Properties of the flux line lattice in hysteretic type II superconductors. I. Neutron diffraction experiments

A detailed study of neutron rocking curves on flux line lattices was made in single-crystalline hysteretic type II superconductors with Ginzburg-Landau parameters between 1.0 and 2.5. Information was obtained about the symmetry and the quality of the flux line lattice as a function of crystal orientation, sample purity, and magnetic field. The flux line lattice is always observed to form a single crystal. The width of the rocking curves, which is a measure of the misorientation of flux line crystallites in the plane perpendicular to the external field, is found to decrease strongly with increasing field along the initial magnetization curve, and to be much smaller upon decreasing the field from aboveH _c2 . This width varied between 8 and 1.5°. The minimum size of a coherently scattering flux line crystallite was estimated to be about 2–3 µm. Along the initial magnetization nearH _c1 the flux is found to form flux line bundles of constant lattice spacing. Although large flux density gradients have been observed earlier with field probes nearH _c1 ^1,2 , the lattice parameter measured with neutrons remained constant in this field range.     

Vortex Molecules in Thin Films of Layered Superconductors

Both the equilibrium and transport properties of the vortex matter are essentially affected by the behavior of the intervortex interaction potential. In isotropic bulk superconductors this potential is well known to be repulsive and is screened at intervortex distances R greater than the London penetration depth λ. As a result, in perfect crystals quantized Abrikosov vortices form a triangular lattice. In thin films of anisotropic superconductors this standard interaction potential behavior appears to be strongly modified because of the interplay between the long-ranged repulsion predicted in the pioneering work by J. Pearl and the attraction caused by the tilt of the vortex lines with respect to the anisotropy axes. This interplay results in a new type of vortex arrangement formed by finite-size vortex chains, i.e., vortex molecules. Tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or/and can arrange into multiquanta flux lattice. The magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number N of flux quanta. Thus, the increase in the field tilting (or varying temperature) should be accompanied by the series of the phase transitions between the vortex lattices with different N. A similar scenario should be realized in strongly anisotropic BSCCO high-T _c superconductors where in tilted field a crossing lattice of Abrikosov vortices (the stacks of pancakes in this case) and Josephson vortices appears. This crossing leads to the zigzag deformation of the pancakes stacks which is responsible for the attraction interaction competing with the long-ranged Pearl’s repulsion.     

Magnetization curves and Bean's model in high-T c superconductors

High-T _c superconductors have critical currents that decay sharply with increasing magnetic field. We solve Bean's model forJ _c decaying exponentially withH and obtain qualitative agreement with existing magnetization data. We show thatH _c1 cannot be obtained from the linear part of the magnetization curve; it can only be inferred from a low-field anomaly in the hysteresis curve. Presently quoted values ofH _c1 ,based on the linear part of the magnetization curve, are gross overestimates.     

A study of the flux density distribution in type II superconductors rotating in a magnetic field

Torque measurements on type II superconductors rotating in a magnetic field H ₀ directed perpendicular to the rotational axis can be used to determine pinning and viscous friction of vortices. The exact analysis of these measurements requires a knowledge of the vortex configuration in the rotating specimen, which is studied for the case of a circular cylinder of infinite length. A method is developed to calculate numerically the vortex configuration if the dependence of critical current density J _c and flux flow conductivity _f on flux density B and if the equilibrium magnetization curve are known. An inverse procedure also allows us to determine these material parameters from the measured torque and magnetization of the rotating sample. Results obtained by applying this procedure to different materials are reported.     

Application of a new formulation of Gor'kov's theory to clean type II superconductors

The explicit free energy functional derived from Gor'kov's theory in a previous paper is shown to reduce, in special cases, to the free energies of the Meissner state, the mixed state, the nonlocal theory, and of the Ginzburg-Landau theory. For superconductors with small magnetization the free energy for arbitrary structure of the flux line lattice is given, for the first time, for the entire temperature range. For isotropic materials the triangular lattice turns out to be the stable one. The shear modulusc ₆₆of the triangular flux line lattice nearH _c2is obtained for arbitrary temperature.     

Vibrating superconductors

This review is concerned with effects in the energy dissipation and elastic modulus of superconductors vibrating in a magnetic field. The physics of superconducting vibrating reeds and reeds made of superconducting suspensions is thoroughly described as well as the main features observed in other oscillators applied to flux pinning studies. It is argued that among the diversity of methods to study superconducting and pinning properties as a function of magnetic field and temperature, the vibrating reed technique is one of the most sensitive due to the accurate measurement of frequency and dissipation with feasible magnetometry applications. Results of the elastic coupling between the flux line lattice and the atomic lattice in high- and low-T _c superconductors obtained with the vibrating reed are summarized as well as the behavior of vibrating type II superconductors near their lower critical field. Results from mechanical measurements in high-temperature superconductors are reviewed, which support the model of thermally activated depinning and vortex diffusion.     

Order parameter and magnetic field of the distorted vortex lattice and their application to flux pinning in type II superconductors. I. Parallel flux lines

A program for the rigorous calculation of the volume pinning force exerted by-imperfections on the flux line lattice in type II superconductors is outlined. As one step of this program, the order parameter, local magnetic field, supervelocity, and elastic energy of the distorted lattice of still parallel flux lines are calculated from the Ginzburg-Landau theory. These general solutions provide a transformation of the Ginzburg-Landau free energy functional of an imperfect material into a mere function of the flux line positions, and thus allow a definition of elastic and pinning force densities which for the first time apply also to large inductions. First, exact solutions for small strains and for fields close toH _c2 are derived. Then, approximate solutions are presented applying to larger strains and to arbitrary inductions. The forces on each flux line exerted by a small needle-shaped inclusion parallel to the flux lines are calculated.     

Vibrating reed study of the flux line dissipation of ceramic and single-crystal (Ba,K)BiO3

Vibrating reed (VR) and dc and ac magnetic susceptibility measurements were performed on a nominal single crystal of composition (Ba_0.64K_0.36)BiO₃ in an applied magnetic fieldH. Field-cooling and field-sweep data revealed multiple peaks in the reed dissipation 1/Q located below the superconducting transition temperatureT _c (≈29.6 K forH=0). A shoulder or onset (with increasingT) of dissipation appears forT≤18 K, which may be a signature of a flux lattice melting transition. VR data for dense ceramic samples of composition (Ba_0.625K_0.375)BiO₃ (T _c=28.6K) exhibit a relatively narrow and smooth peak in 1/Q that corresponds well to a broad, intermediate-temperature peak in the crystal data. Resistivity experiments demonstrate that the single ceramic peak occurs well below the temperature at which the electrical resistanceR≈0, suggesting that the higher-temperature crystalline peaks are positioned close to the upper critical field line and may be strongly dependent upon grain size or surface properties. Both ac and dc susceptibility data show no clear evidence for multiple phases or gross compositional inhomogeneities in the crystalline sample. Our results demonstrate that the VR technique is an extremely sensitive method to probe sample inhomogeneities and their role in flux pinning phenomena.     

Some Remarks on Vortex Matter in High-T c Superconductors

We show that some experimentally observed features of vortex matter in high-T _c superconductors may be interpreted in simpler ways than it is usually done. In particular, we consider magnetic flux creep at low temperatures as well as the irreversibility line in the H–T phase diagram. We also discuss a new approach to the analysis of the equilibrium magnetization in the mixed state of type-II superconductors and we suggest an alternative configuration for the mixed state in magnetic fields close to the upper critical field.     

Surface magnetism of type II superconductors

The magnetization of a type II superconductor in the mixed state is a sum of two contributions, one from an array of flux lines and the other from shielding currents flowing along the surface. The former can be evaluated with the help of results of neutron diffraction experiments, using an extrapolation procedure. The observed magnetization curve thus enables us to estimate the surface contribution. This process is applied to the data on niobium obtained by Schelten, Ullmaier, and Lippmann. It is found that at low temperatures (T/T _c =0.161 and 0.457), the surface contribution may not be reduced atH _c2 as much as theories predict. At higher temperatures (T/T _c =0.717 and 0.891), it is likely to be paramagnetic in a region rather close toH _c1 . Attractive interaction between flux lines is suggested to be a mechanism of this anomaly. However, more experimental and theoretical work is needed to establish these findings to help us understand the surface magnetism of type II superconductors.     

NMR Lineshape in Anisotropic Superconductors with Nonregular Vortex Lattice

The nuclear magnetic resonance line shapes within a primitive cell of the vortex lattice of the type II anisotropic superconductors in a case when a vortex is displaced on small distance a from a regular position in a primitive cell are constructed. The results of the numerical calculations show that displacement of the flux line lattice essentially changes the NMR lineshape. The derivative of the power of the absorption energy with respect to the magnetic field is calculated. It allows to obtain more detailed information about the real vortex lattice of a superconductor.     

Magnetization curves and Bean''s model in high-Tcsuperconductors

High-T _c superconductors have critical currents that decay sharply with increasing magnetic field. We solve Bean's model forJ _c decaying exponentially withH and obtain qualitative agreement with existing magnetization data. We show thatH _c1 cannot be obtained from the linear part of the magnetization curve; it can only be inferred from a low-field anomaly in the hysteresis curve. Presently quoted values ofH _c1 ,based on the linear part of the magnetization curve, are gross overestimates.     

Theory of superconductivity. 3. 2D conduction bands for high Tc. Bose-Einstein condensation transition of the third order

A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V ₁₁,V ₂₂,V ₁₂) among and between “electron” (1) and “hole” (2) Cooper pairs are differentiated, and identifying “electrons” (“holes”) with positive (negative) masses as those Bloch electrons moving on the empty (filled) side of the Fermi surface. The supercondensate is shown to be composed of equal numbers of “electron” and “hole” ground (zero-momentum) Cooper pairs with charges ±2e and different masses. This picture of a neutral supercondensate naturally explains the London rigidity and the meta-stability of the supercurrent ring. It is proposed that for a compound conductor the supercondensate is formed between “electron” and “hole” Fermi energy sheets with the aid of optical phonons having momenta greater than the minimum distance (momentum) between the two sheets. The proposed model can account for the relatively short coherence lengthsξ observed for the compound superconductors including intermetallic compound, organic, and cuprous superconductors. In particular, the model can explain why these compounds are type II superconductors in contrast with type I elemental superconductors whose condensate is mediated by acoustic phonons. A cuprous superconductor has 2D conduction bands due to its layered perovskite lattice structure. Excited (nonzero momentum) Cooper pairs (bound by the exchange of optical phonons) aboveT _c are shown to move like free bosons with the energy-momentum relation?=1/2v_Fq. They undergo a Bose-Einstein condensation atT _c = 0.977?v _F k _b ^?1 n ^1/2, wheren is the number density of the Cooper pairs. The relatively high value ofT _c (～100 K) arises from the fact that the densityn is high:n ^1/2～ξ^?1 ～10⁷ cm^?1. The phase transition is of the third order, and the heat capacity has a reversed lambda (λ)-like peak atT _c .     

Fishtail magnetization in single crystal Tl2Ba2CuO6

We report extensive magnetization measurements on single crystals of Tl₂Ba₂CuO₆ superconductors. The fishtail magnetization is found to disappear above a characteristic temperature (60 K), which corresponds to a crossover temperature in the temperature dependence of the irreversibility line. Since the low temperature irreversibility field can be modeled by a Josephson coupled layered system, we propose that the fishtail magnetization in the Tl₂Ba₂CuO₆ system is due to dimensional crossover.     

Electronic structure and possible martensitic transformation in Ni2FeIn alloy

The electronic structure and magnetic properties of Heusler alloys (Ni₂FeIn) have been studied by first principle calculations. The possible tetragonal martensitic transformation has been predicted and the structure optimization was made on cubic austenitic Ni₂FeIn in Cu₂MnAl type. The equilibrium lattice constant of austenitic Ni₂FeIn is 6.03 Å. In tetragonal phase, the global energy minimum occurs at c/a = 1.29. The corresponding equilibrium lattice constants for martensite Ni₂FeIn are a = b = 5.5393 Å and c = 7.1457 Å, respectively. In the austenitic phase, E _F is located at the peak in the minority DOS for c/a = 0.96 to 1.20, but in the martensitic phase, E _F moves to the bottom of the valley in the minority DOS, reducing the value of N(E _F ) effectively. Both austenitic and martensitic phases are ferromagnetic and the Ni and Fe partial moments contribute mainly to the total moments. Therefore, the martensitic transformation behavior in Ni₂FeIn is predicted.     

Scaling of the equilibrium magnetization in the mixed state of type-II superconductors

We discuss the analysis of mixed-state magnetization data of type-II superconductors using a recently developed scaling procedure. It is based on the fact that, if the Ginzburg-Landau parameter κ does not depend on temperature, the magnetic susceptibility χ(H,T) is a universal function of H/H_c2(T), leading to a simple relation between magnetizations at different temperatures. Although this scaling procedure does not provide absolute values of the upper critical field H_c2(T), its temperature variation can be established rather accurately. This provides an opportunity to validate theoretical models that are usually employed for the evaluation of H_c2(T) from equilibrium magnetization data. In the second part of the paper we apply this scaling procedure for a discussion of the notorious first order phase transition in the mixed state of high-T_c superconductors. Our analysis, based on experimental magnetization data available in the literature, shows that the shift of the magnetization accross the transition may adopt either sign, depending on the particular chosen sample. We argue that this observation is inconsistent with the interpretation that this transition always represents the melting transition of the vortex lattice.     

Effect of Pre-magnetization on Quasi-static Force Characteristics in a Space Superconducting Interface Structure Adopting High T c Superconductors

Flux-pinned interaction between high T _c superconductors (HTSs) and an applied magnetic field provides a new, no-contact interface approach that can be used in docking and assembling process of space module systems. Unlike operations on the Earth, the magnetization of the HTS happens in orbit which differs from the traditional field cooling (FC) magnetization, and the additional field has to be used to magnetize the HTS in advance and make it produce a self-stable force in the interacting process with the interfacing magnet. This paper presents a type of superconducting interface structure configuration consisting of bulk HTSs, actuation electromagnets and interfacing magnets, and discusses the effects of different magnetization conditions on the quasi-static force interaction between the HTS and the interfacing magnet. Primary experiments show that the HTS after pre-magnetization can show self-stable force behavior, which often happens in the traditional FC magnetization, and the self-stable force is further enhanced with the increase of the pre-magnetizing current. Multi-pulse field magnetization after the pre-magnetization is also applied to raise the trapped field strength (B _T ) of the superconductor. The results show that B _T is added with the increasing number of the pulsed field, and the corresponding self-stable force properties are also improved. Therefore, the pre-magnetization combined with the pulsed field magnetization can enhance the flux trapping in the HTS and bring more stable force for the superconducting interface structure.     

Normalized Free Energy and Normalized Entropy Applied to Some Lambda (λ) Transitions

The λ-anomaly occurs for a system that can undergo a boson – fermion thermodynamic equilibrium. It is shown that a λ-transition figure can be interpreted in terms of the normalized Gibbs–Helmholtz equation, the Maxwell–Boltzmann energy distribution function, and properties of the statistics of the relevant species. There are three variations of a “λ-transition” curve. These are: (A) the classical λ curve, (B) a saw-tooth line shape that is characteristic of the Bardeen–Cooper–Schrieffer theory of superconductivity, and (C) a single line δ type figure. The low temperature He-4 transition, and Type II superconductor transitions are typical of the line shape A. Type I superconductors typically have type B line shapes. The line shapes for variations A and C result from classical thermodynamic equilibria. The type B line shape occurs in systems that do not have a classical thermodynamic equilibrium at the superconducting transition. Analysis of type B line shapes provides interesting concepts and data for some low- and high-temperature superconductors. Several applications and physical property consequences of these line shapes are discussed.