Magnetic Entropy Change Research Articles

Analytical modeling of magnetocaloric effect in dense nanoparticle systems

AbstractDetermining the magnetocaloric effect (MCE) in dense nanoparticle systems (DNSs) poses a challenge due to the increased complexity of matter at the nanoscale. Given the interparticle magnetic interactions, diverse particle size and shape distributions, and the presence of inhomogeneous magnetic phases, selecting a suitable phenomenological model is essential to describe the temperature dependence of magnetic behavior in DNSs. Herein, we chose a cost‐effective Ni100‐xCrx DNS with adjustable magnetic transitions to showcase the resilience of the MCE across a broad temperature range (147–614 K). While the hyperbolic tangent model appears more fitting for materials with a single Curie temperature (TC), such as its parent bulk alloys, in the presence of a TC distribution a Gaussian distribution model proves to be better suited for DNSs. The latter model yields a magnetic entropy change, ΔSmax = 0.09–0.15 J kg‐K−1 in the DNS at a tiny field of 0.1T. The correlations between the broadening of the MCE peak and TC distribution are attributed to the particle size distribution and chemical inhomogeneity present in the DNS, paving the way for fine‐tuning MCE‐related properties such as the relative cooling power (13.17–33.45 J kg−1) and adiabatic temperature change (0.03–0.17 K). Our methodology not only enhances the potential for designing innovative MCE materials with broader operating ranges but also validates the universality of our phenomenological model for other families of nanocrystalline/nanogranular oxides/alloys thin films.

Magnetocaloric effect in aluminum doped ErCr1−xAlxO3 orthochromites

Aluminum-doped ErCr1-xAlxO3 orthochromites prepared via autocombustion technique were investigated for their magnetic and magnetocaloric properties. X-ray diffraction confirmed that samples were orthorhombic phases with the Pbnm space group without a trace of any impurity. As analyzed via Rietveld refinement of XRD data, structural parameters such as lattice parameters, volume, bond angle, and bond lengths were affected by doping nonmagnetic Al3+ in the compound. ErCrO3 possesses the long-range antiferromagnetic ordering with a weak display ferromagnetism at TN =133 K. Low-temperature high-field magnetic study shows a decrease in Neel temperature (TN ∼ 114 K for x = 0.5), suggesting magnetic ordering suppression due to Al3+ doping. The asymptotic paramagnetic Curie temperature Tcw = −25 K suggests the predominance of antiferromagnetic interactions in ErCrO3 orthochromites, which was observed to increase with Al3+ doping. Isothermal magnetization data show changes in magnetic entropy (−ΔSMmax) and relative cooling power (RCP). The magnetic entropy change, −ΔSMmax, for ErCrO3 estimated from magnetization measurements show 11.60 J kg−1 K−1 at 11 K and a relative cooling power (RCP) of 209.4 J kg−1 at 5 T applied field. While ErCr0.75Al0.25O3 show a maximum magnetic entropy of 11.52 J kg−1 K−1 at 11 K with a 5 T applied field and RCP of 186.66 J kg−1, whereas ErCr0.5Al0.5O3 displayed −ΔSMmax of 11.63 J kg−1 K−1 at 5 K with a 5 T applied field and RCP value of 160.78 J kg−1. The results show that nonmagnetic doping, such as Al3+, could maintain the compound’s magnetocaloric property to an extent.

Magnetic and magnetocaloric properties of rare earth intermetallic compound Gd3Co4Ge13

Magnetic and magnetocaloric properties of polycrystalline Gd3Co4Ge13 (Cubic, Yb3Rh4Sn13-type, Space group Pm-3n, No. 223, cP40) have been studied by carrying out dc magnetization measurements in applied magnetic fields up to 140 kOe. The compound Gd3Co4Ge13 orders antiferromagnetically at 9 K (TN). The antiferromagnetism appears to be weak and with increasing applied magnetic fields, ferromagnetic interactions become dominant. This field-induced antiferromagnetic to ferromagnetic state that is marked as a change from inverse to normal magnetocaloric effect in the isothermal magnetic entropy change vs temperature plot around TN. At 2 K, the magnetization shows a tendency toward saturation in applied magnetic field and a magnetic moment of 5.3 µB per Gd3+ is obtained in 140 kOe field.

Transformation behavior and inverse magnetocaloric effect in Ni45Co5Mn36.7In13.3-xGex melt-spun ribbons

In the present work the influence of Ge doping on crystal structure, microstructure, martensitic transformation (MT) and magnetocaloric effect (MCE) of Heusler-type Ni45Co5Mn36.7In13.3-xGex (x = 0, 2, and 3 at. %) metamagnetic shape memory alloys (MetaMSMAs) have been studied. Melt-spinning was used to prepare ribbons of these alloys since the ribbon shape ensures a high surface-to-volume ratio favoring a high heat exchange rate in a solid-state refrigeration. Furthermore, melt-spinning can induce a specific microstructure and stabilize metastable phases at room temperature. The ribbons were examined by X-ray diffraction at different temperatures, scanning electron microscopy, calorimetry, thermomagnetization, and magnetic field induced adiabatic temperature change measurements carried out across MT. It was found that Ge doping gave rise to enhanced antiferromagnetic interactions, stabilized martensitic phase, increased the MT temperature, causing larger magnetization jumps at MT and making narrower MT hysteresis. The x = 3 ribbon exhibited an inverse MCE at 303 K characterized by the isothermal magnetic entropy change value of |26.9|J/kgK at μ0H = 5 T and an adiabatic temperature change of ǀ1.5ǀ K at μ0H = 1.96 T. These values are comparable with the previously reported data on the Ni–Mn-based metamagnetic shape memory alloys in a bulk form.

Magnetic properties and large low-field cryogenic magnetocaloric effect in the divalent europium borate Eu2B2O5 compound

We herein investigated the divalent europium borate Eu2B2O5 compound regarding its structural, magnetic and magnetocaloric properties by means of experimental determinations and first principal calculations. The Eu2B2O5 compound was found to crystallize in a monoclinic structure (P21/c space group) and order ferromagnetically at ground state. A large cryogenic reversible MCE was observed in the Eu2B2O5 compound around 2.7 K. The maximum values of magnetic entropy change of Eu2B2O5 compound reach 13.7, 28.2 and 46.9 J/kgK under the magnetic field changes of 0–1, 0–2, and 0–5 T, respectively. The corresponding values of adiabatic temperature change and refrigerant capacity are obtained to be 3.3, 7.0, and 13.3 K and to be 37.8, 102.5, and 317.3 J/kg. These magnetocaloric parameters, especially under relatively low-field changes, are better than those of the reported candidate materials, which makes the Eu2B2O5 compound attractive for cryogenic MR applications.

Giant Low-Field Cryogenic Magnetocaloric Effect in a Polycrystalline EuB4O7 Compound.

To deal with the shortage and high price of helium-3 resources, adiabatic demagnetization refrigeration technology as an alternative to helium-3-based refrigeration technology has received much attention. The magnetism and ultralow-temperature magnetocaloric effect (MCE) of the EuB4O7 compound have been investigated. The results of magnetic and quasi-adiabatic demagnetization measurements suggest the absence of a magnetic order above 0.4 K for EuB4O7. The dipolar interaction between the nearest-neighbor Eu atoms has a characteristic energy of about 800 mK, which may induce a large MCE. The maximum magnetic entropy change reaches 22.8, 36.2, and 47.6 J·kg-1 K-1 at μ0H = 0-10 kOe, 0-20 kOe, and 0-50 kOe, respectively. Measurements by a quasi-adiabatic demagnetization device show that the lowest temperature achievable (289 mK) for polycrystalline EuB4O7 is lower than that (362 mK) for the commercial refrigerant Gd3Ga5O12 (GGG) single crystals. The hold time is more than 70 min below 700 mK, with an environment temperature of 2 K, proving that EuB4O7 exhibits superior cooling performance.

Magnetic properties and large cryogenic magnetocaloric effects in the RE2SiO5 (RE = Gd, Dy, Ho, and Er) silicates

We herein investigated four rare earth (RE)-based oxides, the RE2SiO5 (RE = Gd, Dy, Ho, and Er) silicates, regarding their structural and cryogenic magnetic properties. All the RE2SiO5 silicates are found to crystallized in a monoclinic structure. X-ray photoemission spectroscopy spectra illustrate that RE, Si and O elements in RE2SiO5 silicates are present as RE3+, Si4+, and O2−, respectively. The Dy2SiO5 reveals a first-order magnetic transition around 4.5 K. The magnetic phase transition temperatures are probably below 2 K for the RE2SiO5 (RE = Gd, Ho, and Er) silicates. Large cryogenic magnetocaloric effects (MCE) and good magnetocaloric performances were observed in the RE2SiO5 silicates. The MCE parameters in terms of the maximum magnetic entropy changes, the temperature-averaged entropy change (5 K-lift) and refrigerant capacity under a magnetic field change of 0–5 T are determined to be 35.5, 30.4 J/kgK, and 215.7 J/kg for Gd2SiO5, to be 13.3, 12.9 J/kgK, and 190.5 J/kg for Dy2SiO5, to be 15.3, 15.1 J/kgK, and 274.1 J/kg for Ho2SiO5 and to be 17.9, 16.5 J/kgK, and 181.14 J/kg for Er2SiO5, respectively. These derived values of MCE parameters of the RE2SiO5 silicates, especially for Gd2SiO5, are at similarly high level with or better than those of the updated candidate materials, making them also of potential for practical magnetic refrigeration applications.

Studies on the Arrott plots of inhomogeneous first order magnetic phase transitions

First order ferromagnetic to paramagnetic phase transition is studied using the Bean-Rodbell model within the mean-field framework. The presence of sample inhomogeneities is modeled by considering distributions of the Bean-Rodbell parameter. The corresponding Arrott plots with and without distributions of the Bean-Rodbell parameter are generated and compared. Results indicate that in the presence of inhomogeneities, ferromagnetic to paramagnetic phase transition is broadened. The initial negative slopes in the Arrott plots due to first order phase transition changes to positive slopes for temperatures lying in the broadened tail region of the ferromagnetic to paramagnetic phase transitions. However, the initial negative slopes in the paramagnetic regime (for temperatures above the broadened tail region) are preserved even in the presence of sample inhomogeneities. Also, the effect of inhomogeneities on the magnetic entropy change near the first order transition is studied.

Atomic‐resolution Interfacial Microstructure and Thermo‐electro‐magnetic Energy Conversion Performance of Gd/Bi0.5Sb1.5Te3 Composites

Thermo‐electro‐magnetic materials with simultaneously large magnetocaloric (MC) and thermoelectric (TE) effects are the core part for designing TE/MC all‐solid‐state cooling devices. Compositing MC phase with TE material is an effective approach. However, the elemental diffusion and chemical reaction occurring at the two‐phase interfaces could significantly impair the cooling performance. Herein, Gd/Bi0.5Sb1.5Te3 (Gd/BST) composites were prepared by a low‐temperature high‐pressure spark plasma sintering method with an aim to control the extent of interfacial reaction. The reaction of Gd with the diffusive Te and the formation of GdTe nanocrystals were identified at the Gd/BST interfaces by the atomic‐resolution microscope. The formed antisite defects and enhanced {000 l} preferential orientation in BST are responsible for the increased carrier concentration and mobility, which leads to optimized electrical properties. The heterogeneous interface phases, along with antisite defects, favor the phonon scattering enhancement and lattice thermal conductivity suppression. The optimized composite sintered at 693 K exhibited a maximum ZT of 1.27 at 300 K. Furthermore, the well‐controlled interfacial reaction has a slight impact on the magnetic properties of Gd and a high magnetic entropy change is retained in the composites. This work provides a universal approach to fabricating thermo‐electro‐magnetic materials with excellent MC and TE properties.

Exploring the magnetic and magnetocaloric behavior of nanocrystalline melt-spun R2Fe17 (R = Pr, Nd) ribbons

Single-phase nanocrystalline R2Fe17 (R = Pr and Nd) ribbons with rhombohedral Th2Zn17-type crystalline structure (space group R3̅m) have been fabricated by melt-spinning technique. The microstructure of the polycrystalline ribbons is composed of quasi-spherical grains with an average size below 100 nm. Transmission electron microscopy reveals that these grains are formed by agglomeration of smaller nanocrystalline entities around 15 nm in diameter, separated by disordered boundaries where the long-range crystalline order is lost. Two different ferro-to-paramagnetic phase transitions are observed, one of them coincides with that of the parent bulk alloy (290 and 326 K for R = Pr and Nd, respectively), and the other one can be ascribed to the disordered boundaries (323 and 350 K for R = Pr and Nd, respectively). For R= Pr, this fact gives rise to a significant broadening (c.a. 120 K under a magnetic field change of 2 T) of the full-width at the half-maximum of the magnetic entropy change curve, |∆SM(T)| (that adopts a "table-like" shape), resulting in a considerable increase of the refrigerant capacity.

Phase transition and magneto-caloric properties of perovskites Pr0.55Sr0.45MnO3: Modeling versus experiments

Experimental data obtained with the perovskite compounds Pr0.55Sr0.45MnO3 show that the magnetization decreases with increasing temperature T and undergoes a very sharp phase transition to the paramagnetic phase. The sharp transition in a system with a strong disorder is very rare, if not non-existent, in the theory of phase transition in systems of short-range pairwise exchange interactions. To understand this remarkable property, we introduce a model including a multispin (cluster-like) interaction between Mn ions, in addition to the usual pairwise exchange terms between these ions and the Mn–Pr interactions. We carry out Monte Carlo (MC) simulations using this model. The crystal is a body-centered tetragonal lattice where the corner sites are occupied by Mn ions and the center sites by Pr or Sr ions. Due to the doping, Mn4+ with S=3/2 has the concentration of Pr3+ (S=1) and Mn3+ with S=2 has the Sr concentration. After attempts with different spin models and various Hamiltonians, we find that the many-state Ising spin model reproduces most of the experimental results. For the Hamiltonian, we find that pairwise interactions alone between ions cannot reproduce the sharp transition and the magnetization below TC. We have to include a multispin interaction as said above. We fit the MC results with experimental data, and we estimate values of various exchange interactions in the system. These values are found to be in the range of those found in perovskite manganite compounds. We also study the applied-field effect on the magnetization in the temperature region below and above the transition temperature TC. We calculate the magnetic entropy change |ΔSm| and the Relative Cooling Power, for magnetic field from 1 to 3 T. Our simulation results are in good agreement with experiments. The role of the multispin interaction is analyzed and discussed.

Effect of bismuth doping on structural, morphological, Griffiths-like phase, and magnetocaloric properties in La0.9−xBixBa0.1MnO3 (x = 0, 0.05, and 0.1)

In this recent work, we have carried out the structural, morphological, Griffiths-like phase, and magneto-caloric studies of sol–gel-synthesized, nanocrystalline manganite La0.9−xBixBa0.1MnO3 (x = 0, 0.05, and 0.1). The Rietveld analysis of X-ray diffraction patterns of nanocrystalline La0.9−xBixBa0.1MnO3 (x = 0, 0.05, and 0.1) confirm the single-phase nature and orthorhombic crystal structure with Pnma space group for all samples. The images acquired with a transmission electron microscope reveal the average particle sizes ranges from 32 nm to 65 nm. The temperature-dependent magnetization measurements, for 0.05 T external applied magnetic field, have revealed paramagnetic (PM) to ferromagnetic (FM) phase transition with transition temperatures (TC) ∼ 228 K, 219 K, and 233 K for x = 0, 0.05, and 0.1, respectively. The downward divergence of temperature dependence inverse susceptibility from the Curie-Weiss fit, indicates a pronounced Griffiths singularity in the samples. The positive slopes of Arrott plots for nanocrystalline La0.9−xBixBa0.1MnO3 (x = 0.05, 0.1) confirm the second-order magnetic phase transition. We have estimated the magnetic entropy change at different values of applied magnetic field for nanocrystalline La0.9−xBixBa0.1MnO3 (x = 0.05, 0.1) samples. Further, using this magnetic entropy data, we have also estimated the magnetic cooling capacity.

{GdIII7} and {GdIII14} Cluster Formation Based on a Rhodamine 6G Ligand with a Magnetocaloric Effect.

Heptanuclear {GdIII7} (complex 1) and tetradecanuclear {GdIII14} (complex 2) were synthesized using the rhodamine 6G ligand HL (rhodamine 6G salicylaldehyde hydrazone) and characterized. Complex 1 has a rare disc-shaped structure, where the central Gd ion is connected to the six peripheral GdIII ions via CH3O-/μ3-OH- bridges. Complex 2 has an unexpected three-layer double sandwich structure with a rare μ6-O2- ion in the center of the cluster. Magnetic studies revealed that complex 1 exhibits a magnetic entropy change of 17.4 J kg-1 K-1 at 3 K and 5 T. On the other hand, complex 2 shows a higher magnetic entropy change of 22.3 J kg-1 K-1 at 2 K and 5 T.

Magnetocaloric properties of Mn5(Si,P)B2 compounds for energy harvesting applications

The magnetocaloric properties of Mn5Si1-xPxB2 (0 ≤ x ≤ 1) compounds were studied for energy harvesting applications. The crystal structure and the magnetic structure were characterized by powder X-Ray Diffraction and powder Neutron Diffraction. The results indicate that these magnetocaloric materials crystallize in the tetragonal Cr5B3-type crystal structure. The introduction of P causes a stretching of the c axis and compression of the a-b plane, leading to a decrease in the unit-cell volume V. In the ferromagnetic state the magnetic moments align within the a-b plane, and the magnetic moment of the Mn1 atom on the 16 l site is larger than that of the Mn2 atom on the 4c site. The Curie temperature TC can be adjusted continuously from 305 K (x = 1) to 406 K (x = 0) by replacing Si with P. The corresponding magnetic entropy change varies from 1.90 Jkg−1K−1 (x = 0) to 1.35 Jkg−1K−1 (x = 1) for a magnetic field change of 1 T. The PM-FM transition in these compounds corresponds to a second-order phase transition. Mn5Si1-xPxB2 compounds exhibit a magnetization difference of 28.1 - 31.3 Am2kg−1 for a temperature span of 30 K around TC in an applied magnetic field of 1 T. The considerable change in magnetization, the tunable TC near and above room temperature and the absence of thermal hysteresis make these compounds promising candidates for magnetocaloric energy harvesting materials.

Large magnetic entropy change in Ni–Mn–In–Sb alloys via directional solidification and calculated by first-principles calculations

In this work, the magnetocaloric effect in Ni50Mn36In5Sb9 alloy was increased by more than 50% through directional solidification, and the magnetic entropy change increased to 36.2 J kg−1 K−1 under the field of 5 T. The calculated results of differential scanning calorimetry curves confirmed the enhanced entropy change, which also increased from 29.7 to 40.7 J kg−1 K−1. Moreover, first-principles calculations show that the surface formation energy along the L21 (220) plane is the lowest at room temperature, and it is easy to form and undergo martensitic transformation from the (220) crystal plane. Directional solidification causes the alloy to grow basically toward the (220) crystal plane, improve atomic ordering, reduce grain boundaries, and increase grain size. Thereby, the magnetic entropy change is enhanced.

Assessing rapid solidification processing to produce magnetocaloric RFeSi alloys (R= Tb, Dy) for natural gas liquefaction

This work addressed the synthesis of melt-spun ribbons of the ternary intermetallic ferromagnetic phases RFeSi with R = Tb and Dy, presenting a thorough characterization of their structural, magnetic, and magnetocaloric behavior. Both compounds have been referred to as suitable magnetic refrigerants in the natural gas liquefaction temperature range. The primary phase in ribbon samples of both compounds shows the CeFeSi-type tetragonal crystal structure (space group P4/nmm), with Curie temperatures of 124 K and 89 K for TbFeSi and DyFeSi, respectively. Notably, a sizeable increase in the coercive field appeared below 20 K. However, for a magnetic field change of 2 T, the maximum values of the magnetic entropy change (|ΔSM|max) were 3.4 J kg−1 K−1 and 3.8 J kg−1 K−1 for TbFeSi and DyFeSi ribbon samples, respectively, reflecting a reduction of approximately 60% compared to reported findings for bulk alloys. In contrast, the refrigerant capacity under a magnetic field change of 2 T measured 120 J kg−1 for TbFeSi and 109 J kg−1 for DyFeSi. The reduction in |ΔSM|max is mainly due to a broader magnetic transition compared to the previous results for bulk alloys. Based on the RFeSi ribbons obtained, a biphasic magnetocaloric composite with a broad table-like magnetic entropy change curve, as that required for an Ericsson-type refrigeration cycle, is designed.

Exploration of Griffiths phase, spin glass behaviour and memory effect in a frustrated Al2MnCoO7 pyrochlore compound

Al2MnCoO7 pyrochlore compound has been synthesized following the multistep solid-state ceramics route. The compound exhibits a monoclinic structure, which was confirmed through the X-ray diffraction pattern analysis. The magnetization measurements in both zero-field-cooled (ZFC) and field-cooled (FC) modes indicate that the compound undergoes a phase transition from paramagnetic (PM) to antiferromagnetic (AFM) state at the Néel transition temperature TN ∼31 K. Notably, below TN, there is a substantial discrepancy between the ZFC and FC curves, which can be ascribed to the existence of competing ferromagnetic (FM) and AFM interactions, resulting in a glassy behaviour. Additionally, the compound demonstrates a Griffiths phase above TN, signifying the presence of ferromagnetic clusters within the PM region of the material. The spin-glass behaviour is confirmed by the shift of maxima towards higher temperatures with increasing frequency in the ac susceptibility measurement. The memory effect also confirms the spin-glass nature of the compound. The Arrott's plots confirmed that the magnetic phase transition in the material to be a second-order type. Additionally, the material exhibited a maximum magnetic entropy change (−ΔS) value of 1.08 J/kg.K and a relative cooling power of 36.60 J/kg under an applied magnetic field of 5 T.

Magnetic and magnetocaloric effect of Er20Ho20Dy20Cu20Ni20 high-entropy metallic glass

Er20Ho20Dy20Cu20Ni20 high-entropy metallic glass exhibited excellent magnetic refrigeration material with a wide temperature range and high refrigeration capacity (RC) was reported. Er20Ho20Dy20Cu20Ni20 high-entropy metallic glass was observed with typical spin glass behavior around 15.5 K. In addition, we find that the magnetic entropy change (−ΔS M) originates from the sample undergoing a ferromagnetic (FM) to paramagnetic (PM) transition around 20 K. Under a field change from 0 T to 7 T, the value of maximum magnetic entropy change ( −ΔSMmax ) reaches 12.5 J/kg⋅K, and the corresponding value of RC reaches 487.7 J/kg in the temperature range from 6 K to 60 K. The large RC and wide temperature range make the Er20Ho20Dy20Cu20Ni20 high-entropy metallic glass be a promising material for application in magnetic refrigerators.

Magnetic effect and chemical distribution study of LCMNO3 perovskite by photoelectron spectroscopy

The crystal structure, x-ray photoemission spectroscopy, magnetic characteristics, and magnetocaloric performance of perovskite La0.55Ca0.45Mn0.8Nb0.2O3 (LCMNO) ceramic powder were analyzed. The orthorhombic structure with a Pnma space group was found as the main phase in the as-received compound after the XRD pattern refinement. The mixed-valence states of manganese were detected by x-ray photoemission spectroscopy (XPS). The analysis of the La3d line revealed the complex nature of the lanthanum states. The evaluation of Zero-Field-Cooled and Field-Cooled magnetization performance provided conclusive evidence for the existence of the antiferromagnetic Mn3O4 phase at a temperature of TN = 42 K and the coexistence of CO- AFM and FM domains in LCMNO. Despite the observed significant (δTFWHM) value due to relatively low magnetic entropy change (ΔSM), the relative cooling power (RCP) is relatively moderate. By adding Nb4+, the changes in Mn valences and their effect on the magnetic cooling effect are lessened.

Investigation of the impact of A-site cation disorder on the structure, magnetic properties, and magnetic entropy change of trisubstituted divalent ions in La0.7(Ba,Ca,Sr)0.3MnO3 manganite.

This study investigates the effect of A-site disorder, characterized by the average ionic radius (〈rA〉) and the cation mismatch (σ2), on the structural, magnetic, critical behavior, and magnetic entropy changes in La0.7(Ba,Ca,Sr)0.3MnO3 manganites with trisubstituted Ba, Ca, and Sr. The sol-gel method was used to prepare polycrystalline samples. All series of compounds crystallize in rhombohedral symmetry with the R3̄c space group. A linear relationship between lattice parameters, unit cell volume, and 〈rA〉 was observed. This reveals an unusual behavior in the correlation between 〈rA〉 and σ2 concerning magnetic properties, which is attributed to the complex simultaneous trisubstitution of divalent ions. Energy dispersive spectroscopy (EDS) and X-ray photoelectron spectroscopy (XPS) were utilized to validate the chemical composition of compounds. All the samples crystallized in rhombohedral symmetry, and the lattice parameters increased continuously with increasing 〈rA〉. A-site disorder causes distortions in the Mn-O bond length and Mn-O-Mn bond angle in the MnO6 octahedral structure, which influences the double-exchange interaction and electronic bandwidth (W). The Curie temperature (TC) increases linearly with increasing W. The critical behavior around TC for all the samples was investigated by determining the values of the critical exponents (β, γ, and δ) using the modified Arrott plot (MAP) method. The estimated critical exponents show that the unconventional model establishes a short-range ferromagnetic order. The maximum magnetic entropy change (-ΔSM) was obtained with the lowest 〈rA〉 and σ2 value. The analysis of the critical behavior and universal curve indicates a second-order phase transition (SOPT) nature for all samples.