{"title":"Anomalous Proximity Effect Under Andreev and Majorana Bound States","authors":"Eslam Ahmed, Yukio Tanaka, Jorge Cayao","doi":"10.1007/s10948-025-07057-9","DOIUrl":"10.1007/s10948-025-07057-9","url":null,"abstract":"<div><p>We theoretically study the anomalous proximity effect in a clean normal metal/disordered normal metal/superconductor junction based on a Rashba semiconductor nanowire model. The system hosts two distinct phases: a trivial helical phase with zero-energy Andreev bound states and a topological phase with Majorana bound states. We analyze the local density of states and induced pair correlations at the edge of the normal metal region. We investigate their behavior under scalar onsite disorder and changing the superconductor and disordered region lengths in the trivial helical and topological phases. We find that both phases exhibit a zero-energy peak in the local density of states and spin-triplet pair correlations in the clean limit, which we attribute primarily to odd-frequency spin-triplet pairs. Disorder rapidly splits the zero-energy peak in the trivial helical phase regardless of the lengths of the superconductor and disordered normal regions. The zero-energy peak in the topological phase shows similar fragility when the superconductor region is short. However, for long superconductor regions, the zero-energy peak in the topological phase remains robust against disorder. In contrast, spin-singlet correlations are suppressed near zero energy in both phases. Our results highlight that the robustness of the zero-energy peak against scalar disorder, contingent on the superconductor region length, serves as a key indicator distinguishing trivial Andreev bound states from topological Majorana bound states.</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10948-025-07057-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Qinghui Li, Panpan Zhang, Hongbing Li, Yuliang Xu, Xiangmu Kong
{"title":"Quantum Entanglement and Phase Transitions in XY Model with a Transverse Magnetic Field","authors":"Qinghui Li, Panpan Zhang, Hongbing Li, Yuliang Xu, Xiangmu Kong","doi":"10.1007/s10948-025-07060-0","DOIUrl":"10.1007/s10948-025-07060-0","url":null,"abstract":"<div><p>In this paper, we use the quantum renormalization group method to study the quantum entanglement and phase transitions of the XY system with the transverse magnetic field and discuss the relations between the entanglement and the magnetic field <i>B</i>, the anisotropy parameter <span>(gamma )</span>, and particle number <i>N</i>. The quantum phase transition point of the system can be found through the strange behavior entangled at a certain point, and the relationship between the entanglement and the critical exponent of the correlation length can also be found. The results show that when the magnetic field is fixed, there is a maximum value of entanglement at the critical point <span>(gamma =0)</span>, and with the increase of the number of iterations, the maximum value of entanglement gradually increases and approaches one. In addition, we find that <span>(gamma )</span> has an inhibiting effect on entanglement, and <i>B</i> has a promoting effect on entanglement. At the thermodynamic limit, entanglement exists only at the critical point, in the region where <span>(gamma ne 0)</span>, the system corresponds to the Ising-like phase, and at <span>(gamma =0)</span>, it corresponds to the spin liquid phase. By studying the entanglement derivatives, we also find that there are two extreme values of the first derivative, and with the increase of the number of iterations, the extreme point gradually approaches the critical point. The first derivative of the entanglement exhibits a nonanalytic behavior at the critical point, indicating that the system has a second-order phase transition. Finally, the scaling behavior of entanglement at the critical point is detected, and the critical exponent of entanglement equals one.</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Advancing Theranostics with CoFe2O4 Nanoparticles: Comprehensive Approaches to Synthesis, Biofunctionalization, and Their Potential in Precision Medicine and Targeted Therapeutic Applications","authors":"Rabiya Riffath Syed Altaf, Puruchothaman Venkatesan, Naveen Palani, Keren Celestina Mendonce, Agilandeswari Mohan, T. G. Nithya, Mohankumar Srinivasan, Shakthivel Rajendran, Parthasarathy Surya, Suriyaprakash Rajadesingu","doi":"10.1007/s10948-025-07047-x","DOIUrl":"10.1007/s10948-025-07047-x","url":null,"abstract":"<div><p>Cobalt ferrite (CoFe<sub>2</sub>O<sub>4</sub>) nanoparticles are gaining attention in biomedical science for applications in imaging, drug delivery, and cancer therapy. As a hard magnetic material, CoFe<sub>2</sub>O<sub>4</sub> exhibits moderate magnetism and high coercivity, 1235 Oe–2.2 kOe at room temperature, up to 10.5 kOe at low temperatures. Its saturation magnetization decreases with smaller particle sizes, ranging from ∼69 emu/g for larger particles to ∼35 emu/g for smaller ones. CoFe<sub>2</sub>O<sub>4</sub> crystallizes in a cubic spinel (AB<sub>2</sub>O<sub>4</sub>) structure, with a lattice parameter of 8.358 Å. Core–shell architectures enhance thermal stability up to 650 °C, while thermogravimetric analysis confirms stability up to 600 °C. This review explores recent advances in synthesis techniques, such as sol–gel and hydrothermal methods, which have enabled precise control over size, shape, and magnetic properties, optimizing CoFe<sub>2</sub>O<sub>4</sub> for biomedical applications. Functionalization strategies, including polymer coatings and biomimetic approaches, enhance biocompatibility and targeted therapeutic performance. One promising innovation is cell membrane coating, which improves immune evasion and drug delivery. By exploring these advancements and addressing the barriers to clinical implementation, this review provides insights into how CoFe<sub>2</sub>O<sub>4</sub> nanoparticles could become a key player in the future of nanomedicine.</p><h3>Graphical Abstract</h3>\u0000<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div><p>Biofunctionalized CoFe<sub>2</sub>O<sub>4</sub> nanoparticles for targeted theranostics</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Microstructural and Magnetic Properties of La-Ce co-Doped Soft-Hard Ferrites Synthesized by the Co-precipitation Method","authors":"Amna Azhar, Mozaffar Hussain, Rizwan Akram, Zahid Sarfraz, Ayesha Iqbal","doi":"10.1007/s10948-025-07050-2","DOIUrl":"10.1007/s10948-025-07050-2","url":null,"abstract":"<div><p>Hexaferrites’ magnetic and structural properties are highly sensitive to changes in sintering temperature and cationic replacements. We report the phase, microstructural analysis, and magnetic behavior of La-Ce co-doped ferrites with a wide range of compositions, including strontium ferrite [SrFe<sub>12-x</sub>(La<sub>0.5</sub>Ce<sub>0.5</sub>)<sub>x</sub>O<sub>19</sub>] and cobalt ferrite [CoFe<sub>2-x</sub>(La<sub>0.5</sub>Ce<sub>0.5</sub>)<sub>x</sub>O<sub>4</sub>] with varying La-Ce contents (x = 0.0–0.4) using a modified co-precipitation method at room temperature. The results confirmed the hexagonal and cubic structure for La-Ce co-doped strontium and cobalt ferrite compounds, respectively. Morphological studies show particles with a rod-like to plate-like morphology, featuring irregular edges and a moderate degree of agglomeration, suggesting anisotropic grain growth. The lattice parameters <b>a</b> (lattice constant in the basal plane) and <b>c</b> (lattice constant along the vertical direction) for strontium ferrite decrease from 5.84 to 5.20 Å and 23.01 to 21.92 Å, respectively, while for cobalt ferrite they increase from 8.29 to 8.38 Å. The optimum magnetic investigations include saturation magnetization (M<sub>s</sub>), remanent magnetization (M<sub>r</sub>), and coercivity (H<sub>c</sub>) up to 71.6 emu/g, 30 emu/g, 1284 Oe, and 39 emu/g, 16 emu/g, and 349 Oe with 10% La-Ce substitution for Fe in strontium and cobalt ferrite, respectively. Thirty percent La-Ce substitution for Fe in cobalt ferrite results in an unexpected increase in M<sub>s</sub> (50.92 emu/g) and M<sub>r</sub> (20.86 emu/g) that could be attributed to the cation redistribution. The M<sub>r</sub>/M<sub>s</sub> ratio decreases with the increase of La-Ce contents in both compounds, which is attributed to the reduced exchange interaction between magnetic particles. The moderate values of magnetic parameters make them suitable for permanent magnets in motors and generators, loudspeakers, and audio equipment. </p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Laid Latreche, Hamza Abbassa, El Habib Abbes, Abdelkader Boukortt
{"title":"First-Principles Investigation of the Influence of Disorder on Electronic and Magnetic Properties in CoFeMnAl Quaternary Heusler Alloys","authors":"Laid Latreche, Hamza Abbassa, El Habib Abbes, Abdelkader Boukortt","doi":"10.1007/s10948-025-07048-w","DOIUrl":"10.1007/s10948-025-07048-w","url":null,"abstract":"<div><p>First-principles calculations, combined with the supercell approach, are employed to investigate the effects of atomic disorder on the electronic properties of the CoFeMnAl quaternary Heusler alloy (LiMgPdSn-type). The ordered alloy is a half-metallic ferromagnet; its moment obeys the Slater-Pauling rule with <i>T</i><sub>C</sub> > 300 K. We analyse twelve antisite and six swap disorder configurations. Calculations show that the Fe<sub>Mn</sub> antisite is the most energetically favourable defect (−1.25 eV), followed by the FeCo antisite and the MnAl swap. The disorder generally contracts the spin-down gap. Half-metallicity is largely preserved but completely lost for Co<sub>Al</sub>, Co<sub>Mn</sub> antisite and CoAl, CoMn swap defects. Disorder has a significant effect on the magnetic moment and Curie temperature. The Fe<sub>Mn</sub> antisite gives 3.12 µ<sub>B</sub>, which is very close to the experimental value of 3.10 µ<sub>B</sub>. This study demonstrates the importance of considering disorder when predicting the properties of Heusler alloys.\u0000</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Geeta Chavan, Papanna B. Belavi, Pradeep Chavan, Lalsingh R. Naik
{"title":"Optimization and Tunability of Dielectric, Magnetic Properties, and Magnetoelectric Coupling of Cadmium Nickel Ferrite–BZT ME Composites","authors":"Geeta Chavan, Papanna B. Belavi, Pradeep Chavan, Lalsingh R. Naik","doi":"10.1007/s10948-025-07054-y","DOIUrl":"10.1007/s10948-025-07054-y","url":null,"abstract":"<div><p>Lead-free magnetoelectric (ME) ceramic particulate composites of the type (y)Cd<sub>1-x</sub>Ni<sub>x</sub>Fe<sub>2</sub>O<sub>4</sub> + (1–y) BaZr<sub>0.2</sub>Ti<sub>0.8</sub>O<sub>3</sub> (with weight fractions <i>y</i> = 0.1, 0.2, 0.3 and <i>x</i> = 0.1, 0.2, 0.3)were synthesized using the conventional solid-state reaction technique. Powder X-ray diffraction (XRD) confirmed the coexistence of ferrite and ferroelectric phases in the composites sintered at 1100 °C. Scanning electron microscopy (SEM) revealed detailed information on surface morphology, grain size, and porosity, with average grain sizes ranging from 1.08 to 3.80 µm. Energy-dispersive X-ray spectroscopy (EDX) was employed for elemental analysis and detection of possible foreign phases. Dielectric studies were carried out by measuring the dielectric constant (<i>ε</i>′) and dielectric loss tangent as functions of frequency (40 Hz–1 MHz) and temperature (30–650 °C) at four fixed frequencies (1 kHz, 10 kHz, 100 kHz, and 1 MHz).The dielectric constant showed a sharp decrease at lower frequencies, stabilizing to a constant value at higher frequencies. Magnetic characterization at room temperature exhibited well-defined M–H hysteresis loops, confirming the presence of an ordered magnetic structure in the ferrite–ferroelectric composites. The magnetoelectric effect, measured as a function of magnetic field intensity, displayed a linear variation. The static ME voltage coefficient [(dE/dH)H] was composition-dependent, with the maximum magnetoelectric voltage coefficient (<i>α</i>) recorded as 15.103 mV/cm·Oe for the composite with <i>y</i> = 0.2 and <i>x</i> = 0.3. The nearly constant magnetoelectric conversion factor further indicated that magnetostriction reached saturation during magnetic poling, resulting in a stable induced electric field in the ferroelectric phase.\u0000</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Influence of Microwave Radiation on Current–voltage Characteristic of Non-ideal Josephson Junctions","authors":"Alexander N. Lykov, Ivan A. Lykov","doi":"10.1007/s10948-025-07052-0","DOIUrl":"10.1007/s10948-025-07052-0","url":null,"abstract":"<div><p>We theoretically study Josephson junctions that contain higher Josephson harmonics in the current-phase relationship using numerical simulations in the resistive-shunt junction model. We call these junctions non-ideal Josephson junctions. Our main focus is on the current–voltage characteristics of non-ideal junctions in the current-bias case. Deviations of the characteristics of these junctions from those of ideal (standard) junctions are studied numerically. It is established that the current–voltage characteristics remain unchanged with significant deviations of the current-phase relationship from a simple sinusoidal dependence. Also, the dependences of the height of the Shapiro current steps on the amplitude of the incident radiation are calculated. Some deviations of these dependences from the corresponding dependences for ideal Josephson junctions are found. In our work, we consider the features of the appearance of additional current steps on the current–voltage characteristics of non-ideal Josephson junctions, and also show the possibility of their absence in the case of the existence of additional Josephson harmonics. The results of our work prove that by analyzing the structure of the Shapiro steps of the current–voltage characteristics, it is possible to obtain information about the properties of Josephson junctions and the superconductors that form them.</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Assessing the Thermophysical Properties of Gd, Tb, and GdxTb(1-x) Materials for Magnetic Cooling Application","authors":"Prakash Chandra Singh, Pabitra Halder","doi":"10.1007/s10948-025-07051-1","DOIUrl":"10.1007/s10948-025-07051-1","url":null,"abstract":"<div><p>This study investigates the thermophysical properties of gadolinium (Gd), terbium (Tb), and their binary compounds Gd<sub>x</sub>Tb<sub>(1-x)</sub> (<i>x</i> = 0.25, 0.50, 0.75) using mean field theory. The study focuses on calculating magnetocaloric parameters, including magnetic entropy, its variation with magnetic field, specific heat, and the adiabatic temperature change, across magnetic field (<i>B</i>) intensities from 0 to 9 T. The findings indicate that the magnetic entropy has a considerable response to the applied magnetic field, demonstrating a 9.28% reduction in magnetic entropy for Gd at a temperature of 300 K when the field strength escalates from 1.5 to 9 T. Tb has a larger <span>(Delta {S}_{text{m}})</span> than Gd under similar conditions. In Gd<sub>x</sub>Tb<sub>(1-x)</sub> compounds, increasing Gd concentration results in a higher Curie temperature, approaching pure Gd, while the peak <span>(Delta {T}_{text{ad}})</span> shows a little decline. The peak values of <span>(Delta {T}_{text{ad}})</span> are 6 K, 5.86 K, and 5.76 K for <i>x</i> values of 0.25, 0.5, and 0.75 in Gd<sub>x</sub>Tb<sub>(1-x)</sub>, respectively, at <i>B</i> 1.5 T. Moreover, Tb demonstrates a significantly higher relative cooling power than Gd, being approximately 34.91% higher at a given <i>B</i> of 1.5 T, whereas Gd and Gd-rich compounds display higher refrigeration capacity in the 250–320 K range. These results provide theoretical insights into the magnetic field–dependent magnetocaloric behavior of Gd, Tb, and Gd<sub>x</sub>Tb<sub>(1-x)</sub> compounds, while highlighting the compositional effects in Gd<sub>x</sub>Tb<sub>(1-x)</sub> compounds.</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Alternative Material for Semiconductor Technologies: Li2VMnBr6 Double Perovskite","authors":"Evren Görkem Özdemir","doi":"10.1007/s10948-025-07056-w","DOIUrl":"10.1007/s10948-025-07056-w","url":null,"abstract":"<div><p>Li<sub>2</sub>VMnBr<sub>6</sub> double perovskite material was obtained as a ferromagnetic semiconductor. The semiconductor band gaps for the spin-up orientations are 0.3725 eV, 1.7943 eV, and 2.0627 eV for the GGA + PBE, GGA + 3 eV, and GGA + 4 eV approximations, respectively. For the spin-down orientations, these gaps are -2.4070 eV, 3.0968 eV, and 3.0875 eV. The 10.52 Å is the lattice constant at the equilibrium point. Li<sub>2</sub>VMnBr<sub>6</sub> is mechanically stable. While it shows ductile character at 0 GPa pressure, it turns into a brittle structure after 10 GPa with increasing pressure. According to the Gibbs energy value, it is also structurally stable at low pressure. According to elastic and thermodynamic calculations, the Debye temperatures at the initial conditions were 212.264 K and 240.76 K. The Curie temperature and formation energy values were obtained as 303 K and -1.291 eV, respectively. The total magnetic moment of Li<sub>2</sub>VMnBr<sub>6</sub> double perovskite is obtained as 8.00 µ<sub>B</sub>. The most partial contributions come from Mn and V-atoms with the values of 4.4699 µ<sub>B</sub> and 2.6219 µ<sub>B</sub>. The structural, electronic, and magnetic characteristics of Li<sub>2</sub>VMnBr<sub>6</sub> double perovskite material and its elastic properties make it a highly efficient alternative material for semiconductor technologies.</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145090444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Critical Behavior and Landau Theory in Pr0.55Sr0.45-xNaxMnO3 Manganites","authors":"W. Mabrouki, A. Krichene, W. Boujelben","doi":"10.1007/s10948-025-07055-x","DOIUrl":"10.1007/s10948-025-07055-x","url":null,"abstract":"<div><p>In this work, we investigated the critical behavior and magnetocaloric effect of Pr<sub>0.55</sub>Sr<sub>0.45-x</sub>Na<sub>x</sub>MnO<sub>3</sub> manganites (x = 0, 0.05 and 0.1) by using critical exponent analysis and Landau theory. The study revealed that the mean-field, 3D-Heisenberg and 3D-XY models are the best for describing the magnetic interactions for x = 0, 0.05 and 0.1 samples, respectively. With increasing sodium content, the magnetic interactions display a striking change from long-range to short-range interactions, which may be ascribed to an increase in Mn<sup>4+</sup> ions concentration and magnetocrystalline anisotropy. Using Landau theory, we have confirmed that the magnetic transition around T<sub>C</sub> is of second-order. An agreement was found between the magnetic entropy change values estimated by Landau theory and those obtained using Maxwell relation for a magnetic field equal to 2 T. This confirms the validity of Landau theory to estimate the magnetocaloric effect of Pr<sub>0.55</sub>Sr<sub>0.45-x</sub>Na<sub>x</sub>MnO<sub>3</sub> samples. The small deviation obtained for our samples below T<sub>C</sub> can be attributed to the existence of magnetic disorder in the ferromagnetic phase.</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145090443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}