Hard Superconductors Research Articles

A fresh class of superconducting and hard pentaborides

On the basis of the current theoretical understanding of boron-based hard superconductors under ambient conditions, numerous studies have been conducted with the aim of developing superconducting materials with favorable mechanical properties using boron-rich compounds. In this paper, first-principles calculations reveal the existence of an unprecedented family of tetragonal pentaborides MB5 (M = Na, K, Rb, Ca, Sr, Ba, Sc, and Y), comprising B20 cages and centered metal atoms acting as stabilizers and electron donors to the boron sublattice. These compounds exhibit both superconductivity and high hardness, with the maximum superconducting transition temperature Tc of 18.6 K being achieved in RbB5 and the peak Vickers hardness Hv of 35.1 GPa being achieved in KB5 at 1 atm. The combination of these properties is particularly evident in KB5, RbB5, and BaB5, with Tc values of ∼14.7, 18.6, and 16.3 K and Hv values of ∼35.1, 32.4, and 33.8 GPa, respectively. The results presented here reveal that pentaborides can provide a framework for exploring and designing novel superconducting materials with favorable hardness at achievable pressures and even under ambient conditions.

Fabrication of high-quality joints between Gd–Ba–Cu–O bulk superconductors

This work reports a technique for fabricating superconducting joints between GdBCO-Ag bulk superconductors, using YBCO-Ag as an intermediate joining material. The ability to provide reliable joints between multiple bulk superconductors overcomes many of the challenges of fabricating large superconductors or machining hard and brittle bulk superconductors into practical shapes. We report on nine single grains of GdBCO-Ag which have been joined with a YBCO-Ag intermediate. Samples were cut and joined in a variety of c-plane orientations to refine and understand the effect this had on the superconducting properties of jointed samples. The trapped field of pre-jointed and jointed bulk superconductors were compared; the maximum trapped field achieved was 59% of the pre-jointed sample. Further analysis showed that the critical temperature and critical current of the samples were degraded by the jointing process. Microstructural and chemical analysis showed that the jointing process facilitated diffusion of silver towards the joint and in some cases large pores were formed at the joint interface. These factors consequently inhibited current flow across the joint and thus reduced the maximum trapped field achievable when compared to the original unjointed sample.

Clathrate‐Like Alkali and Alkaline‐Earth Metal Borides: A New Family of Superconductors with Superior Hardness

AbstractConventional hard and superhard materials, such as diamond and cubic boron nitride, are attractive for fundamental material science and practical industrial application, but severely limited by their poor electrical conductivity. Therefore, it is desirable to design and fabricate novel materials for superior hardness and conductivity. Herein, a class of hard superconductors in alkali or alkaline‐earth metal (AM) borides, namely AMB7, constituted by a B23 cage with one centered metal atom (Li, Na, K, Mg, Ca, and Sr) is reported, which is the first stable clathrate structure in AMB systems. The theoretical calculations demonstrate that all these pressure‐stabilized clathrate structures can be quenched down to ambient conditions, which provides an essential prerequisite for experimental synthesis at moderate pressures. Among them, the highest hardness and maximum superconducting transition temperature (Tc) value are achieved in SrB7 (25.1 GPa) and MgB7 (29.3 K), respectively. Interestingly, the results show that KB7 simultaneously behaves high hardness (22.5 GPa) and superconducting transition temperature (Tc ≈26.2 K). This study opens up a new way to search and design novel superconductors with favorable mechanical properties under high pressure and high‐temperature conditions.

Magnetic field screening in hydrogen-rich high-temperature superconductors

In the last few years, the superconducting transition temperature, Tc, of hydrogen-rich compounds has increased dramatically, and is now approaching room temperature. However, the pressures at which these materials are stable exceed one million atmospheres and limit the number of available experimental studies. Superconductivity in hydrides has been primarily explored by electrical transport measurements, whereas magnetic properties, one of the most important characteristic of a superconductor, have not been satisfactory defined. Here, we develop SQUID magnetometry under extreme high-pressure conditions and report characteristic superconducting parameters for Im-3m-H3S and Fm-3m-LaH10—the representative members of two families of high-temperature superconducting hydrides. We determine a lower critical field Hc1 of ∼0.82 T and ∼0.55 T, and a London penetration depth λL of ∼20 nm and ∼30 nm in H3S and LaH10, respectively. The small values of λL indicate a high superfluid density in both hydrides. These compounds have the values of the Ginzburg-Landau parameter κ ∼12–20 and belong to the group of “moderate” type II superconductors, rather than being hard superconductors as would be intuitively expected from their high Tcs.

Моделирование особенностей магнитных свойств осесимметричных гранул жестких сверхпроводников II рода

Based on the equations of electrodynamics and the concept of a critical state for hard superconductors of the 2nd kind, numerical simulation of the magnetic properties of axisymmetric superconducting samples, in particular, granules, is performed for a number of models of the dependence of the critical current density on the magnetic field induction. The magnetic moment loops are calculated directly by integrating the integral equation for the current density over time. The phenomena of the peak effect and the asymmetry of the magnetization hysteresis loop are also considered using the indicated equation. Various versions of the functions used in the literature were used as peak functions. In addition to the hysteresis loop of the magnetic moment, the magnetic field induction at the center of axisymmetric samples, and the total penetration field, the profiles of the critical current density Jc(B) and the equilibrium magnetic moment for spherical granules were obtained. The method used for calculating the magnetic moment of superconductors makes it possible to take into account the equilibrium and nonequilibrium regions of the magnetization of the samples independently.

Simulation of the features of the magnetic properties of axisummetric granules of hard type II superconductors

Based on the equations of electrodynamics and the concept of a critical state for hard superconductors of the 2nd kind, numerical simulation of the magnetic properties of axisymmetric superconducting samples, in particular, granules, is performed for a number of models of the dependence of the critical current density on the magnetic field induction. The magnetic moment loops are calculated directly by integrating the integral equation for the current density over time. The phenomena of the peak effect and the asymmetry of the magnetization hysteresis loop are also considered using the indicated equation. Various versions of the functions used in the literature were used as peak functions. In addition to the hysteresis loop of the magnetic moment, the magnetic field induction at the center of axisymmetric samples, and the total penetration field, the profiles of the critical current density Jc(B) and the equilibrium magnetic moment for spherical granules were obtained. The method used for calculating the magnetic moment of superconductors makes it possible to take into account the equilibrium and nonequilibrium regions of the magnetization of the samples independently Keywords: magnetic moment, axisymmetric granules, type II superconductor, critical state, peak effect, equilibrium magnetic moment.

A novel hard superconductor obtained in di-molybdenum carbide (Mo2C) with Mo–C octahedral structure

Hard superconducting materials are of particular interest for electromechanical applications under high strain and stress. In this work, Mo2C was synthesized using high temperature and high pressure (HPHT) methods. In view of characterizations, Mo2C transforms into a superconductivity state below the temperature of 7.5 K and the asymptotic Vickers hardness is about 13.4 GPa. Its hardness is compatible with that of commonly used hard alloys, which is a potential hard superconducting material. Based on the results of our first-principle calculations, superconductivity and hardness come from the high density of states at the Fermi energy level and high hardness originates from the strong hybridization between Mo-4d orbitals and C-2p orbitals. By introducing the light element C atoms into the transition metal Mo to form a ‘covalent metal’ structure, the hardness and mechanical properties of the superconducting material can be improved which gives a way to design hard superconducting materials.

Mathematical modeling of the magnetic properties of axisymmetric hard superconductors of the second kind in the Kim model

Authors perform mathematical modeling of magnetic properties, such as current distribution, intrinsic magnetic field and magnetization of a number of axisymmetric superconductors of the second kind, for example, of a sphere with the dependence of the critical current density on the local magnetic field in the Kim model. The simulation is based on equation that is integral with respect to coordinate and differential with respect to time. The equation describes time evolution of the critical current density and is solved numerically for a uniformly varying external magnetic field. The shape of the sample is set using a distorted rectangular irregular mesh with compaction to the edges of the sample. While solving the equation of current motion, the total magnetic field iscalculated at the points of the superconductor to calculate the value of the critical current density. In the article, the obtained solutions are used to visualize the current distribution in the volume of a superconductor and to construct magnetization hysteresis loops. Also, thanks to the calculations of the magnetic field in the center of the sample, the dependencies of the total penetration field for samples with different aspect ratios are obtained.

A Critical Current Measurement Method for Strip Hard Superconductors Utilizing Pulsed Current

Long wire critical current (Ic) characterization is important for fabrication of superconducting magnets. Many inductive and transport Ic measurement methods have been developed for km scale rare earth cuprate (REBCO) based Coated conductors (CC), which is a very promising high temperature superconducting material for magnet applications. As a direct indication of the current carrying capability, transport measurement is favored by most tape users. However, the traditional transport measurement technique has its limitations for long tape characterization. The speed of transport measurement is usually not high enough for km scale tapes, and direct current (DC) measurement also has a certain risk of tape damage due to the Joule heating at current contacts, especially for some special CCs with higher contact resistance, e.g., stainless-steel encapsulated CCs. For long wire measurements, the risk of tape damage is generally higher than acceptable. A pulse measurement method based on induction principle is proposed and tested in this work, the feasibility of this method is verified by experiments. Where pulsed current is used to reduce Joule heating thus reduce the risk of tape damage. Moreover, the speed of measurement can also be improved by the technique compared with DC measurements.

Mathematical modeling of the magnetic properties of spheroids of hard second kind superconductors in the Bean model

Authors have modelled magnetic field in hard II-type superconductor bodies with cylindric symmetry by means of Bean model. Using the equations of electrodynamics and the Poisson equation for the vector potential, the Fredholm equation of the first kind is derived for the screening supercurrent density. By introducing the explicit form of the current-voltage characteristic and the law of electromagnetic induction, the equation for the supercurrent density is reduced to an integral equation of the 2nd kind, which is solved numerically in matrix form on a non-uniform grid with compaction to the edges of the sample. Density distribution of the screened superconductive current, sample-self magnetic field and hysteresis loops of magnetization in the cases of cylinders and spheroids are obtained.

Flux-Pinned Dynamics Model Parameterization and Sensitivity Study

Flux-pinned interfaces maintain a passively stable equilibrium between two spacecraft in close proximity. Although flux-pinning physics has been studied from a materials science perspective and at the system level, the sensitivities and implications of system-level designs on the dynamics need to be better understood, especially in interfaces with multiple magnets and superconductors. These interfaces have highly nonlinear coupled dynamics that are influenced by physical parameters, including strength of magnetic-field sources, field-cooled position, and superconductor geometry. Kordyuk’s frozen-image model (“Magnetic Levitation for Hard Superconductors,” Journal of Applied Physics, Vol. 83, No. 1, Jan. 1998, pp. 610–612) successfully approximates the characteristics of flux-pinning dynamics, but could provide a more precise state prediction with the addition of these physical parameter refinements. This paper addresses that gap by offering parametric terms to improve the dynamics model, which may better simulate the behavior of a multiple-magnet-and-multiple-superconductor interface. The sensitivity of the general flux-pinned dynamics model is studied by varying the physical parameters and simulating the system-level dynamics. This work represents a critical step in the development of a model suited to spacecraft performance verification.

Electron-phonon coupling, superconductivity, and nontrivial band topology in NbN polytypes

In this paper, we investigate the electronic band structure, lattice dynamics and electron-phonon interaction in $\delta$-NbN, $\varepsilon$-NbN and WC-NbN by performing systematic ab initio calculations based on DFT-GGA. The calculated electronic band structures show that all three polytypes are metallic with the Nb $d$-orbital dominated energy bands near the Fermi level ($E_F$). The calculated phonon dispersion relations of $\delta$-NbN are in good agreement with neutron scattering experiments. The electron-phonon coupling ($\lambda$) in $\delta$-NbN ($\lambda=0.98$) is much stronger than in $\varepsilon$-NbN ($\lambda=0.16$) and WC-NbN ($\lambda=0.11$). This results in a much higher superconducting transition temperature ($T_c =18.2$ K) than in $\varepsilon$-NbN and WC-NbN ($T_c \le 1.0$ K). The stronger $\lambda$ and higher $T_c$ in $\delta$-NbN are attributed to its large density of states at $E_F$ and small Debye temperature. The calculated $T_c$ of $\delta$-NbN is in good agreement with the experimental values. However, the predicted $T_c$ of $\varepsilon$-NbN is much smaller than the recent experiment (11.6 K) but agrees well with the earlier experiment. Finally, the calculated relativistic band structures reveal that all three NbN polytypes are topological metals. Specifically, $\varepsilon$-NbN and $\delta$-NbN are, respectively, type-I and type-II Dirac metals, while WC-NbN is an emergent topological metal that has rare triply degenerate nodes. All these results indicate that all the three NbN polytypes should be hard superconductors with nontrivial band topology that would provide valuable opportunities for studying fascinating phenomena arising from the interplay of band topology and superconductivity.

Bulk superconducting tube subjected to the stray magnetic field of a solenoid

Hard type-II hollow superconductors are well suited for low frequency magnetic shielding. The properties and performances of superconducting magnetic shields subjected to homogeneous magnetic fields have been extensively discussed in the literature. In the present work, we investigate the magnetic shielding and the penetration of magnetic flux in a bulk high temperature superconducting tube subjected to the inhomogeneous fringe field of a solenoidal coil. Thanks to a bespoke microdisplacement measurement system, we measure the magnetic field distribution around the tube. We develop a full 3D finite element model based on an H formulation to understand the flux penetration mechanisms and predict the shape of the current loops. Using constitutive law parameters obtained from previous independent experiments, our model is found to be in excellent agreement with the measurements. We discuss how to assess the degree of inhomogeneity of the magnetic field and show that, in our case study, the field can be treated as the magnetic field of an equivalent magnetic dipole. We also show that some features of the flux penetration in inhomogeneous field can be also observed when the tube is subjected to an oblique homogeneous magnetic field, which offers a better understanding of the shielding current density distribution inside the shield. Finally, we discuss the magnetic field concentration occurring around the shield for different magnetic field configurations. In particular, we show that the extremities of the tube on the side not facing the magnetic field source experience the highest flux concentration.

3-D New Calculation Principle of Levitation Force Between Permanent Magnet and Hard Type-II Superconductor Using Integral Approach

A new contribution is given for the calculation of interaction forces between the permanent magnet (PM) and a hard type-II superconductor (SC) used as a classical levitation system. The forces and also mutual inductances are developed via Green’s functions using an Amperian model, assuming a cuboidal thin coil for PM and a superposition of closed loops of rectangular cross section of the SC. In the superconductor, the critical current ( $J_{c})$ is known, but the variable penetration thickness of $J_{c}$ is given from external magnetic fields by Bean’s critical-state models. All the analytical results are obtained with a dynamic representation of all penetration thicknesses of $J_{c}$ depending on applied external magnetic field variations. The most important parts are the original mathematical process of considering current penetration in superconductors and the new analytical development of vertical forces between PM and SC, realized after several analytical integral calculations. The results have been evaluated for vertical displacements of a PM above the SC, proving the accuracy of our analytical model compared with those realized by Flux3D finite-element method software.

Anti-Lenz supercurrents in superconducting spin valves

Here, we present a study on Si(111)/\-Ta($150$\AA )/\-IrMn($150$\AA )/\-NiFe($50$\AA )/\-Nb($x$)/\-NiFe($50$\AA )/\-Ta($50$\AA ) and Si(111)/\-Ta($150$\AA )/\-NiFe($50$\AA )/\-Nb($x$)/\-NiFe($50$\AA )/\-IrMn($150$\AA )/\-Ta($50$\AA ) spin-valves with $x=100$ to $500$\AA . For both sample families, above a specific critical thickness of the Nb-layer and below $T_c$, the superconducting Nb-layer contributes strongly to the magnetization. These systems show an anomalous hysteresis loop in the magnetization of the superconducting layer; the hysteresis loop is similar to what is generally expected from hard superconductors and many superconductor/ferromagnet hybrid systems, but the direction of the hysteresis loop is inverted, compared to what is generally observed (paramagnetic for up sweeping fields and diamagnetic for down sweeping fields). This means that the respective samples exhibit a magnetization, which is contrary to what should be expected from the Lenz' rule.

Transformation of the critical state in hard superconductors resulting from thermomagnetic avalanches

The results of experimental studies of magnetic flux dynamics in finite-size superconductors, obtained using integral and local measurements methods, are presented. Local methods were aimed at clarifying the role of the demagnetizing factor in the dynamic formation of a complex magnetic structure of the critical state of hard superconductors. To understand the reasons for drastic transformation of the magnetic induction, we further analyzed the literature data on the visualization of flux dynamics in the presence of avalanches, obtained by magneto-optical methods. New features in the behavior of the magnetic flux during and after an avalanche were revealed and characterized: two stages in the formation of the magnetic induction distribution inside the avalanche region were established—homogeneous and heterogeneous filling with magnetic flux; the mechanism of inversion of the induction profile; velocity oscillations in the propagating magnetic flux front; transformation of the critical state band near the edge of the sample; and the role of the thermal effects and demagnetizing factor in the dissipative flux dynamics. The generalized information allowed us to present, within the framework of the Bean concept, a model of the transformation of the patterns of magnetic induction in the critical state and superconducting currents in a finite superconductor occurring as a result of flux avalanches in two different regimes—shielding and trapping of magnetic flux.

Discovery of Superconductivity in Hard Hexagonal ε-NbN.

Since the discovery of superconductivity in boron-doped diamond with a critical temperature (TC) near 4 K, great interest has been attracted in hard superconductors such as transition-metal nitrides and carbides. Here we report the new discovery of superconductivity in polycrystalline hexagonal ε-NbN synthesized at high pressure and high temperature. Direct magnetization and electrical resistivity measurements demonstrate that the superconductivity in bulk polycrystalline hexagonal ε-NbN is below ∼11.6 K, which is significantly higher than that for boron-doped diamond. The nature of superconductivity in hexagonal ε-NbN and the physical mechanism for the relatively lower TC have been addressed by the weaker bonding in the Nb-N network, the co-planarity of Nb-N layer as well as its relatively weaker electron-phonon coupling, as compared with the cubic δ-NbN counterpart. Moreover, the newly discovered ε-NbN superconductor remains stable at pressures up to ∼20 GPa and is significantly harder than cubic δ-NbN; it is as hard as sapphire, ultra-incompressible and has a high shear rigidity of 201 GPa to rival hard/superhard material γ-B (∼227 GPa). This exploration opens a new class of highly desirable materials combining the outstanding mechanical/elastic properties with superconductivity, which may be particularly attractive for its technological and engineering applications in extreme environments.

Corrections to "Macroscopic Modeling of Magnetization and Levitation of Hard Type-II Superconductors: The Critical-State Model" [Feb 13 Article ID 8201023

The authors of the above paper (ibid., vol. 23, no. 1, Feb. 2013, Art. ID 8201023) would like to correct Table I with the following table.

Movement of a vortex filament near oscillating pinning centers in the hard superconductor

A problem on a vortex behavior near oscillating pinning centers in the type III superconductors (SCs) is considered. The movement of a vortex filament is described by the parabolic free boundary problem, where an a priori unknown free boundary is the set of points, at which a transition from superconducting to normal state and vice versa occurs. A number of statements on the qualitative properties of a phase boundary superconductor - nonsuperconductor are considered.

Modeling the Effect of Thermal Field in Formation of Magnetic Flux Avalanches in Hard Superconductors

Magnetothermal instabilities are one of the uncharacteristic phenomena of interest in conventional type-II as well as in high-T c superconductors. Historically, some authors undertake to analyze the nature and origin of the magnetothermal instabilities of the critical state and flux jumps phenomena in superconductors in the light of theoretical and experimental results (Wipf, Phys. Rev. 161:404, 1967; Wipf, Cryogenics 31:936, 1992; Lee at al., J. Appl. Phys. 107:013902, 2010) [1, 2]. In contrast to previous reported works which had studied the magnetic flux avalanches in hard superconductors postulating an instability criterion, in this paper, we report the development of a theoretical model for describing the magnetization curves of type-II superconductors considering the fact that the jumps should arise naturally, i.e., without the need to impose a priori conditions of instability. The model developed is applied to make numerical calculations in order to get magnetization curves of MgB2 as well as to calculate and analyze the impact of changes in the thermal field and functions that describe the critical current. We investigate the effect of initial magnetic state on generation of magnetic flux avalanches. The initial state determines the evolution of the magnetization curves and their jumps. The results obtained with the application of this model allow us to reproduce the experimental conditions with greater accuracy than that achieved with models based on unstable conditions; further, the model predicts the impact of initial nonzero fields in the formation of avalanches.