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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Spin-Polarized Oxygen Evolution Reaction Enabled by Chiral Molecules Coupled with Ferromagnetic Electrocatalysts

The discovery of chirality-induced spin selectivity (CISS) revolutionized our understanding of the capabilities of chiral molecules, revealing that chiral molecules can function as spin filters, aligning the spin orientation of electrons when they transmit through them. Recently, CISS has been exploited to direct energy conversion, especially the oxygen evolution reaction (OER). However, despite the remarkable progress that has been achieved, the effect of CISS in influencing the intermediate species formation and changing the rate-determining step (RDS) is still vague. To understand those key reaction mechanism steps, electrocatalysts with distinct magnetic characteristics, ferromagnetic CoFe2O4 and paramagnetic Co3O4, were synthesized. The results show that spin-polarized charge carriers retain their spin alignment when coupled with ferromagnetic CoFe2O4, akin to the behavior observed under a magnetic field. The Tafel analysis and kinetic isotope studies (kinetic isotope effect) suggest that in the absence of chiral molecules, the initial electron transfer step, the formation of O* species, governs the rate-determining step (RDS). However, introducing chiral molecules shifts the RDS to a combination of the first and second electron transfers, leading to the formation of OOH*. This conclusion was further supported by in situ infrared spectroscopy, which shows that l-methionine-modified CoFe2O4 (l-CoFe2O4) promotes the formation of OOH*, a key intermediate for O2 generation. This study highlights the critical role of CISS in affecting the OER mechanism and intermediate species formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Spin-Glass-like State and Reversible Room-Temperature Magnetocaloric Effect in Double Distorted Perovskites Nd(Cu 3– x Mn x )Mn 4 O 12

The preparation, complex magnetic properties and room-temperature magnetocaloric effect in Nd(Cu 3–x Mn x )Mn 4 O 12 with cation distribution (Nd 3+ ) A (Cu 3–x 2+x Mn x 3+ ) A' (Mn 1+x 3+ Mn 3–x 4+ ) B O 12 2– (x = 1 and 1.5) have been reported. Both compounds show a sharp paramagnetic-ferromagnetic (FM) transition at T C of 300 and 280 K, respectively. The substitution of Cu by Mn at the A' site induces the emergence of a spin glass state below ≈63 K for x = 1 and ≈72 K for x = 1.5 compound. Another antiferromagnetic-like magnetic transition is also observed in both compounds at 23 and 28 K, respectively, which is discussed as the antiferromagnetic coupling between Nd 3+ at the A' site and (Mn 3+ /Mn 4+ ) at the B site. These two compounds exhibit room-temperature magnetocaloric effect. For a small field of 2 T, the maximum magnetic entropy changes –ΔS M are 1.5 J/kg K at 300 K and 1.4 J/kg K at 280 K, respectively. Furthermore, the –ΔS M (T) curves show an asymmetric distribution, resulting in high refrigerant capacity values for both compounds. We further demonstrate the distinct roles of the A'- and B-site spins on the magnetic properties and the origin of the spin-glass-like state in double distorted perovskites Ln(Cu 3–x Mn x )Mn 4 O 12 family of compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Correlating Crystallography, Magnetism, and Electronic Structure Across Anhysteretic First-Order Phase Transition in Pr 2 In

Here, temperature-dependent powder X-ray diffraction and magnetization measurements of Pr 2 In conclusively prove that the unusual anhysteretic first-order paramagnetic-ferromagnetic phase transition in the compound is related to concurrent changes in both the magnetic and crystallographic lattices. At the same time, the hexagonal Ni 2 In-type structure is stable at least between 6 and 298 K, including at T C = ~57 K. From the density functional theory calculations, the electronic structure of the compound is extraordinarily sensitive to minor changes in lattice parameters that occur across the phase transition, revealing the origin of strong magnetoelastic coupling. In the vicinity of T C , the maximum entropy change, ΔS Max = -16 J Kg -1 K -1 induced by a moderate magnetic field change of 20 kOe (ΔS Max = -20 J Kg -1 K -1 for 50 kOe magnetic field change) is comparable to other known potentially functional materials demonstrating large cryogenic magnetocaloric effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Low energy electrodynamics of CrI 3 layered ferromagnet

We report on the optical properties from terahertz (THz) to Near-Infrared (NIR) of the layered magnetic compound CrI 3 at various temperatures, both in the paramagnetic and ferromagnetic phase. In the NIR spectral range, we observe an insulating electronic gap around 1.1 eV which strongly hardens with decreasing temperature. The blue shift observed represents a record in insulating materials and it is a fingerprint of a strong electron-phonon interaction. Moreover, a further gap hardening is observed below the Curie temperature, indicating the establishment of an effective interaction between electrons and magnetic degrees of freedom in the ferromagnetic phase. Similar interactions are confirmed by the disappearance of some phonon modes in the same phase, as expected from a spin-lattice interaction theory. Therefore, the optical properties of CrI 3 reveal a complex interaction among electronic, phononic and magnetic degrees of freedom, opening many possibilities for its use in 2-Dimensional heterostructures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Unusual first-order magnetic phase transition and large magnetocaloric effect in Nd 2 In

A large magnetocaloric effect with its maximum near the boiling point of natural gas occurs in a rare-earth intermetallic compound Nd 2 In. While behaviors of physical properties indicate that paramagnetic-ferromagnetic transformation supporting the large magnetocaloric effect is firstorder in nature, temperature dependent crystallographic study reveals no changes in lattice symmetry and lack of discontinuities either in phase volume or lattice parameters. In this work we discuss how the borderline first-order nature of phase transformation in Nd 2 In is markedly different from conventional firstorder magnetic transitions occurring in other members of the family – isostructural Pr 2 In and non-isostructural Eu 2 In.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Magnetic and transport behaviors of non-centrosymmetric Nd 7 Ni 2 Pd

Crystallographic, magnetic, electrical transport and thermodynamic properties of pseudo-binary Nd 7 Ni 2 Pd compound have been studied using temperature-dependent x-ray powder diffraction and physical property measurements. Compared to the ferromagnetic parent Nd 7 Pd 3 , the ground state of Nd 7 Ni 2 Pd is antiferromagnetic, and it exhibits strong metamagnetism. The measurements indicate two antiferromagnetic transitions in fields less than 8 kOe: a second-order paramagnetic to antiferromagnetic at T N2 = 29 K and a weak first-order antiferromagnetic to antiferromagnetic transition at T N1 = 24.5 K. Here, the compound becomes ferromagnetic in fields of 8 kOe and higher with T C = 30 K. Temperature dependence of lattice parameters is anomalous, most prominently in the basal plane at ~30 K; however, there is no detectable structural distortion or clear volume discontinuity around 25 K, suggesting a significant weakening of the first-order transition when compared to the binary Nd 7 Pd 3 .

36 MATERIALS SCIENCE↗
DOE OSTI2020

Magnetocaloric effect in the vicinity of the magnetic phase transition in NdCo 2–x Fe x compounds

In the present paper, the magnetocaloric effect (MCE) of NdCo 2-x Fe x (x = 0, 0.2, 0.4, 0.6) compounds was investigated by magnetization measurements. Here, the temperature-dependent high-resolution synchrotron x-ray diffraction study shows a magnetostructural transition from the paramagnetic cubic phase to the ferromagnetic tetragonal phase below their Curie temperatures. Differential scanning calorimetry analysis shows the absence of thermal hysteresis, indicating the second-order nature of the magnetostructural phase transition in these compounds. The maximum values of magnetic entropy change (ΔS M ) and wide operating temperature (OT) are obtained under a field change of 5 T, which are 7.33 Jkg -1 K -1 , 6.45 Jkg -1 K -1 , 5.71 Jkg -1 K -1 , 4.70 Jkg -1 K -1 and 78 K, 82 K, 85 K, 92 K for x = 0, 0.2, 0.4, and 0.6, respectively. The corresponding values of relative cooling power (RCP) are 529.96 Jkg -1 , 497.25 Jkg -1 , 470.55 Jkg -1 , and 428.31 Jkg -1 . The observed wide OT range and large RCP values are comparable with Gd, Gd 5 Ge 2 Si 2 , and some rare-earth-based giant magnetocaloric materials, making this series of compounds suitable for magnetic refrigeration.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Free-energy analysis of the nonhysteretic first-order phase transition of Eu 2 In

Binary intermetallic Eu 2 In was recently reported to exhibit a giant anhysteretic magnetocaloric effect due to a first-order magnetic phase transition between paramagnetic and ferromagnetic states. Experimentally, the transition occurs with a small phase volume change, ΔV/V, of approximately 0.1% around T C of ca. 55 K. We representmagnetic and computemagnetocaloric properties of a Eu 2 In compound using a microscopic description based on a model Hamiltonian that takes into account magnetic exchange and magnetoelastic interactions. In the model the thermodynamic nature of the transition is conveniently represented by a single magnetoelastic interaction parameter. We report a good agreement between the theoretical results and earlier published experimental data confirms the effectiveness of our approach.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Strong Ferromagnetic Exchange Coupling and Single-Molecule Magnetism in MoS 4 3– -Bridged Dilanthanide Complexes

We report the synthesis and characterization of the trinuclear 4d-4f compounds [Co(C 5 Me 5 ) 2 ][(C 5 Me 5 ) 2 Ln(μ-S) 2 Mo(μ-S) 2 Ln(C 5 Me 5 ) 2 ], 1-Ln (Ln = Y, Gd, Tb, Dy), containing the highly polarizable MoS 4 3 - bridging unit. UV-Vis-NIR diffuse reflectance spectra and DFT calculations of 1-Ln reveal a low-energy metal-to-metal charge transfer transition assigned to charge transfer from the singly occupied 4d z 2 orbital of Mo V to the empty 5d orbitals of the lanthanides (4d in the case of 1-Y ), mediated by sulfur-based 3p orbitals. Electron paramagnetic resonance spectra collected for 1-Y in a tetrahydrofuran solution show large 89 Y hyperfine coupling constants of A ⊥ = 23 MHz and A || = 26 MHz, indicating the presence of significant yttrium-localized unpaired electron density. Magnetic susceptibility data support similar electron delocalization and ferromagnetic Ln-Mo exchange for 1-Gd , 1-Tb , and 1-Dy . This ferromagnetic exchange gives rise to an S = 15/2 ground state for 1-Gd and one of the largest magnetic exchange constants involving Gd III observed to date, with J Gd-Mo = +16.1(2) cm -1 . Additional characterization of 1-Tb and 1-Dy by ac magnetic susceptibility measurements reveals that both compounds exhibit slow magnetic relaxation. Although a Raman magnetic relaxation process is dominant for both 1-Tb and 1-Dy , an extracted thermal relaxation barrier of U eff = 68 cm -1 for 1-Dy is the largest yet reported for a complex containing a paramagnetic 4d metal center. Furthermore, these results provide a potentially generalizable route to enhanced n d-4f magnetic exchange, revealing opportunities for the design of new n d-4f single-molecule magnets and bulk magnetic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Paramagnon heat capacity in (Ti,Zr,Hf)NiFe x NiSn half-Heusler composites

As a measure of the temperature response of the energy of matter, the heat capacity $C_p$ is a fundamental thermodynamic property. Its dependence on magnetic field, especially at low temperatures, yields insight into the electronic, phononic, and magnetic states of condensed matter. Here, we present a set of paramagnetic and ferromagnetic (Ti, Zr, Hf)NiFe x Sn half-Heusler composites that exhibit low-field (<3 T) maxima in $C_p$ and higher-field magnetic quenching of the heat capacity at temperatures below 10 K. Using rigorous statistical analysis, we attribute the effect to the existence of paramagnons within the compounds. To explain the lowest-temperature (<4 K), low-field declines in $C_p$, we derive a magnon model up to fourth order in dispersion. While the combined paramagnon and magnon model matches the data well, the fit parameters are significantly underdetermined. Further, we provide a qualitative explanation of the secondary effect based on superconducting phases within the composites. Overall, our work highlights the insight of field-dependent heat capacity studies at fixed temperatures that cannot be as easily gleaned from the temperature-dependent heat capacity at fixed magnetic fields.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Rare-earth monopnictides: Family of antiferromagnets hosting magnetic Fermi arcs

We report since the discovery of topological insulators a great deal of research effort has been devoted to magnetic topological materials, in which nontrivial spin properties can be controlled by magnetic fields, culminating in a wealth of fundamental phenomena and possible applications. The main focus was on ferromagnetic materials that can host Weyl fermions and therefore spin-textured Fermi arcs. The recent discovery of Fermi arcs and new magnetic band splitting in the antiferromagnet (AFM) NdBi has opened up new avenues for exploration. Here we show that these uncharted effects are not restricted to this specific compound, but also emerge in CeBi and NdSb when they undergo paramagnetic to AFM transition. Our data show that the Fermi arcs in NdSb have twofold symmetry, leading to strong anisotropy that may enhance effects of spin textures on transport properties. Our findings thus demonstrate that the RBi and RSb series are materials that host magnetic Fermi arcs and may be a potential platform for modern spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Extraordinarily strong magneto-responsiveness in phase-separated LaFe 2 Si

Materials responding vigorously to minor variations of external stimuli with negligible hysteresis could revolutionize many of the energy technologies, including refrigeration, actuation, and sensing. Here, we report a combined experimental and theoretical study of a two-phase composite, naturally formed at the LaFe 2 Si stoichiometry, which exhibits a nearly anhysteretic, two-step first-order ferromagnetic-to-paramagnetic phase transformation with enhanced sensitivity to an external magnetic field. Other unusual properties include a large plateau-like positive magnetoresistance, magnetic-field-induced temperature and entropy changes occurring over a wide temperature range, and a Griffiths-like phase associated with short-range ferromagnetic clustering in the paramagnetic state. The heat capacity, magnetization, Mössbauer spectroscopy, and electrical resistivity, all exhibit characteristic, unusually sharp, first-order discontinuities even in magnetic fields as high as 100 kOe. We expect that similar phenomena could be designed in other mixed-phase systems, leading to novel functionalities, such as giant caloric effects in many yet undiscovered or/and underperforming intermetallic compounds.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Machine learning study of magnetism in uranium-based compounds

Actinide and lanthanide-based materials display exotic properties that originate from the presence of itinerant or localized f electrons and include unconventional superconductivity and magnetism, hidden order, and heavy-fermion behavior. Due to the strongly correlated nature of the 5f electrons, magnetic properties of these compounds depend sensitively on applied magnetic field and pressure, as well as on chemical doping. However, precise connection between the structure and magnetism in actinide-based materials is currently unclear. In this investigation, we established such structure-property links by assembling and mining two datasets that aggregate, respectively, the results of high-throughput density functional theory simulations and experimental measurements for the families of uranium- and neptunium-based binary compounds. Various regression algorithms were utilized to identify correlations among accessible attributes (features or descriptors) of the material systems and predict their cation magnetic moments and general forms of magnetic ordering. Descriptors representing compound structural parameters and cation f-subshell occupation numbers were identified as most important for accurate predictions. The best machine learning model developed employs the random forest regression algorithm. It can predict both spin and orbit moment size with root-mean-square error of 0.17 μ B and 0.19 μ B , respectively. Lastly, the random forest classification algorithm is used to predict the ordering (paramagnetic, ferromagnetic, and antiferromagnetic) of such systems with 76% accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Ferromagnetism and structural phase transition in rhombohedral PrI r 3

The synthesis, structural, magnetic, thermal, and transport properties are reported for polycrystalline PrI⁢r 3 . At room temperature PrI⁢r 3 displays the rhombohedral space group R–3m and a PuNi 3 -type structure. At around 70 K a phase transition to a monoclinic C⁢2/m structure is observed and continued cooling reveals temperature independent behavior of the unit cell volume. Further, PrI⁢r 3 undergoes a paramagnetic to ferromagnetic transition with T c =7.5K. The temperature dependent magnetic susceptibility follows the Curie-Weiss law with a positive Curie-Weiss temperature, and an effective moment that is close to the theoretical effective moment for a free P⁢r +3 ion. Finally, the structural transition introduces further complexity into the behavior of PuNi 3 -type materials and highlights the importance of temperature-dependent structural studies to complement physical property measurements in intermetallic compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Coexistence of low and high spin states in La 18 Co 28 Pb 3

The electronic structure and magnetic properties of a newly predicted stable ternary compound La 18 ⁢Co 28 ⁢Pb 3 are studied using electronic structure analysis. The ground state of this compound is ferromagnetic, with three positions of nonequivalent magnetic Co atoms. A strong dependence of magnetic properties on volume shows that this system is situated near the point of magnetic instability. The coexistence of high- and low-spin ferromagnetic states as a function of volume near equilibrium was discovered. A corresponding spin tunneling splitting was estimated. The stability of the theoretically predicted magnetic ground state was tested by varying the Hubbard parameter. The thermal spin fluctuations were added to estimate the paramagnetic moment and a Curie temperature. Finally, the necessity of experimental verification of the obtained results is emphasized.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Magnetism and finite-temperature effects in UZr 2 : A density functional theory analysis

The structure and the thermophysical properties of d-UZr 2 are investigated using 0 K density functional theory and ab initio molecular dynamics (AIMD). Modeling the true paramagnetic state of this intermetallic compound has been challenging using first-principles calculations. For the first time, we find that the generalized gradient approximation method without applying an on-site Coulomb interaction term (Hubbard U) can result in a ground state that is antiferromagnetic (AFM). We believe that this weak AFM ground state is the closest to the real paramagnetic state. We found that structure optimization at finite temperatures using AIMD is necessary to achieve this ground state instead of the non-magnetic and ferromagnetic states previously reported in the literature. Our findings indicate that applying the Hubbard U on uranium f-orbitals in this metallic system is unnecessary and not recommended, as it leads to a large overestimation of the volume and introduces an unphysical strong spin polarization. Finally, our approach results in atomic volume, thermal expansion, and heat capacities that have strong agreement with experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Development of (NO)Fe(N 2 S 2 ) as a Metallodithiolate Spin Probe Ligand: A Case Study Approach

The ubiquity of sulfur–metal connections in nature inspires the design of bi- and multimetallic systems in synthetic inorganic chemistry. Common motifs for biocatalysts developed in evolutionary biology include the placement of metals in close proximity with flexible sulfur bridges as well as the presence of π-acidic/delocalizing ligands. This Account will delve into the development of a (NO)Fe(N 2 S 2 ) metallodithiolate ligand that harnesses these principles. The Fe(NO) unit is the centroid of a N 2 S 2 donor field, which as a whole is capable of serving as a redox-active, bidentate S-donor ligand. Its paramagnetism as well as the ν(NO) vibrational monitor can be exploited in the development of new classes of heterobimetallic complexes. We offer four examples in which the unpaired electron on the {Fe(NO)} 7 unit is spin-paired with adjacent paramagnets in proximal and distal positions. First, the exceptional stability of the (NO)Fe(N 2 S 2 )-Fe(NO) 2 platform, which permits its isolation and structural characterization at three distinct redox levels, is linked to the charge delocalization occurring on both the Fe(NO) and the Fe(NO) 2 supports. This accommodates the formation of a rare nonheme {Fe(NO)} 8 triplet state, with a linear configuration. A subsequent FeNi complex, featuring redox-active ligands on both metals (NO on iron and dithiolene on nickel), displayed unexpected physical properties. Our research showed good reversibility in two redox processes, allowing isolation in reduced and oxidized forms. Various spectroscopic and crystallographic analyses confirmed these states, and Mössbauer data supported the redox change at the iron site upon reduction. Oxidation of the complex produced a dimeric dication, revealing an intriguing magnetic behavior. The monomer appears as a spin-coupled diradical between {Fe(NO)} 7 and the nickel dithiolene monoradical, while dimerization couples the latter radical units via a Ni 2 S 2 rhomb. Magnetic data (SQUID) on the dimer dication found a singlet ground state with a thermally accessible triplet state that is responsible for magnetism. A theoretical model built on an H 4 chain explains this unexpected ferromagnetic low-energy triplet state arising from the antiferromagnetic coupling of a four-radical molecular conglomerate. For comparison, two (NO)Fe(N 2 S 2 ) were connected through diamagnetic group 10 cations producing diradical trimetallic complexes. Antiferromagnetic coupling is observed between {Fe(NO)} 7 units, with exchange coupling constants (J) of -3, -23, and -124 cm –1 for Ni II , Pd II , and Pt II , respectively. This trend is explained by the enhanced covalency and polarizability of sulfur-dense metallodithiolate ligands. A central paramagnetic trans-Cr(NO)(MeCN) receiver unit core results in a cissoid structural topology, influenced by the stereoactivity of the lone pair(s) on the sulfur donors. This {Cr(NO)} 5 radical bridge, unlike all previous cases, finds the coupling between the distal Fe(NO) radicals to be ferromagnetic (J = 24 cm –1 ). The stability and predictability of this S = 1/2 moiety and the steric/electronic properties of the bridging thiolate sulfurs suggest it to be a likely candidate for the development of novel molecular (magnetic) compounds and possibly materials. The role of synthetic inorganic chemistry in designing synthons that permit connections of the (NO)Fe(N 2 S 2 ) metalloligand is highlighted as well as the properties of the heterobi- and polymetallic complexes derived therefrom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Magnetism in EuAlSi and the Eu 1−𝑥 ⁢Sr 𝑥 ⁢ AlSi solid solution solid solution

The magnetic properties of EuAlSi, a compound comprising a honeycomb lattice of Al/Si atoms and a triangular lattice of Eu atoms, are presented. By means of single-crystal x-ray diffraction, we find that EuAlSi crystallizes in an AlB 2 -type structure with space group 𝑃⁢6/mmm and unit cell parameters 𝑎 = 4.2229⁢ (10) ⁢Å and 𝑐 = 4.5268 ⁢(12)⁢ Å. Our magnetic measurements indicate that EuAlSi is a soft ferromagnetic material with 𝑇 Curie = 25.8 K. The susceptibility follows the Curie-Weiss law at high temperatures, which allowed us to determine the paramagnetic Curie temperature 𝜃 𝑃 = 36.2 ⁢(1) ⁢K and an effective magnetic moment 𝜇 eff = 8.07 ⁢(1)⁢ µ 𝐵 /Eu. This value is in agreement with the theoretical value of 7.9 µ 𝐵 for Eu 2+ free ion. Moreover, we have prepared the Eu 1−𝑥 ⁢Sr 𝑥 ⁢ AlSi solid solution, where the atoms in the triangular lattice were systematically exchanged, in order to study the evolution of the collective quantum properties from the ferromagnetic EuAlSi toward the superconducting SrAlSi. Across the Eu 1−𝑥 ⁢Sr 𝑥 AlSi solid solution, the unit cell parameters change linearly, following Vegard’s law, and making the system reliable for studying composition dependence of the interplay between the crystal structure and physical properties. As the Sr content increases, i.e., 𝑥 increases, we note a consistent reduction of 𝜇 eff and 𝑇 Curie . Long-range magnetic order in Eu 1−𝑥 ⁢Sr 𝑥 ⁢ AlSi persists up to 𝑥 = 0.95, whereas superconductivity is only observed for samples with 𝑥 > 0.97.

Walicka, Dorota I. [University of Geneva (Switzerl↗