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At least 505 records · Page 28

Spectroscopic evidence for the direct involvement of local moments in the pairing process of the heavy-fermion superconductor CeCoIn 5

The microscopic mechanism for electron pairing in heavy-fermion superconductors remains a major challenge in quantum materials. Some form of magnetic mediation is widely accepted with spin fluctuations as a prime candidate. A novel mechanism, “composite pairing” based on the cooperative two-channel Kondo effect directly involving the f -electron moments, has also been proposed for some heavy-fermion compounds including CeCoIn 5 . The origin of the spin-resonance peak observed in neutron-scattering measurements on CeCoIn 5 is still controversial and the corresponding hump-dip structure in the tunneling conductance is missing. This is in contrast to the cuprate and Fe-based high-temperature superconductors, where both characteristic signatures are observed, indicating spin fluctuations are likely involved in the pairing process. In this study, we report results from planar tunneling spectroscopy along three major crystallographic orientations of CeCoIn 5 over wide ranges of temperature and magnetic field. The pairing gap opens at T p ~ 5 K , well above the bulk T c = 2.3 K , and its directional dependence is consistent with d x 2 – y 2 symmetry. With increasing magnetic field, this pairing gap is suppressed as expected but, intriguingly, a gaplike structure emerges smoothly, increasing linearly up to the highest field applied. This field-induced gaplike feature is only observed below T p . The concomitant appearance of the pairing gap and the field-induced gaplike feature, along with its linear increase with field, indicates that the f -electron local moments are directly involved in the pairing process in CeCoIn 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Chemical bond and phase stability of Ga-doped Sm2Fe17Cx magnet

Sm2Fe17C3 phase (2:17) is metastable and exhibits excellent intrinsic hard magnetic properties. Doping elements such as Ga facilitate the formation of a single-phase 2:17 structure in arc-melted Sm2Fe17Cx alloys, which opens a promising route for fabricating fully dense bulk Sm2Fe17Cx magnets via high-temperature techniques such as melting and sintering. First-principles electronic structure calculation indicates that Ga prefers to partially replace Fe at the 9d and 18h crystallographic sites in Sm2Fe17C3 and Sm2Fe17, respectively. This difference in site preference is attributed to the distinct chemical environments surrounding the Fe atoms in the two compounds. Ga substitution favors the Sm–Ga bonding formation while avoiding Ga–C interactions. Doped Ga atoms result in more negative formation energy in Sm2(Fe, Ga)17C3, indicating improved structural stability. Crystal Orbital Hamilton Population analysis reveals that carbon insertion weakens the bonding of Sm-Fe (18h) and Sm-Fe (18f) in Sm2Fe17C3. Ga doping facilitates electron redistribution across chemical bonds, thereby reinforcing Fe(18h)–Sm and Fe(18f)–Sm interactions and stabilizing the carbon-centered octahedral local structure. This synergistic effect contributes significantly to the observed enhancement in phase stability of Sm2(Fe, Ga)17Cx. These findings suggest that chemical bond engineering through the selective doping of Ga can enhance phase stability and facilitate the synthesis of Sm2Fe17C3, providing a viable strategy for developing advanced magnets.

Liu, Xubo [Critical Materials Innovation Hub, Divi↗

Structural, electronic, and magnetic properties of nearly ideal J eff = 1/2 iridium halides

Heavy transition metal magnets with J e f f = 1 2 electronic ground states have attracted recent interest due to their penchant for hosting new classes of quantum spin liquids and superconductors. Unfortunately, model systems with ideal J e f f = 1 2 states are scarce due to the importance of noncubic local distortions in most candidate materials. In this work, we identify a family of iridium halide systems [i.e., K 2 Ir Cl 6 , K 2 Ir Br 6 , ( NH 4 ) 2 Ir Cl 6 , and Na 2 Ir Cl 6 · 6 ( H 2 O ) ] with Ir 4 + electronic ground states exhibiting extremely small deviations from the ideal J e f f = 1 2 limit. We also find ordered magnetic ground states for the three anhydrous systems, with single-crystal neutron diffraction on K 2 Ir Br 6 revealing type-I antiferromagnetism. This spin configuration is consistent with expectations for significant Kitaev exchange in a face-centered-cubic magnet. This work establishes that incorporating isolated Ir X 6 octahedra in materials, where X is a halogen ion with a low electronegativity, is an effective design principle for realizing unprecedented proximity to the pure J e f f = 1 2 state. However, at the same time, we highlight undeniable deviations from this ideal state, even in clean materials with ideal Ir X 6 octahedra as inferred from the global cubic crystal structures.

36 MATERIALS SCIENCE↗

Structure transition and zigzag magnetic order in Ir/Rh-substituted honeycomb lattice α - RuCl 3

Here, we report magnetization and neutron diffraction studies on crystal and magnetic structures of Ir- and Rh-substituted honeycomb lattice α-RuCl 3 . The iridium or rhodium atoms are distributed at the Ru site with little structural modification. Both systems undergo a room-temperature monoclinic C2/m to low-temperature trigonal $R\bar{3}$ phase transformation with a large recoverable hysteresis. At low temperature, a zigzag spin order is observed with the same characteristic wave vector (0,0.5,1) as in the parent α-RuCl 3 . Detailed magnetic structure refinement reveals an ordered moment of 0.32(5)µB/Ru and an upper boundary of canting angle of 15(4)º away from the basal plane at 5 K for the 10% Ir-substituted α-RuCl 3 , which is different from the 0.45–0.73 µB/Ru and 32°–48° canting angle reported in the parent compound α-RuCl 3 . The observation of unchanged RuCl 6 local octahedral environment, reduced ordered magnetic moment size and canting angle compared to previously reported highlights the potential to study quantum spin-liquid behavior through nonmagnetic ion doping.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetic field line reconnection experiments. V - Current disruptions and double layers

An investigation is conducted of the stability of a large laboratory plasma current sheet, which has been generated in the process of magnetic field line reconnection, with respect to local current increases. Magnetic flux variations in regions remote from the current sheet generate an inductive voltage in the current loop that drops off inside the plasma in the form of a potential double layer, leading to particle acceleration with velocities much larger than those expected from the steady state electric fields in the plasma. A model for the mechanism of the current disruptions is formulated in which the potential structure leads to ion expulsion, creating a localized density drop. The associated current drop in an inductive circuit drives the potential structure, providing feedback for the disruptive instability. Similarities to, and differences from, magnetospheric substorm phenomena are noted.

Stenzel, R. L.↗

Insights into Molecular Magnetism in Metal–Metal Bonded Systems as Revealed by a Spectroscopic and Computational Analysis of Diiron Complexes

A pair of bimetallic compounds featuring Fe–Fe bonds, [Fe( i PrNPPh 2 ) 3 FeR] (R = PMe 3 , ≡N t Bu), have been investigated using High-Frequency Electron Paramagnetic Resonance (HFEPR) as well as field- and temperature-dependent 57 Fe nuclear γ resonance (Mössbauer) spectroscopy. To gain insight into the local site electronic structure, we have concurrently studied a compound containing a single Fe(II) in a geometry analogous to that of one of the dimer sites. Our spectroscopic studies have allowed for the assessment of the electronic structure via the determination of the zero-field splitting and 57 Fe hyperfine parameters for the entire series. We also report on our efforts to correlate structure with physical properties in metal–metal bonded systems using ligand field theory guided by quantum chemical calculations. Through the insight gained in this study, we discuss strategies for the design of single-molecule magnets based on polymetallic compounds linked via direct metal–metal bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops

The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.

Parhi, S.↗

Electron Beam-Induced Phase Transformations in Different Crystal Orientations of a 2D van der Waals Magnet

To control materials properties at the nanoscale, the well-focused electron beam of the scanning transmission electron microscope (STEM) can be used as a tool to engineer structure with atomic precision. For 2D magnets, especially the highly anisotropic materials AgCrP2S6 and CrSBr, we find here that the STEM serves as a powerful tool for sculpting the arrangement of atoms, with the potential to modulate local magnetic properties.

Park, Eugene [Massachusetts Inst. of Technology (M↗

Magnetic excitations, nonclassicality, and quantum wake spin dynamics in the Hubbard chain

Recent work has demonstrated that quantum Fisher information (QFI), a witness of multipartite entanglement, and magnetic Van Hove correlations G(r,t), a probe of local real-space real-time spin dynamics, can be successfully extracted from inelastic neutron scattering on spin systems through accurate measurements of the dynamical spin structure factor S(k,ω). In this work, we apply theoretically these ideas to the half-filled Hubbard chain with nearest-neighbor hopping, away from the strong-coupling limit. This model has nontrivial redistribution of spectral weight in S(k,ω) going from the noninteracting limit (U = 0) to strong coupling (U→∞), where it reduces to the Heisenberg quantum spin chain. We use the density matrix renormalization group to find S(k,ω), from which QFI is then calculated. We find that QFI grows with U. With realistic energy resolution it becomes capable of witnessing bipartite entanglement above U=2.5 (in units of the hopping), where it also changes slope. This point is also proximate to slope changes of the bandwidth W(U) and the half-chain von Neumann entanglement entropy. We compute G(r,t) by Fourier transforming S(k,ω). The results indicate a crossover in the short-time short-distance dynamics at low U characterized by ferromagnetic light-cone wavefronts, to a Heisenberg-type behavior at large U featuring antiferromagnetic light cones and spatially period-doubled antiferromagnetism. We find this crossover has largely been completed by U=3. Our results thus provide evidence that, in several aspects, the strong-coupling limit of the Hubbard chain is reached qualitatively already at a relatively modest interaction strength. We discuss experimental candidates for observing the G(r,t) dynamics found at low U.

1-dimensional systems↗

The Solar Wind

The first evidence of the solar wind was provided through observations of comet tail deflections by L. Biermann in 1951. A cometary ion tail is oriented along the difference between the cometary and solar wind velocities, whereas the dust tail is in the antisunward direction; the ion tail directions demonstrated the existence of an outflow of ionized gas from the Sun (the solar wind) and allowed estimates of solar wind speed. Spacecraft observations have now established that at 1 AU the solar wind has a typical ion number density of about 7 /cc and is composed by number of about 95% protons and 5% Helium, with other minor ions also present. The solar wind as observed at 1 AU in the ecliptic has speeds typically in the range 300-700 km/ s. At such speeds ions travel from the Sun to 1 AU in from 2.5 to 6 days. The impact of the solar wind on planets with magnetic fields (Earth, Jupiter, Saturn, Uranus, Neptune) causes phenomena such as magnetospheres, aurorae, and geomagnetic storms, whereas at objects lacking magnetospheres (Mars, Venus, comets), atmospheric neutrals undergo charge exchange and are picked up by the solar wind flow. The solar wind also shields the Earth from low energy cosmic rays, and is responsible for the existence of the anomalous component of the cosmic rays a low energy component that is created locally rather than in the galaxy. Presented here is a brief introduction to the solar wind and a description of some current topics of research. Solar wind properties vary a great deal due to the changing magnetic structure on the Sun.

Goldstein, B. E.↗

Correlated Spatio-temporal Evolution of Extreme-Ultraviolet Ribbons and Hard X-Rays in a Solar Flare

We analyze the structure and evolution of ribbons from the M7.3 SOL2014-04-18T13 flare using ultraviolet images from the Interface Region Imaging Spectrograph and the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA), magnetic data from the SDO/Helioseismic and Magnetic Imager, hard X-ray (HXR) images from the Reuven Ramaty High Energy Solar Spectroscopic Imager, and light curves from the Fermi/Gamma-ray Burst Monitor, in order to infer properties of coronal magnetic reconnection. As the event progresses, two flare ribbons spread away from the magnetic polarity inversion line. The width of the newly brightened front along the extension of the ribbon is highly intermittent in both space and time, presumably reflecting nonuniformities in the structure and/or dynamics of the flare current sheet. Furthermore, the ribbon width grows most rapidly in regions exhibiting concentrated nonthermal HXR emission, with sharp increases slightly preceding the HXR bursts. The light curve of the ultraviolet emission matches the HXR light curve at photon energies above 25 keV. In other regions the ribbon-width evolution and light curves do not temporally correlate with the HXR emission. This indicates that the production of nonthermal electrons is highly nonuniform within the flare current sheet. Our results suggest a strong connection between the production of nonthermal electrons and the locally enhanced perpendicular extent of flare ribbon fronts, which in turn reflects the inhomogeneous structure and/or reconnection dynamics of the current sheet. Despite this variability, the ribbon fronts remain nearly continuous, quasi-one-dimensional features. Thus, although the reconnecting coronal current sheets are highly structured, they remain quasi-two-dimensional and the magnetic energy release occurs systematically, rather than stochastically, through the volume of the reconnecting magnetic flux.

S. J. Naus↗

Hidden magnetism and split off flat bands in the insulator metal transition in VO 2

Transition metal d -electron oxides with an odd number of electrons per unit cell are expected to form metals with partially occupied energy bands, but exhibit in fact a range of behaviors, being either insulators, or metals, or having insulator-metal transitions. Traditional explanations involved predominantly electron-electron interactions in fixed structural symmetry. The present work focuses instead on the role of symmetry breaking local structural motifs. Viewing the previously observed V-V dimerization in VO 2 as a continuous knob, reveals in density functional calculations the splitting of an isolated flat band from the broad conduction band. This leads past a critical percent dimerization to the formation of the insulating phase while lowering the total energy. In VO 2 this transition is found to have a rather low energy barrier approaching the thermal energy at room temperature, suggesting energy-efficient switching in neuromorphic computing. Interestingly, sufficient V-V dimerization suppresses magnetism, leading to the nonmagnetic insulating state, whereas magnetism appears when dimerization is reduced, forming a metallic state. This study opens the way to design novel functional quantum materials with symmetry breaking-induced flat bands.

Chemistry↗

Local Inversion Symmetry Breaking and Thermodynamic Evidence for Ferrimagnetism in Fe 3 GaTe 2

The layered compound Fe 3 GaTe 2 is attracting attention due to its high Curie temperature, low dimensionality, and the presence of topological spin textures above room temperature, making Fe 3 GaTe 2 a good candidate for applications in spintronics. Here, in this study, we show, through transmission electron microscopy (TEM) techniques, that Fe 3 GaTe 2 single crystals break local inversion symmetry while maintaining global inversion symmetry according to X-ray diffraction. Coupled to the observation of Néel skyrmions via Lorentz-TEM, our structural analysis provides a convincing explanation for their presence in centrosymmetric materials. Magnetization measurements as a function of the temperature displays a sharp first-order thermodynamic phase-transition leading to a reduction in the magnetic moment. This implies that the ground state of Fe 3 GaTe 2 is globally ferrimagnetic and not a glassy magnetic state composed of ferrimagnetic, and ferromagnetic domains as previously claimed. Neutron diffraction studies indicate that the ferromagnetic to ferrimagnetic transition upon reducing the external magnetic field is associated with a change in the magnetic configuration/coupling between Fe1 and Fe2 moments. We observe a clear correlation between the hysteresis observed in both the skyrmion density and the magnetization of Fe 3 GaTe 2 . This indicates that its topological spin textures are affected by the development of ferrimagnetism upon cooling. Observation, via magnetic force microscopy, of magnetic bubbles at the magnetic phase boundary suggests skyrmions stabilized by the competition among magnetic phases and distinct exchange interactions. Our study provides an explanation for the observation of Néel skyrmions in centrosymmetric systems, while exposing a correlation between the distinct magnetic phases of Fe 3 GaTe 2 and topological spin textures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Persistent flat band splitting and strong selective band renormalization in a kagome magnet thin film

Magnetic kagome materials provide a fascinating playground for exploring the interplay of magnetism, correlation and topology. Many magnetic kagome systems have been reported including the binary Fe m X n (X = Sn, Ge; m:n = 3:1, 3:2, 1:1) family and the rare earth RMn 6 Sn 6 (R = rare earth) family, where their kagome flat bands are calculated to be near the Fermi level in the para magnetic phase. While partially filling a kagome flat band is predicted to give rise to a Stoner-type ferromagnetism, experimental visualization of the mag netic splitting across the ordering temperature has not been reported for any of these systems due to the high ordering temperatures, hence leaving the nature of magnetism in kagome magnets an open question. Here, we probe the electronic structure with angle-resolved photoemission spectroscopy in a kagome magnet thin film FeSn synthesized using molecular beam epitaxy. We identify the exchange-split kagome flat bands, whose splitting persists above the magnetic ordering temperature, indicative of a local moment picture. Such local moments in the presence of the topological flat band are consistent with the compact molecular orbitals predicted in theory. We further observe a large spin-orbital selective band renormalization in the Fe d xy + d x 2 -y 2 spin majority channel reminiscent of the orbital selective correlation effects in the iron based superconductors. Our discovery of the coexistence of local moments with topological flat bands in a kagome system echoes similar findings in magic-angle twisted bilayer graphene, and provides a basis for theoretical effort towards modeling correlation effects in magnetic flat band systems.

36 MATERIALS SCIENCE↗

Electron energy spectrum and magnetic interactions in high-T(sub c) superconductors

The character of magnetic interactions in La-Sr-Cu-O and Y-Ba-Cu-O systems is of primary importance for analysis of high-T(sub c) superconductivity in these compounds. Neutron diffraction experiments showed the antiferromagnetic ground state for nonsuperconducting La2CuO4 and YBa2Cu3O6 with the strongest antiferromagnetic superexchange being in the ab plane. The nonsuperconducting '1-2-3' system has two Neel temperatures T sub N1 and T sub N2. The first one corresponds to the ordering of Cu atoms in the CuO2 planes; T sub N2 reflects the antiferromagnetic ordering of magnetic moments in CuO chains relatively to the moments in the planes T sub N1 and T sub N2 depend strongly on the oxygen content. Researchers describe magnetic interactions in high-T superconductors based on the Linear Muffin-Tin Orbitals (LMTO) band structure calculations. Exchange interaction parameters can be defined from the effective Heisenberg hamiltonian. When the magnetic moments are not too large, as copper magnetic moments in superconducting oxides, J sub ij parameters can be defined through the non-local magnetic susceptibility of spin restricted solution for the crystal. The results of nonlocal magnetic susceptibility calculations and the values of exchange interaction parameters for La CuO and YBa2Cu3O7 systems are given in tabular form. Strong anisotropy of exchange interactions in the ab plane and along the c axis in La2CuO4 is obviously seen. The value of Neel temperature found agrees well with the experimental data available. In the planes of '1-2-3' system there are quite strong antiferromagnetic Cu-O and O-O interaction which appear due to holes in oxygen subbands. These results are in line with the magnetic model of oxygen holes pairing in high-T(sub c) superconductors.

Turshevski, S. A.↗

Electron energy spectrum and magnetic interactions in high-Tc superconductors

The character of magnetic interactions in La-Sr-Cu-O and Y-Ba-Cu-O systems is of primary importance for analysis of high-T(sub c) superconductivity in these compounds. Neutron diffraction experiments showed the antiferromagnetic ground state for nonsuperconducting La2CuO4 and YBa2Cu3O6 with the strongest antiferromagnetic superexchange being in the ab plane. The nonsuperconducting '1-2-3' system has two Neel temperatures T(sub N1) and T(sub N2). The first one corresponds to the ordering of Cu atoms in the CuO2 planes; T(sub N2) reflects the antiferromagnetic ordering of magnetic moments in CuO chains relatively to the moments in the planes T(sub N1) and T(sub N2) which depend strongly on the oxygen content. Researchers describe magnetic interactions in high-T superconductors based on the Linear Muffin-Tin Orbitals (LMTO) band structure calculations. Exchange interaction parameters can be defined from the effective Heisenberg Hamiltonian. When the magnetic moments are not too large, as copper magnetic moments in superconducting oxides, J(sub ij) parameters can be defined through the non-local magnetic susceptibility of spin restricted solution for the crystal. The results of nonlocal magnetic susceptibility calculations and the values of exchange interaction parameters for La CuO and YBa2Cu3O7 systems are given in tabular form. Strong anisotropy of exchange interactions in the ab plane and along the c axis in La2CuO4 is obviously seen. The value of Neel temperature found agrees well with the experimental data available. In the planes of '1-2-3' system there are quite strong antiferromagnetic Cu-O and O-O interaction which appear due to holes in oxygen subbands. These results are in line with the magnetic model of oxygen holes pairing in high-T(sub c) superconductors.

Turshevski, S. A.↗

Magnetic field induced structural changes in magnetite observed by resonant x-ray diffraction and Mössbauer spectroscopy

When a magnetic field is applied to a single crystal of magnetite at 124 K > T > 50 K , the monoclinic c M axis, which is the easy magnetization axis, switches to one of the $\langle$100$\rangle$ cubic directions, nearest to the direction of the magnetic field, and the phenomenon known as an axis switching (AS) occurs. Here, a global symmetry probe, resonant x-ray scattering, and a local probe, Mössbauer spectroscopy, are used to better understand the mechanism of axis switching. The behavior of three subsystems ordered below the Verwey transition temperature T V , i.e., lattice distortion, an orbital, and charge orderings, was observed via resonant x-ray scattering as a function of an external magnetic field. This was preceded by calculation of selected peak intensities using the fdmnes code. The Mössbauer spectroscopy studies confirmed that the magnetic field triggers electronic rearrangements and atomic displacements. The structure observed after the process of axis switching is very similar to the one obtained after cooling below T V with the magnetic field applied along one of the initial $\langle$100$\rangle$ cubic directions and distinct from the cooling in the absence of a magnetic field. From all the experimental observations of the phenomenon done so far, it is clear that AS starts from the fluctuations between octahedral iron orbitals that ultimately lead to the Verwey transition, but also to the higher-temperature trimeron dynamics. Therefore, further observation of the axis switching may be a key point to the understanding of a majority of strongly correlated electronic behavior in magnetite as well as in other transition metal oxides.

36 MATERIALS SCIENCE↗

Robustness of magnetocrystalline anisotropy and coercivity in Fe–Co–B

As a potential candidate for critical chemical element free permanent magnet, (Fe 0.7 Co 0.3 ) 2 B, shows promising intrinsic magnetic properties, including large magnetization, high Curie temperature and moderate magnetocrystalline anisotropy (MCA). Still, the coercivity that has been achieved is relatively low. To understand and improve coercivity, here we study the robustness of MCA related to the fluctuation of chemical composition and the structural distortion and its effect on coercivity in (Fe 0.7 Co 0.3 ) 2 B from first principles DFT (density functional theory) calculation and micromagnetic simulation. A fluctuation of cobalt content of 10%, or 1% isotropic lattice strain, or 2% tetragonal distortion reduces MCA energy up to 30%. By considering randomly distributed local MCA energy reduction up to 30%, the calculated coercivity of anisotropic bulk magnets reduced from 3.6 kOe to 2.2 kOe. Rational microstructure design, such as grain size refinement and development of strong crystal texture of MCA easy-axis (i.e., degree of alignment for (Fe 0.7 Co 0.3 ) 2 B grains), can enhance coercivity and mitigate the effect of local MCA reduction. In addition to acceptable intrinsic magnetic properties, the promising hard magnetic phase needs good MCA robustness to facilitate the development of practical magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗