impact of the \(\:{Cr}^{3+}\) ion on the magnetic exchange processes inside the crystal lattice is shown by this dependence. Using isothermal magnetization data and the Maxwell thermodynamic laws, the magnetocaloric effect MCE was thoroughly examined. The outcomes for a 5 T change in magnetic field are very encouraging. For the x = 0.1 composition, the highest magnetic entropy change \(\:{-\varDelta\:S}_{M}^{max}\) was found to peak at 3.87 J/kg.K. More significantly, the Pr 0.55 Sr 0.45 Mn 0.95 Cr 0.05 O 3 sample had the highest relative cooling power (RCP) value, measuring 254.1 J/kg. Considering that its RCP value is roughly 58% of that of pure gadolinium, an accepted industrial measurement, this performance places the x = 0.05 material in a very promising category for magnetic refrigeration applications. In conclusion, the Pr 0.55 Sr 0.45 Mn 1−x Cr x O 3 family of manganites is an attractive class of magnetocaloric materials for the creation of effective and eco-friendly magnetic cooling devices, especially because chromium concentration can be used to adjust the operating temperature. Declarations Declaration of interest statement ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Contribution 1-Ahmed Selmi: Conceptualization, methodology, investigation, data curation, formal analysis, writing—original draft.2-A. 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Vagadia, M.D. Daivajna, Finite-size effects on the evolution of magnetic correlations and magnetocaloric properties of Pr 0.4 Bi 0.2 Sr 0.4 MnO 3 . Appl. Phys. A 127 (2021). https://doi.org/10.1007/s00339-021-04828-8 A. Selmi, R. M’nassri, W. Cheikhrouhou-Koubaa, N.C. Boudjada, A. Cheikhrouhou, Influence of transition metal doping (Fe, Co, Ni and Cr) on magnetic and magnetocaloric properties of Pr 0.7 Ca 0.3 MnO 3 manganites. Ceram. Int. 41 , 10177–10184 (2015). https://doi.org/10.1016/j.ceramint.2015.04.123 M. Földeàki, R. Chahine, T.K. Bose, Magnetic measurements: A powerful tool in magnetic refrigerator design. J. Appl. Phys. 77 , 3528–3537 (1995). https://doi.org/10.1063/1.358648 V.K. Pecharsky, K.A. Jr Gschneidner, Giant Magnetocaloric Effect InGD 5 (SI 2 GE 2 ). Phys. Rev. Lett. 78 , 4494–4497 (1997). https://doi.org/10.1103/PhysRevLett.78.4494 C.P. Bean, D.S. Rodbell, Magnetic Disorder as a First-Order Phase Transformation. Phys. Rev. 126 , 104–115 (1962). https://doi.org/10.1103/PhysRev.126.104 V. Franco, J.S. Blázquez, B. Ingale, A. Conde, The Magnetocaloric Effect and Magnetic Refrigeration Near Room Temperature: Materials and Models. Annu. Rev. Mater. Sci. 42 , 305–342 (2012). https://doi.org/10.1146/annurev-matsci-062910-100356 J.Y. Law, V. Franco, L.M. Moreno-Ramírez, A. Conde, D.Y. Karpenkov, I. Radulov, K.P. Skokov, O. Gutfleisch, A quantitative criterion for determining the order of magnetic phase transitions using the magnetocaloric effect. Nat. Commun. 9 , 2680 (2018). 10.1038/s41467-018-05111-w R. M’nassri, M.M. Nofal, P. De Rango, N. Chniba-Boudjada, Magnetic entropy table-like shape and enhancement of refrigerant capacity in La1.4Ca1.6Mn2O7 La1.3Eu0.1Ca1.6Mn2O7 composite. RSC Adv. 9 , 14916–14927 (2019). https://doi.org/10.1039/C9RA00984A V. Suresh Kumar, R. Mahendiran, B. Raveau, Effect of Ru-Doping on Magnetocaloric Effect in Pr Based Charge Ordered Manganites. IEEE Trans. Magn. 46 , 1652–1655 (June 2010). https://doi.org/10.1109/tmag.2010.2044754 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8638249","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":585110100,"identity":"9dabb1f1-a4e8-4a74-87d5-c34c8a912810","order_by":0,"name":"Ahmed Selmi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuklEQVRIiWNgGAWjYBACAwYeBoYENgY5EOfAA1K0GIO1JBCthYGNIbEBxCNKizl779END8rq0ueHHX4ItMVOTreBgBbLnnNpNxLOHc7deDvNAKgl2djsACGH3cgxu5HYdiB34+wEkJYDiduI1FKXbjg7/QNJWpgT5KVziLTFsueMGcgvhhukcwoOJBgQ4Rdz9h6zmz/K6uTlZ6dv/vChwk6OoBaEC8EqDYhVDgLyDaSoHgWjYBSMghEFAKtrSiIbZFV2AAAAAElFTkSuQmCC","orcid":"","institution":"University of Monastir","correspondingAuthor":true,"prefix":"","firstName":"Ahmed","middleName":"","lastName":"Selmi","suffix":""},{"id":585110101,"identity":"027447bb-8728-4ab6-a092-a25d189887b3","order_by":1,"name":"A. Hela","email":"","orcid":"","institution":"University of Monastir","correspondingAuthor":false,"prefix":"","firstName":"A.","middleName":"","lastName":"Hela","suffix":""},{"id":585110102,"identity":"4d784a4e-9ff6-495d-9931-83419d5adb9a","order_by":2,"name":"Malek Gassoumi","email":"","orcid":"","institution":"University of Monastir","correspondingAuthor":false,"prefix":"","firstName":"Malek","middleName":"","lastName":"Gassoumi","suffix":""},{"id":585110103,"identity":"13f1eb7e-daee-4738-9115-e2d4f5cb69a8","order_by":3,"name":"E. K. Hlil","email":"","orcid":"","institution":"Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel","correspondingAuthor":false,"prefix":"","firstName":"E.","middleName":"K.","lastName":"Hlil","suffix":""},{"id":585110104,"identity":"50857a7d-51a9-4e73-94b4-52701e9fa349","order_by":4,"name":"Abdelaziz Bouazizi","email":"","orcid":"","institution":"University of Monastir","correspondingAuthor":false,"prefix":"","firstName":"Abdelaziz","middleName":"","lastName":"Bouazizi","suffix":""}],"badges":[],"createdAt":"2026-01-19 10:24:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8638249/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8638249/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101946999,"identity":"e6fa5e9c-693c-4863-b146-8f22411730c9","added_by":"auto","created_at":"2026-02-05 10:03:15","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":179609,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eX-ray powder diffraction patterns and refinement at room temperature for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMn\u003c/em\u003e\u003csub\u003e\u003cem\u003e1-x\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eCr\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e (\u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(a)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003ex=0, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(b)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.05, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(c)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.1 and \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(d)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.15) showing the calculated, observed, difference intensities along and the Bragg positions (the vertical bars in green).\u003c/em\u003e\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/748d74c44bc6d1b8baecc686.jpg"},{"id":101947287,"identity":"c0a27829-fe0a-47de-8f60-7d08c9dc0774","added_by":"auto","created_at":"2026-02-05 10:04:15","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":96968,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003e(a)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e The temperature dependence of magnetization for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMn\u003c/em\u003e\u003csub\u003e\u003cem\u003e1-x\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eCr\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e (x=0, x=0.05, x=0.1 and x=0.15) samples. The Inset dM/dT\u003c/em\u003e \u003cem\u003eversus temperature curves of the samples.\u003c/em\u003e\u003cem\u003e\u003cstrong\u003e (b)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e Temperature dependence of magnetization measured at magnetic field m\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eH = 0.05 T for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMnO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e sample and the dM/dT\u003c/em\u003e \u003cem\u003eversus temperature curves. \u0026nbsp;\u003c/em\u003e\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/00998f1ad9a497c949757a71.jpg"},{"id":101947206,"identity":"087053f3-a0f4-406b-bf65-92062e1fcc71","added_by":"auto","created_at":"2026-02-05 10:04:01","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":681136,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eIsothermal magnetization patterns for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMn\u003c/em\u003e\u003csub\u003e\u003cem\u003e1-x\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eCr\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e (\u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(a)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003ex=0, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(b)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.05, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(c)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.1 and \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(d)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.15) samples at various temperatures.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/6ccab9f9efceefbcc6e815b7.jpg"},{"id":101947225,"identity":"41e23ed4-0747-4cf1-9354-5d561a760e83","added_by":"auto","created_at":"2026-02-05 10:04:06","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":759179,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eThe Arrott plots ((M\u003c/em\u003e\u003csup\u003e\u003cem\u003e1/b\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e vs μoH/M)\u003c/em\u003e\u003csup\u003e\u003cem\u003e1/g\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e) β=0.5 and γ=1, of Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMn\u003c/em\u003e\u003csub\u003e\u003cem\u003e1-x\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eCr\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e (\u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(a)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003ex=0, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(b)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.05, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(c)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.1 and \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(d)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.15) compounds.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/246f2ad9d64d297d053d7821.jpg"},{"id":101947286,"identity":"83201c13-05d3-4706-a0bf-74996551402a","added_by":"auto","created_at":"2026-02-05 10:04:15","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":30356,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eThe spontaneous magnetization (Msp) and inverse of susceptibility 1/\u0026nbsp;as a function of temperature for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMnO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e compound.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/d5a091dfc33817dc2d191dda.jpg"},{"id":101946994,"identity":"b3de02a0-a47f-4809-ac13-0160c0219af2","added_by":"auto","created_at":"2026-02-05 10:03:14","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":764198,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e-ΔS\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e, Magnetic entropy change, VS T around the Curie temperature T\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMn\u003c/em\u003e\u003csub\u003e\u003cem\u003e1-x\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eCr\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e (\u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(a)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003ex=0, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(b)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.05, \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(c)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.1 and \u003c/em\u003e\u003cem\u003e\u003cstrong\u003e(d)\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e x=0.15) compounds.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/b8c326a52b7a6807ff656eab.jpg"},{"id":101947133,"identity":"0974221e-0d05-4aea-a481-8b46ea03b79a","added_by":"auto","created_at":"2026-02-05 10:03:43","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":29888,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eThe relation of maximum entropy changes and the RCP ‘relative cooling power’ with μoH for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3 \u003c/em\u003e\u003c/sub\u003e\u003cem\u003ecompound.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/fcd9b9a330ca4b1f070be3ec.jpg"},{"id":101947473,"identity":"0cf01f57-fab0-4a54-af8a-88b0bd929d89","added_by":"auto","created_at":"2026-02-05 10:04:38","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":37371,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eTemperature dependence of the exponent, n (T), of the magnetic entropy -ΔS\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e change for several applied magnetic field values for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/a183f51f0a105ec84d266544.jpg"},{"id":103528235,"identity":"3af33a0a-ed7b-4a6b-9677-f44b49cc77e0","added_by":"auto","created_at":"2026-02-26 16:26:03","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3770125,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8638249/v1/2c10265d-d807-4ec7-aa16-495c845a89b0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Study of Solid-State Synthesized Pr0.55Sr0.45Mn1-xCrxO3 Perovskites with x=0.0, 0.05, 0.1 and 0.15: Rietveld analysis, Magnetic and Magnetocaloric Properties for Magnetic Refrigeration Applications","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe perovskite manganite with a general formula \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRE\u003c/span\u003e\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAE\u003c/span\u003e\u003csub\u003ex\u003c/sub\u003eMnO\u003csub\u003e3\u003c/sub\u003e RE\u0026thinsp;=\u0026thinsp;Rare Earth (La\u003csup\u003e3+\u003c/sup\u003e, Pr\u003csup\u003e3+\u003c/sup\u003e, Nd\u003csup\u003e3+\u003c/sup\u003e, Sm\u003csup\u003e3+\u003c/sup\u003e, etc\u0026hellip;, \u0026amp; AE\u0026thinsp;=\u0026thinsp;alkaline earth (Sr\u003csup\u003e2+\u003c/sup\u003e, Ba\u003csup\u003e2+\u003c/sup\u003e, Bi\u003csup\u003e2+\u003c/sup\u003e\u0026hellip;) have drawn a lot of interest in three recent decades because to their unique physical characteristics, including as phase separation, charge and orbital ordering, metal-to-insulator transition, and Magnetocaloric effect [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. We are interested in a family of perovskite compounds in this paper.\u003c/p\u003e \u003cp\u003eRecently, perovskite manganite compounds have been employed in a variety of applications, such as magnetic refrigeration systems [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], magnetoresistance [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], and high-efficiency photovoltaic solar cells [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] ... showed manganite-family perovskites with different doping atoms have extremely high Relative Cooling Powers (RCP), making them suitable for use as clean refrigeration sources [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The magneto-caloric effects (MCE), which Warburg discovered in 1881 [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] and have since been extensively studied, are the foundation of the so-called \"magnetic refrigeration\".\u003c/p\u003e \u003cp\u003eNumerous researches have examined the crucial character of manganites close to a PM-FM phase transition [\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11 CR12 CR13 CR14 CR15 CR16 CR17 CR18 CR19 CR20 CR21 CR22 CR23 CR24 CR25 CR26 CR27 CR28 CR29 CR30 CR31 CR32\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Several methods of changing the physical characteristics of perovskite manganite \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eRE\u003c/span\u003e\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eAE\u003c/span\u003e\u003csub\u003ex\u003c/sub\u003eMnO\u003csub\u003e3\u003c/sub\u003e, for example replace the trivalent rare earth ions (RE\u003csup\u003e3+\u003c/sup\u003e) in the perovskite structure with a divalent element (AE\u003csup\u003e2+\u003c/sup\u003e). A mixed valence of manganese Mn\u003csup\u003e3+\u003c/sup\u003e and Mn\u003csup\u003e4+\u003c/sup\u003e appears as a result of the partial substitution of RE\u003csup\u003e3+\u003c/sup\u003e. This valence state is at the base of the changes in the physical properties of these perovskites\u0026rsquo; manganites, in particular the appearance of a ferromagnetic FM order of the spins of the Mn ions, following which the electron e\u003csub\u003eg\u003c/sub\u003e becomes itinerant and can hop from a Mn cation, via the oxygen anion, to another manganese having a completely empty e\u003csub\u003eg\u003c/sub\u003e band. The strong relationship between structural, electrical, and magnetic properties is one of the essential features of manganites. The double exchange (DE) mechanism, first proposed by Zener in 1951, provides an explanation for this association [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The replacement of rare earths has an indirect effect on the conduction mechanism, affecting the bandwith and angle of the conncetion between rearby manganese ions, according to a number of recent scientific studies [\u003cspan additionalcitationids=\"CR36\" citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] on manganites. Other way is studying the impacts of Mn doping by other elements is interesting since it is undeniable that Mn ions play a significant part in the double exchange interaction. Over the last few years, a number of research papers and project [\u003cspan additionalcitationids=\"CR39 CR40 CR41 CR42 CR43 CR44 CR45 CR46 CR47 CR48\" citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] have been conducted to comprehend the impact of replacing manganese at the B-Site with a transition element. It has been demonstrated that the addition of a transition metal with an electronic configuration distinct from Mn should result an important change to both Mn and the substituent elements configurations. So, the conduction mechanism is directly impacted by the replacement of Mn, making it possible to more effectively modify the manganite system physical characteristics. Additionally, the replacement of trivalent and tetravalent elements for Mn results in an increase in resistivity and a drop in transition temperature T\u003csub\u003eC\u003c/sub\u003e and magnetism. However, the type of the replacement elements mostly determines the precise effect. Chromium is one of these elements that affects manganites structural and magnetic characteristics. Doping of Mn by magnetic Cr have been cited in the studies like [\u003cspan additionalcitationids=\"CR51 CR52 CR53 CR54\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e] both investigations show that the inclusion of Chromium in both systems has comparable outcomes, specifically a drop in the temperature of the magnetic transition from the FM state to the PM state as the rate of substitution x rises. Additionally, the Mn-O-Mn networks are impacted by the substitution of Mn sites by other elements. [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e] the strong electron\u0026ndash;phonon interaction known as the Jahn\u0026ndash;Teller effect [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e] and the double-exchange interaction (DE) linked Mn\u003csup\u003e3+\u003c/sup\u003e/Mn\u003csup\u003e4+\u003c/sup\u003e ions [\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e]. The characteristics of the magnetocaloric effect have been explained by these considerations. One of the manganites that has been investigated the most is Pr\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSr\u003csub\u003ex\u003c/sub\u003eMnO3, which exhibits a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-{\\varDelta\\:s}_{M}^{max}\\)\u003c/span\u003e\u003c/span\u003e arround 3 J/kg.K under applied magnetic field 5 T and passes through a paramagnetic metal to ferromagnetic metal transition around T\u003csub\u003eC\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\approx\\:\\)\u003c/span\u003e\u003c/span\u003e301 K [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e]. This combination may undergo a ferromagnetic transition at ambient temperature with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{-\\varDelta\\:S}_{M}^{max}\\)\u003c/span\u003e\u003c/span\u003e greater than 4 J/kg.K, either by partially substituting Mn ions with other transition metal ions, such as M\u0026thinsp;=\u0026thinsp;Cr (Chromium).\u003c/p\u003e \u003cp\u003eThe structural, magnetic, and magnetocaloric characteristics of the series of manganites compounds Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1 and 0.15) are thoroughly examined in this paper. Rietveld's method of analysing rayon diffraction diagrams allowed for the precise determination of the structural characteristics of samples. In order to do this, we thoroughly examined the magnetocaloric effect and calculated the relative refroidissement power RCP, a crucial performance indicator.\u003c/p\u003e"},{"header":"2. Experimental details","content":"\u003cp\u003ePr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1 and 0.15) were synthesized using the standard solid-state reaction method at high temperature, by mixing Pr\u003csub\u003e6\u003c/sub\u003eO\u003csub\u003e11\u003c/sub\u003e, SrCO\u003csub\u003e3\u003c/sub\u003e, MnO\u003csub\u003e2\u003c/sub\u003e and Cr\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e. up to 99.9% purity in the desired proportions. In an agate mortar, the initial components were well combined. The obtained powders were then pressed into pellets (of about 1 mm thickness) and sintered at 900, 1100\u0026deg;C for 24h and 1200, 1300\u0026deg;C for 12h for each cycle to ensure a better crystallization with intermediate regrinding and repelling [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e]. Phase purity, homogeneity and cell dimensions were determined by powder X-ray diffraction XRD at room temperature using a \u0026lsquo;Panalytical-X-pert-Pro\u0026lsquo; diffractometer with Cu-Kα radiation with λ\u0026thinsp;=\u0026thinsp;1.5406 \u0026Aring;.\u003c/p\u003e \u003cp\u003eStructural analysis was carried out by the standard Rielveld method [\u003cspan additionalcitationids=\"CR64\" citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e] using Fullprof software. A vibrating sample magnetometer (VSM) was used to detect magnetization against temperature in the range of 20\u0026ndash;400K and against applied magnetic field up to 5 T. Magnetization measurements against applied magnetic fields up to 5 T at several temperatures were used to deduce MCE findings.\u003c/p\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Structural analysis\u003c/h2\u003e \u003cp\u003eThe x-ray diffraction pattern of Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1 and 0.15) at room temperature is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The XRD patterns sharp, well-defined peaks reveal a completely crystalline phase of Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with a distinct orthorhombic phase with Pnma space group. The excellent quality and single phase of the elaborated samples was demonstrated by the absence of secondary phase-corresponding peaks (without impurity). We used Fullprof software to do Rietveld refinement [\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e, \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e] in order to gain a improved understanding of the structural characteristics of the orthorhombic phase. The two reliability factors, R\u003csub\u003ep\u003c/sub\u003e and R\u003csub\u003ewp\u003c/sub\u003e (weighted discrepancies between measured and calculated values), and the goodness of fit, χ\u003csup\u003e2\u003c/sup\u003e, which must tend to 1 and 2, were used to assess the quality of the fitting of the experimental data. Using Rietveld refinement, the values of several structural parameters, lattice parameters (a, b and c), unit volume, Bond lengths, Bond angles and the goodness of fit χ\u003csup\u003e2\u003c/sup\u003e etc\u0026hellip;are showed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eStructural properties of compounds Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMn\u003c/em\u003e\u003csub\u003e\u003cem\u003e1-x\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eCr\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e \u003cem\u003ewith (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1, and 0.15) at room temperature as determined by the Rietveld method.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ex\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ea (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.4409(3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.4372(2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.43928(20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.4455(5)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eb (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7.6558(3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.6502(3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.6548(3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.6514(6)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ec (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.4807(2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.48076(19)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.48331(17)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.4739(5)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eV (\u0026Aring;\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e228.296(0.018)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e227.976(0.015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e228.305(0.013)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e228.073(0.035)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBragg R-factor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRf-factor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;dMn1\u0026thinsp;\u0026minus;\u0026thinsp;O2\u0026gt;) (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.06232\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.91294\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.96855\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.90844\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(Mn1) -( O2) -( Mn1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e173.244\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e168.219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e168.224\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e154.745\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;dMn2\u0026thinsp;\u0026minus;\u0026thinsp;O2\u0026gt;) (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.80577\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.96766\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.91368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.04774\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(Mn2) -( O2) -( Mn2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e173.244\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e168.219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e168.224\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e154.745\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;dMn1\u0026thinsp;\u0026minus;\u0026thinsp;O1\u0026gt;) (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.94945\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.93545\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.93661\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.93427\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(Mn1) -( O1) -( Mn1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e158.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e162.355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e162.357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e162.932\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003ee\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e16.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003ep\u003c/sub\u003e (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e31.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e33.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e33.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003ewp\u003c/sub\u003e (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e21.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e22.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ec\u0026sup2; (%)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1.56\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1.57\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1.64\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1.63\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eSummary of\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-\\varDelta\\:{S}_{M}^{max}\\)\u003c/span\u003e\u003c/span\u003e, \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e \u003cem\u003eand RCP values for Pr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.55\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eSr\u003c/em\u003e\u003csub\u003e\u003cem\u003e0.45\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eMn\u003c/em\u003e\u003csub\u003e\u003cem\u003e1-x\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eCr\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eO\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e \u003cem\u003ewith (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1, and 0.15).\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ex\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT\u003csub\u003eC\u003c/sub\u003e (K)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e275\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:S}_{M}^{max}\\)\u003c/span\u003e\u003c/span\u003e(J/kg.K)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3,80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eδT\u003csub\u003eFWHM\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRCP(J/kg)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e247\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e254.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e205.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e201\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eA thorough comprehension of the structural and functional characteristics intrinsic to our Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e compound series (where x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1, and 0.15) requires a careful examination of the crystallographic parameters, especially the Manganese-Oxygen\u0026thinsp;\u0026lt;\u0026thinsp;dMn\u0026thinsp;\u0026minus;\u0026thinsp;O\u0026thinsp;\u0026gt;\u0026thinsp;distances bond and the inter-octahedral\u0026thinsp;\u0026lt;\u0026thinsp;Mn-O-Mn\u0026thinsp;\u0026gt;\u0026thinsp;angles.\u003c/p\u003e \u003cp\u003eThe size and degree of deformation of the MnO\u003csub\u003e6\u003c/sub\u003e octahedra are directly indicated by the \u0026lt;\u0026thinsp;dMn\u0026thinsp;\u0026minus;\u0026thinsp;O\u0026thinsp;\u0026gt;\u0026thinsp;interatomic distances. In the Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e structure, the substitution of Mn by chromium Cr significantly changes the average oxidation state of the manganese ions, resulting in the introduction of certain structural stresses. The Jahn-Teller effect, which is usually connected to the presence of Mn\u003csup\u003e3+\u003c/sup\u003e cations, is likewise very sensitive to these ensuing variations in \u0026lt;\u0026thinsp;dMn\u0026thinsp;\u0026minus;\u0026thinsp;O\u0026thinsp;\u0026gt;\u0026thinsp;bond lengths. These ions electrical asymmetry forces the octahedra to elongate or compress, which is crucial in establishing the local structural environment.\u003c/p\u003e \u003cp\u003eAt the same time, the connectivity and coupling effectiveness between neighboring MnO\u003csub\u003e6\u003c/sub\u003e octahedra are determined by the \u0026lt;\u0026thinsp;Mn-O-Mn\u0026thinsp;\u0026gt;\u0026thinsp;bond angles. The amount of octahedral inclination is directly influenced by the degree of chromium substitution. The double-exchange DE process (Mn\u003csup\u003e3+\u003c/sup\u003e-O-Mn\u003csup\u003e4+\u003c/sup\u003e) that drives the observed ferromagnetism in these manganites is crucially mediated by this tilting, making it extremely significant.\u003c/p\u003e \u003cp\u003eIn particular, the orbital overlap is maximized when the \u0026lt;\u0026thinsp;Mn-O-Mn\u0026thinsp;\u0026gt;\u0026thinsp;angle gets closer to the optimal 180 degrees, which improves charge carrier mobility and fortifies the magnetic interactions.\u003c/p\u003e \u003cp\u003eIn conclusion, examining the simultaneous changes in \u0026lt;\u0026thinsp;dMn\u0026thinsp;\u0026minus;\u0026thinsp;O\u0026thinsp;\u0026gt;\u0026thinsp;distances controlled by the Jahn-Teller effect and substitution and the \u0026lt;\u0026thinsp;Mn-O-Mn\u0026thinsp;\u0026gt;\u0026thinsp;angles which determine the effectiveness of the double-exchange pathway is crucial to understanding the magnetic properties seen in Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Magnetic properties\u003c/h2\u003e \u003cp\u003eThe temperature dependence of the magnetization, M(T), under an applied magnetic field \u0026micro;\u003csub\u003e0\u003c/sub\u003eH\u0026thinsp;=\u0026thinsp;0.05 T, for all our samples are displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e \u003cb\u003e(a)\u003c/b\u003e. We plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e the magnetization as a function of temperature under a weak applied field of 0.05 T, with the dM/dT curve used to determine the minimum temperature Tc of the parent compound curve, clearly demonstrating the paramagnetic-ferromagnetic transition. For the Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e series (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1, and 0.15), the magnetization versus temperature M(T) curves provide important information on their magnetic behavior. These compounds show a change from the paramagnetic PM to a ferromagnetic FM state as the temperature decreases. The key parameter known as the Curie temperature T\u003csub\u003eC\u003c/sub\u003e indicates the temperature at which a material changes from a paramagnetic to a ferromagnetic state. The Curie temperatures T\u003csub\u003eC\u003c/sub\u003e have determined from the minimum value of the dM/dT versus T curves (refer to the \u003cb\u003einset of\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) The T\u003csub\u003eC\u003c/sub\u003e values for the Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e series are shown to decrease as the Cr concentration increases: for x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.10, and 0.15, T\u003csub\u003eC\u003c/sub\u003e (K)\u0026thinsp;=\u0026thinsp;300 K, 292 K, 286 K and 275 K. This pattern implies that the ferromagnetic interactions are weakened when Mn is replaced with Cr in the lattice, which lowers the Tc, similarly in the literature, that is confirmed in the work of A.K. Saw and all [\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e] and other work [\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e]. Furthermore, when Cr is substituted in Cr-doped manganites, the magnetism in the FM region also decreases. A qualitative explanation for the decline in T\u003csub\u003eC\u003c/sub\u003e and magnetization with increased chromium concentration is the decrease in the Mn\u003csup\u003e3+\u003c/sup\u003e/Mn\u003csup\u003e4+\u003c/sup\u003e ratio. This action increases the SE Super exchange antiferromagnetic state by reducing the Mn\u003csup\u003e3+\u003c/sup\u003e-Mn\u003csup\u003e4+\u003c/sup\u003e couples that cause DE Double exchange ferromagnetism and introducing a small amount of Mn\u003csup\u003e3+\u003c/sup\u003e-Mn\u003csup\u003e3+\u003c/sup\u003e, Mn\u003csup\u003e4+\u003c/sup\u003e-Mn\u003csup\u003e4+\u003c/sup\u003e, Cr\u003csup\u003e3+\u003c/sup\u003e-Cr\u003csup\u003e3+\u003c/sup\u003e, and Mn\u003csup\u003e3+\u003c/sup\u003e-Cr\u003csup\u003e3+\u003c/sup\u003e couples [\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe magnetization isotherms M(H) recorded for all compounds in magnetic fields equal to 5 T over a broad temperature range of 240\u0026ndash;320 K demonstrate that, below Curie temperature, magnetization increases significantly in weak applied fields until approaching saturation for applied fields \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{0}H\\)\u003c/span\u003e\u003c/span\u003e=1 T. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e \u003cb\u003e(a), (b), (c), and (d)\u003c/b\u003e display the usual magnetization isotherm shape for x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1, and x\u0026thinsp;=\u0026thinsp;0.15.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs the temperature decrease, the saturation magnetization increase. The purely ferromagnetic behavior of the samples at low temperatures is confirmed by this result. Important information on the magnetic characteristics and phase transitions of manganites is provided by the magnetization versus magnetic field M(H) measurements. The nature of the magnetic ordering and the transitions between various magnetic phases are revealed by these observations. For example, the M(H) curves in Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e (x\u0026thinsp;=\u0026thinsp;0.00, 0.05, 0.1, and 0.15) show a second-order ferromagnetic FM to paramagnetic PM phase transition, where the Curie temperature T\u003csub\u003eC\u003c/sub\u003e decreases with increasing Cr-doped concentration. Similarly, the M(H) measurements reveal a second-order PM-FM transition in the studie of A. Dhahri \u0026amp; all Pr\u003csub\u003e0.67\u003c/sub\u003eSr\u003csub\u003e0.33\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eM\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e (0.0\u0026thinsp;\u0026lt;\u0026thinsp;x\u0026thinsp;\u0026le;\u0026thinsp;0.09) [\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e]. These findings are also essential for comprehending the magnetic interactions and the materials possible uses in magnetic refrigeration and other technologies.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Critical behavior\u003c/h2\u003e \u003cp\u003eThe analysis of the Arrott curve makes it possible to understand the critical behavior at the critical point. The magnetic equation of state for a system that adheres to the theory of the average field (MFT) is as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\frac{\\text{H}}{\\text{M}}=\\text{A}+\\text{B}{\\text{M}}^{2}\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe order of the magnetic phase transition is revealed by a thorough analysis of M(H) isotherms. From M(H) isotherms near T\u003csub\u003eC\u003c/sub\u003e, we inferred the Arrott plots ((M\u003csup\u003e1/β\u003c/sup\u003e vs \u0026micro;oH/M)\u003csup\u003e1/g\u003c/sup\u003e), which are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e \u003cb\u003e(a), (b), (c), and (d)\u003c/b\u003e Banerjee's criterion [\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e] states that a first-order or second-order magnetic phase transition is indicated by a negative or positive slope of Arrott curves. The results of M\u003csup\u003e2\u003c/sup\u003e against \u0026micro;\u003csub\u003e0\u003c/sub\u003eH/M graphs for Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e reveal the second-order FM to PM phase transition, with a positive slope in all cases throughout the entire M\u003csup\u003e2\u003c/sup\u003e range, the values of exponents β and γ are taken 0.5 and 1, respectively, as expected from mean field theory). Curie temperatures T\u003csub\u003eC\u003c/sub\u003e determined from Arrott plots coincide with those obtained from the low field magnetization curves M(T) for All compounds.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e show the temperature dependence of the spontaneous magnetization (M\u003csub\u003esp\u003c/sub\u003e) deduced from the M(H) curves and the inverse of the susceptibility (1/χ) as a function of temperature for Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMnO\u003csub\u003e3\u003c/sub\u003e sample. In the paramagnetic phase (T\u0026thinsp;\u0026gt;\u0026thinsp;T\u003csub\u003eC\u003c/sub\u003e), this sample exhibit linear inverse susceptibility behavior. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\chi\\:}=C/(\\text{T}-{{\\theta\\:}}_{P})\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\theta\\:}}_{P}\\)\u003c/span\u003e\u003c/span\u003e is the Curie constant and C is the Curie-Weiss temperature. For x\u0026thinsp;=\u0026thinsp;0.0, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\theta\\:}}_{P}\\)\u003c/span\u003e\u003c/span\u003e value is determined to be 303 K. The presence of a ferromagnetic exchange interaction between the closest neighbors is indicated by the positive value of q\u003csub\u003eP\u003c/sub\u003e. The resultant value is marginally above the Curie temperatures. We can deduce that this difference depends on the substance and is related to the presence of short-range ordered slightly above the Curie temperature, which is related to the presence of a magnetic inhomogeneity [\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e]. For x\u0026thinsp;=\u0026thinsp;0.0, the critical exponent β is determined to be 0.362, indicating that all of our samples exhibit ferromagnetic activity at low temperatures. The ferromagnetic condition described for manganites [\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e, \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e, \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e] is in good agreement with this value.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Magnetocaloric measurements\u003c/h2\u003e \u003cp\u003eThe thermodynamic theory states that the magnetic entropy change brought about by the magnetic fields variation from 0 to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{H}}_{max}\\)\u003c/span\u003e\u003c/span\u003e is as follows [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e]:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{{\\Delta\\:}\\text{S}}_{M}\\:(\\text{T},\\text{H})=\\:{\\text{S}}_{M}\\:(\\text{T},\\text{H})\\:-\\:{\\text{S}}_{M}\\:(\\text{T},0)=\\int\\:\\frac{{dM}(T,H)}{dT}dH$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eUsing Maxwell\u0026rsquo;s relation\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:(\\frac{\\partial\\:M}{\\partial\\:T}{)}_{H}=(\\frac{\\partial\\:S}{\\partial\\:H}{)}_{T}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe following expression can be obtained:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{{\\Delta\\:}\\text{S}}_{M}\\:(\\text{T},\\text{H})={\\int\\:}_{0}^{{H}_{max}}{\\left(\\frac{\\partial\\:M}{\\partial\\:T}\\right)}_{H}dH$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEquation (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) states that the magnetic entropy change reaches its highest during the magnetic transition phase. The magnetic entropy change can be it was calculated approximately using the numerical formula employing isothermal magnetization data in small discrete fields and temperature intervals [\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e]:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{{\\Delta\\:}\\text{S}}_{\\text{M}}\\:\\left(\\text{T},\\:\\text{H}\\right)=\\sum\\:\\left(\\frac{{M}_{i}-{M}_{i+1}}{{T}_{i+1}-{T}_{i}}\\right){{\\Delta\\:}\\text{H}}_{\\text{i}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere M\u003csub\u003ei\u003c/sub\u003e and M\u003csub\u003ei+1\u003c/sub\u003e are the experimental magnetization values obtained at the temperatures T\u003csub\u003ei\u003c/sub\u003e and T\u003csub\u003ei+1\u003c/sub\u003e, respectively, in an applied magnetic field H\u003csub\u003ei\u003c/sub\u003e. The magnetic entropy changes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|{\\Delta\\:}{\\text{S}}_{\\text{M}}\\right|\\)\u003c/span\u003e\u003c/span\u003e of Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e samples as a function of temperature under various magnetic applied field variations is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e \u003cb\u003e(a, b, c, and d)\u003c/b\u003e. We find that rises and peaks around the magnetic-transition temperature.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-{\\Delta\\:}{\\text{S}}_{\\text{M}}\\)\u003c/span\u003e\u003c/span\u003e exhibits a broad positive peak around T\u003csub\u003ec\u003c/sub\u003e (normal MCE) for all samples. The maximum values of the magnetic entropy change,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|\\varDelta\\:{S}_{M}^{max}\\right|\\)\u003c/span\u003e\u003c/span\u003eare 3.8 J/kg.K, 3.63 J/kg.K, 3.87 J/kg.K and 2.55 J/kg.K in a magnetic field change of 5 T for x\u0026thinsp;=\u0026thinsp;0.0, x\u0026thinsp;=\u0026thinsp;0.05, x\u0026thinsp;=\u0026thinsp;0.1 and x\u0026thinsp;=\u0026thinsp;0.15 respectively. The relative cooling power (RCP) [\u003cspan additionalcitationids=\"CR77\" citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e] is evaluated as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:RCP=-\\varDelta\\:{S}_{M}(T,H)\\times\\:{\\delta\\:T}_{FWHM}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\delta\\:T}_{FWHM}\\)\u003c/span\u003e\u003c/span\u003eis the full-width at half-maximum of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-{\\Delta\\:}{\\text{S}}_{\\text{M}}\\)\u003c/span\u003e\u003c/span\u003e versus temperature [\u003cspan additionalcitationids=\"CR80\" citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e]. For our samples, the RCP values are respectively 247 J/kg, 254.1 J/kg, 205.1 J/kg and 201 J/kg at 5 T for x\u0026thinsp;=\u0026thinsp;0.0, x\u0026thinsp;=\u0026thinsp;0.05, x\u0026thinsp;=\u0026thinsp;0.1 and x\u0026thinsp;=\u0026thinsp;0.15. Despite having the lowest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|\\varDelta\\:{S}_{M}^{max}\\right|\\)\u003c/span\u003e\u003c/span\u003e, the composition of 5% of chromium doping manganese seems to be the most promising for magnetic refrigeration applications because of its high RCP value. For cooling cycles to be effective, entropy change and temperature range must be balanced. As seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the delta \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|\\varDelta\\:{S}_{M}^{max}\\right|\\)\u003c/span\u003e\u003c/span\u003e values obtained and the RCP values computed using Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) are plotted versus \u0026micro;\u003csub\u003e0\u003c/sub\u003eH.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt was evident that at T\u003csub\u003eC\u003c/sub\u003e, the relative cooling power RCP and maximum entropy change \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|\\varDelta\\:{S}_{M}^{max}\\right|\\)\u003c/span\u003e\u003c/span\u003e are both proportional to \u0026micro;\u003csub\u003e0\u003c/sub\u003eH. RCP is a field-dependent variable, as evidenced by its trend with \u0026micro;\u003csub\u003e0\u003c/sub\u003eH. Our sample RCP (5% of chromium) value of 254.1 J/kg is 58% of Gd RCP value, which is the industry standard for refrigeration [\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e] materials with high \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\delta\\:T}_{FWHM}\\)\u003c/span\u003e\u003c/span\u003e and RCP values can operate over a wide temperature range and have a large cooling capacity. Magnetic refrigeration works well with these materials [\u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e82\u003c/span\u003e, \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNumerous methods for figuring out the order of magnetic phase transitions have been proposed in the literature [\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e, \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e]. One of these is to use the relation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\text{S}}_{\\text{M}}(\\text{H},\\text{T})\\approx\\:{aH}^{n}\\)\u003c/span\u003e\u003c/span\u003e, where a is a constant and n is an exponent related to magnetic order, to examine the field dependence of the samples MCE [\u003cspan additionalcitationids=\"CR86\" citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e]. Important details regarding the type of magnetic phase transition in the investigated materials can be found by calculating the exponent values at specific temperatures. The logarithmic derivative of experimental data can be used to determine the exponent n at a specific temperature and magnetic field \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:\\text{S}}_{\\text{M}}(\\text{H},\\text{T})\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e] :\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:n\\left(T,\\:H\\right)=\\frac{dln\\:(\\varDelta\\:{S}_{M}\\left(T,\\:H\\right))}{dln\\:\\left(H\\right)}\\:\\:\\:\\:\\:\\left(7\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe Curie-Weiss rule causes the n values to approach n\u0026thinsp;=\u0026thinsp;2 at high temperatures in the paramagnetic phase (over the T\u003csub\u003eC\u003c/sub\u003e) [\u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e]. In the ferromagnetic phase, n typically has a value that tends to be n\u0026thinsp;=\u0026thinsp;1 at temperatures well below the transition point. The value of n changes according to the kind of phase transition (first or second-order) of the material within a crucial temperature range surrounding the Curie temperature.\u003c/p\u003e \u003cp\u003ePrevious investigation has demonstrated that a quantitative criterion of n\u0026thinsp;\u0026gt;\u0026thinsp;2 close to the transition temperature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T={T}_{C}\\)\u003c/span\u003e\u003c/span\u003e could be interpreted as a first-order magnetic phase transition of the material. It has also been demonstrated that this criterion could be successfully applied to a variety of magnetocaloric materials in order to identify the type of magnetic phase transition [\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrate the Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMnO\u003csub\u003e3\u003c/sub\u003e compound temperature dependency of exponent n under various magnetic fields n(T). The sample exponent n tends to approach 1 at temperatures significantly below the Curie temperature (ferromagnetic region). The exponent n tends to 2 for temperatures greater than Tc (paramagnetic zone). This behavior for exponent n is typically explained by a second-order phase transition. As the temperature drops near the transition temperature, a fall in n is seen, with a minimum value at the Curie temperature. Other magnetic materials with first and second-order transitions have been reported to exhibit similar behavior. [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e, \u003cspan additionalcitationids=\"CR85\" citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e, \u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn summary, this study concentrated on the structural, magnetic and magnetocaloric characterisation of the Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e Manganites compounds with (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1 and 0.15), which were successfully elaborated using a solid-state reaction method. The crystalline structure was found to be orthorhombic, corresponding to the Pnma space group, and X-ray diffraction investigations verified the production of a single phase over the compositional range without impurity phase.\u003c/p\u003e \u003cp\u003eFor all produced compounds, magnetization measurements as a function of temperature and applied field consistently showed a magnetic phase transition from the ferromagnetic (FM) to the paramagnetic (PM) state. It is remarkable that this transition was found to be of second order. It was discovered that the Curie temperature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{C}\\)\u003c/span\u003e\u003c/span\u003e, which decreased from 300 K to 275 K over the examined substitution period, could be efficiently modulated by gradually adding chromium in place of manganese. The crucial impact of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Cr}^{3+}\\)\u003c/span\u003e\u003c/span\u003e ion on the magnetic exchange processes inside the crystal lattice is shown by this dependence.\u003c/p\u003e \u003cp\u003eUsing isothermal magnetization data and the Maxwell thermodynamic laws, the magnetocaloric effect MCE was thoroughly examined. The outcomes for a 5 T change in magnetic field are very encouraging. For the x\u0026thinsp;=\u0026thinsp;0.1 composition, the highest magnetic entropy change \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{-\\varDelta\\:S}_{M}^{max}\\)\u003c/span\u003e\u003c/span\u003e was found to peak at 3.87 J/kg.K. More significantly, the Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e0.95\u003c/sub\u003eCr\u003csub\u003e0.05\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e sample had the highest relative cooling power (RCP) value, measuring 254.1 J/kg.\u003c/p\u003e \u003cp\u003eConsidering that its RCP value is roughly 58% of that of pure gadolinium, an accepted industrial measurement, this performance places the x\u0026thinsp;=\u0026thinsp;0.05 material in a very promising category for magnetic refrigeration applications. In conclusion, the Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e family of manganites is an attractive class of magnetocaloric materials for the creation of effective and eco-friendly magnetic cooling devices, especially because chromium concentration can be used to adjust the operating temperature.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDeclaration of interest statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cspan lang=\"FR\"\u003e☒\u003c/span\u003e The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003e1-Ahmed Selmi: Conceptualization, methodology, investigation, data curation, formal analysis, writing\u0026mdash;original draft.2-A. Hela: Investigation, experimental validation, data curation.3-Malek Gassoumi: Investigation, resources, experimental support.4-E. K. Hlil: Supervision, validation, writing\u0026mdash;review \u0026amp; editing.5-Abdelaziz Bouazizi: Supervision, project administration, writing\u0026mdash;review \u0026amp; editing.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eY. Tokura, Critical features of colossal magnetoresistive manganites, Reports On Progress. 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Magn. \u003cb\u003e46\u003c/b\u003e, 1652\u0026ndash;1655 (June 2010). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1109/tmag.2010.2044754\u003c/span\u003e\u003cspan address=\"10.1109/tmag.2010.2044754\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Manganite, XRD diffraction, magnetocaloric, critical behavior, paramagnetic PM and ferromagnetic FM, magnetic refrigeration APPLICATION","lastPublishedDoi":"10.21203/rs.3.rs-8638249/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8638249/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn the current study, the structural (X-ray diffraction XRD), magnetic, critical behavior and magnetocaloric properties of the polycrystalline Pr\u003csub\u003e0.55\u003c/sub\u003eSr\u003csub\u003e0.45\u003c/sub\u003eMn\u003csub\u003e1\u0026minus;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e Manganites with (x\u0026thinsp;=\u0026thinsp;0.0, 0.05, 0.1 and 0.15) samples were examined. All our samples have been elaborated by means of the solid-state reaction from stoichiometric powder mixtures of binary oxides at high temperatures. The compounds crystallize in the orthorhombic structure with Pnma space group, according to Rietveld refinement of the XRD pattern. All of the samples exhibit a second-order FM to PM phase transition, according to temperature and field-dependent magnetization measurements; however, the Curie temperature T\u003csub\u003eC\u003c/sub\u003e value decreases from 300 K to 275 K as the Cr (% x) content increases from 0.00 to 0.15. Using Maxwell thermodynamic relations, the magnetocaloric effect MCE in terms of maximum entropy change \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{-\\varDelta\\:S}_{M}^{max}\\)\u003c/span\u003e\u003c/span\u003e, and relative cooling power RCP has been calculated using isothermal magnetization data around T\u003csub\u003eC\u003c/sub\u003e. In a magnetic field shift of 5 T, the highest values of the magnetic entropy change \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{-\\varDelta\\:S}_{M}^{max}\\)\u003c/span\u003e\u003c/span\u003e have been determined to be 3.8 J/kg.K, 3.63 J/kg.K, 3.87 J/kg.K, and 2.55 J/kg.K for x\u0026thinsp;=\u0026thinsp;0.0, x\u0026thinsp;=\u0026thinsp;0.05, x\u0026thinsp;=\u0026thinsp;0.1, and x\u0026thinsp;=\u0026thinsp;0.15, respectively. For x\u0026thinsp;=\u0026thinsp;0.0, x\u0026thinsp;=\u0026thinsp;0.05, x\u0026thinsp;=\u0026thinsp;0.1, and x\u0026thinsp;=\u0026thinsp;0.15 at 5 T, the highest value of the relative cooling power RCP is found to be 247 J/kg, 254.1 J/kg, 205.1 J/kg, and 201 J/kg, respectively. The RCP value of 254.1 J/kg (5% of chromium) is equivalent to 58% of the RCP value of gadolinium metal. Technically, the developed material is highly promising for magnetic refrigeration because of these significant values.\u003c/p\u003e","manuscriptTitle":"Study of Solid-State Synthesized Pr0.55Sr0.45Mn1-xCrxO3 Perovskites with x=0.0, 0.05, 0.1 and 0.15: Rietveld analysis, Magnetic and Magnetocaloric Properties for Magnetic Refrigeration Applications","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-05 09:50:12","doi":"10.21203/rs.3.rs-8638249/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"588447da-08c5-418f-ba88-5520bec324e4","owner":[],"postedDate":"February 5th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-26T16:25:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-05 09:50:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8638249","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8638249","identity":"rs-8638249","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}