Flux Creep Regime Research Articles

The process of magnetic flux penetration into superconductors

Abstract In the present paper the magnetic flux penetration dynamics of type-II superconductors in the flux creep regime is studied by analytically solving the nonlinear diffusion equation for the magnetic flux induction, assuming that an applied field parallel to the surface of the sample and using a power-law dependence of the differential resistivity on the magnetic field induction. An exact solution of nonlinear diffusion equation for the magnetic induction B(r, t) is obtained by using a well-known self-similar technique. We study the problem in the framework of a macroscopic approach, in which all length scales are larger than the flux-line spacing; thus, the superconductor is considered as a uniform medium.

Transport through a network of two-dimensional NbC superconducting crystals connected via weak links

Recent progresses in the growth and fabrication techniques for preparing crystalline two-dimensional (2D) superconductors have stimulated intense interest in the studies of the electronic properties of these systems. Here we investigate the superconducting transport properties based on chemical vapor deposition-grown thin NbC crystals consisting of network structures. The 2D character of the superconductivity in individual NbC crystals is revealed by examining the angular dependence of magnetotransport measurements. At low temperatures, the samples show nonmonotonic double-step superconducting transitions as a function of temperature and magnetic field. We demonstrate that the observed transport characteristics can be understood in terms of coupled Josephson junctions forming between isolated NbC crystals, including the effects of Josephson and quasiparticle tunneling. In particular, detailed analysis of the magnetic field-driven transition suggests the existence of quantum flux-creep regime at low temperatures and small magnetic fields in such thin NbC superconducting crystals. Our work underlines the importance of the morphology on the transport properties of 2D superconducting crystals, providing a comprehensive understanding of crystalline 2D superconductors.

Overcritical Current Resistivity of YBCO-Coated Conductors Through Combination of PCM and Finite-Element Analysis

Understanding the electro-thermal behavior of high-temperature superconductor (HTS) materials is a critical aspect for designing efficient and reliable applications. In order to optimize cost and performance, one needs to understand the role played by the various layers of an HTS tape during a quench. On one hand, the electrical and thermal properties of the materials used in the manufacturing of those tapes (e.g., alloy substrate, silver, and copper) are well known. Knowledge of the functional dependence of the superconductor's resistivity ρ(J, T ) above the critical current in 2G HTS CCs is very limited. In the flux creep or normal state regime, the resistivity can be approximated by empirical laws. In the flux-flow regime, it is difficult to extract ρ(J, T ) due to the presence of Joule heating. In this contribution, using finite-element analysis, we present a method to retrieve the overcritical current resistivity, by estimating the amount of current, temperature, and heat present in the various layers.

Transport properties and pinning analysis for Co-doped BaFe2As2 thin films on metal tapes

We report on the transport properties and pinning analysis of BaFe1.84Co0.16As2 (Ba122:Co) thin films on metal tapes by pulsed laser deposition. The thin films exhibit a large in-plane misorientation of 5.6°, close to that of the buffer layer SrTiO3 (5.9°). Activation energy U0(H) analysis reveals a power law relationship with field, having three different exponents at different field regions, indicative of variation from single-vortex pinning to a collective flux creep regime. The Ba122:Co coated conductors present = 20.2 K and = 19.0 K along with a self-field Jc of 1.14 MA cm−2 and an in-field Jc as high as 0.98 and 0.86 MA cm−2 up to 9 T at 4.2 K for both major crystallographic directions of the applied field, promising for high field applications. Pinning force analysis indicates a significant enhancement compared with similar Ba122:Co coated conductors. By using the anisotropic scaling approach, intrinsic pinning associated with coupling between superconducting blocks can be identified as the pinning source in the vicinity of H//ab, while for H//c random point defects are likely to play a role but correlated defects start to be active at high temperatures.

Intrinsic and extrinsic pinning in NdFeAs(O,F): vortex trapping and lock-in by the layered structure.

Fe-based superconductors (FBS) present a large variety of compounds whose properties are affected to different extents by their crystal structures. Amongst them, the REFeAs(O,F) (RE1111, RE being a rare-earth element) is the family with the highest critical temperature Tc but also with a large anisotropy and Josephson vortices as demonstrated in the flux-flow regime in Sm1111 (Tc ∼ 55 K). Here we focus on the pinning properties of the lower-Tc Nd1111 in the flux-creep regime. We demonstrate that for H//c critical current density Jc at high temperatures is dominated by point-defect pinning centres, whereas at low temperatures surface pinning by planar defects parallel to the c-axis and vortex shearing prevail. When the field approaches the ab-planes, two different regimes are observed at low temperatures as a consequence of the transition between 3D Abrikosov and 2D Josephson vortices: one is determined by the formation of a vortex-staircase structure and one by lock-in of vortices parallel to the layers. This is the first study on FBS showing this behaviour in the full temperature, field, and angular range and demonstrating that, despite the lower Tc and anisotropy of Nd1111 with respect to Sm1111, this compound is substantially affected by intrinsic pinning generating a strong ab-peak in Jc.

Magnetic and magnetotransport studies of iron-chalcogenide superconductor Fe(Se0.4Te0.6)0.82: observation of thermally activated transport and flux jump

The magnetic and magneto-transport behavior of the Fe-based superconductor of nominal composition Fe(Se0.4Te0.6)0.82 has been investigated. Different superconducting parameters such as critical fields, coherence length, penetration depth and the Ginzburg–Landau parameter (κ) have been estimated for the present compound. The large value of κ (∼253) is in line with the unconventional type-II nature of the studied superconductor. Thermally activated transport behavior in the presence of an external magnetic field across the superconducting transition region indicates a crossover from a single-vortex pinning regime to a collective flux creep regime at 50 kOe. The sample shows anomalous field dependence of flux flow resistance, which is presumably connected to the inherent superconducting state of the sample. The isothermal resistivity data as a function of external magnetic field show a signature of flux jump below the superconducting transition temperature (Tc). The effect of hydrostatic pressure on the superconducting properties of the compound has also been investigated and about 3 K shift in Tc has been observed with the application of 10 kbar of pressure.

Far-infrared electrodynamics of thin superconducting NbN film in magnetic fields

We studied a thin superconducting NbN film in magnetic fields up to 8 T above the zero-temperature limit by means of time-domain terahertz and scanning tunneling spectroscopies in order to understand the vortex response. Scanning tunneling spectroscopy was used to determine the optical gap and the upper critical field of the sample. The values obtained were subsequently used to fit the terahertz complex conductivity spectra in the magnetic field in the Faraday geometry above the zero-temperature limit. These spectra are best described in terms of the Coffey–Clem self-consistent solution of a modified London equation in the flux creep regime.

Ac-magnetic susceptibility in the peak-effect region of Nb3Sn

We performed a systematic study of the ac magnetic-susceptibility on a Nb3Sn single crystal which displays a strong peak effect near the upper critical field Hc2. In external magnetic fields above μ0H≈3T, the peak effect manifests itself in a single, distinct peak in the real part χ′(T) of the ac susceptibility as a function of temperature T, the size of which continuously increases with increasing magnetic field H. In the imaginary part χ″(T) of the ac susceptibility, on the other hand, a single peak initially grows with increasing H up to a well-defined value, and then splits into two sharp peaks which separate when H is further increased. We explain this surprising behavior by a flux-creep model and taking into account the enhancement of the critical-current density in the peak-effect region near Tc in which Bean’s critical-state model seems to apply. Outside this region, the crystal is clearly in a flux-creep regime with finite creep exponent n.

Growth, characterization, vortex pinning, and vortex flow properties of single crystals of the iron chalcogenide superconductor FeCr0.02Se

We report the growth and characterization of single crystals of iron chalcogenide superconductor FeCr$_{0.02}$Se. There is an enhancement of the superconducting transition temperature (T$_{\rm c}$) as compared to the T$_{\rm c}$ of the single crystals of the parent compound Fe$_{1+x}$Se by about 25%. The superconducting parameters such as the critical fields, coherence length, penetration depth and the Ginzburg-Landau parameter have been estimated for these single crystals. Analysis of the critical current data suggests a fluctuation in electronic mean free path induced ($\delta l$) pinning mechanism in this material. Thermally activated transport across the superconducting transition in the presence of external magnetic fields suggests a crossover from a single vortex pinning regime at low fields to a collective flux creep regime at higher magnetic fields. The nature of charge carriers in the normal state estimated from the Hall effect and thermal transport measurements could provide crucial information on the mechanism of superconductivity in Fe-based materials.

Vortex lattice motion in the flux creep regime on asymmetric pinning potentials

Vortex lattice dynamics is investigated in the adiabatic regime in superconducting/magnetic nanostructures for strong and weak asymmetric pinning potentials, provided by a rectangular array of Ni triangles and a kagomé-like array of Ni dots, respectively. The AC voltage response of the AC-driven superconducting vortex lattice is measured in addition to the DC voltage response. The results allow us to link voltage rectification effects with the vortex lattice dynamics. In particular, for the weaker pinning kagomé-like array, a high-temperature zero critical current regime is identified, in which both AC and DC voltage responses can be described in terms of a simple model of thermal activation of single vortices over finite asymmetric barriers.

Vortex Dynamics in YBa2Cu2O7−δ Films and Superlattices: A Magnetization Relaxation Study

The relaxation of the irreversible magnetization of optimally doped YBa2Cu3O7−δ (YBCO) films and YBa2Cu3O7−δ/PrBa2Cu3O7−δ (YBCO/PrBCO) superlattices in a magnetic field H oriented along the c axis was investigated over a large temperature T interval. The observed behavior is dominated by the presence of a crossover elastic vortex creep at low T–plastic creep at high T generated by the T-dependent current density J of the macroscopic currents induced in the specimen during experiments. Magnetization relaxation in the flux-creep annealing regime indicates the reduction of the creep crossover temperature with decreasing J, which suggests that in static conditions the disordered vortex phase at high H behaves like a plastically pinned vortex assembly, rather than an elastic vortex glass. The often reported scaling of the electric field E–transport current density J characteristics in agreement with an elastic vortex glass–vortex fluid transition seems to originate from the creep crossover generated by an increasing J.

Effect of Critical Current Density and Critical Temperature on ac Susceptibility

Based on the flux creep equation, the effect of critical current density and critical temperature on ac susceptibility is investigated numerically in a superconducting slab immersed in an ac magnetic field. The current density dependence of the flux creep activation barrier is employed as the logarithmic law. The fundamental ac susceptibilities of the slab as a function of temperature for the same ac field have been derived in a unified picture. The results show that ac susceptibility in flux creep regime is affected by critical current density and critical temperature.

Thermal effects in the flux-creep regime of YBa2Cu3O7-δ thin film microbridges under high current densities in self field

currents well above the critical current density Jc but below the quenching current density J* (the current inducing the full transition to the normal state), the electric field vs current density (E-J) curves may be deeply affected by self-heating effects. Until now the influence of these thermal effects on the E-J curves was mainly studied around J*. Here we will first present measurements of the E-J curves in several YBa2Cu3O7-δ thin film microbridges in the whole range between Jc and J*. Our results confirm that whereas Jc is almost independent on the microbridge width (w), J* and E* strongly increase when the width decreases. It is also shown that the width dependence on the E-J curves manifests itself already for current densities well below J*(w). Then by using a finite-element method (FEM), it is shown that the measured E-J curves may be explained, from the dissipation onset (Jc) up to the jump itself (J*), in terms of a conventional (smooth) flux-creep plus self-heating effects. An important aspect of our results is that the same flux-creep behaviour in the low dissipation regime allows us to explain the whole E-J curves in film microbridges with different widths.

On the Applicability of the Magnetic Susceptibility Models for the Magnetic Superconductor Ru-1212

The applicability of theoretical models for the ac susceptibility measurements of polycrystalline RuSr2GdCu2O8 superconductor has been examined within the temperature range between 8–50 K, ac magnetic field 0.5–25 G, and frequency 20–12500 Hz. In general, a reasonable qualitative agreement between theory and experiment was attained. An evident and detectable asymmetry was observed within the Cole–Cole polar plots with a peak enhancement for both theoretical and experimental data. The modified critical state models are found to generate much better explanation of the ac susceptibility measured data than Bean’s model. For fields above 20 G, the results are agreed roughly with the Bean critical state model, while below 20 G, the Kim–Anderson model is more suitable to account of the magnetic performance. The temperature and field amplitude dependencies of the flux-creep exponent, n, were extracted from the real part of susceptibility, χ′, dependence on frequency. The flux-creep exponent was found to decrease with both temperature and ac field amplitude in accordance to a power-law of the form: n(T,H)=n0(H)T−s(H). Such dependence might be an indication of a crossover to flux-creep bundles regime.

Relaxation of remnant magnetisation in YBa 2Cu 3O 7− δ films

The relaxation of the remnant magnetisation in optimally doped disk-shaped YBa 2Cu 3O 7− δ films with the initially applied magnetic field H oriented along the c axis was measured using dc SQUID magnetometry. The temperature ( T) dependence of the experimentally observed normalised magnetisation relaxation rate S exhibits three distinct regions. At high T, S( T) increases with increasing T, which can be explained in terms of plastic vortex creep. The well known plateau in the S( T) variation at intermediate T appears to be caused by collective (elastic) creep in a dynamically ordered vortex system. At low T, where S increases again with increasing T, the magnetisation relaxation is not in a pure thermally activated flux-creep regime, due to the occurrence of micro-flux jumps. This seems to be the origin of the recently proposed exponential current density dependence of the effective vortex pinning potential.

Flux creep in type-II superconductors: The self-organized criticality approach

We consider the current density distribution function of a flux creep regime in type-II superconductors by mapping the flux creep process to the dynamics of a model with a self-organized criticality. We use an extremal Robin Hood type model which evolves to Been's type critical state to treat magnetic flux penetration into a superconductor and derive an analog of the current-voltage characteristics in the flux creep region.

Numerical modeling of the superconducting flux flow transistor with a nanobridge

We have fabricated superconducting flux flow transistors (SFFTs) with a nanobridge from epitaxial superconducting thin films by photolithography and electron-beam lithography. We have tried to simulate their I– V characteristics by building a model. The simulation was performed by varying the penetration depth as a function of the width and the thickness in the nanobridge and the gate current. This model showed the dependence of the critical current density on the spatial distribution of an applied magnetic field induced by the gate current. The simulated I– V curves were well in agreement with the measured curves in the flux creep regime of an SFFT with a nano-scale channel. This model is suitable for prediction of the I– V characteristics in the flux creep regime of the SFFT with a nano-scale channel.

Influence of Sr doping on the second magnetization peak and the critical current density of YBa 2Cu 3O 7− δ single crystals

Magnetic hystheresis loops of a series of YBa 2− x Sr x Cu 3O 7− δ ( x=0.1, 0.25, 0.37 and 0.5) single crystals reveal a huge “peak effect” over a wide range of low temperatures. Previous magnetoresistivity and magnetic irreversibility measurements already have evidenced that the superconducting state of these samples has a granular character and that their magnetic irreversibility line crosses over from the high field flux-creep (fc) regime to low field regimes, characterized by the intergrain Josephson flux-dynamics in a frustrated superconducting-grain aggregate. The present work adds to this that the peak effect vanishes at the temperature limit where the crossover from the fc to the low field regimes takes place. This is a clear indication that the peak effect is entirely related to the intragrain Abrikosov flux-dynamics.

Vortex motion in YBa2Cu3O7−δ twinned single crystals and epitaxial films

The transport properties of superconductive YBa2Cu3O7−δ (YBCO) twinned single crystals and epitaxial thin films are similar in the flux creep regime. In particular, the activation energy of the individual vortices is proportionnal to the temperature in the low temperature range. As a matter of fact, data from the literature show that this energy takes the form Ea=4πνkBT, where ν is an integer. To investigate this behavior, the current–voltage characteristics of epitaxial YBCO thin film microbridges were measured. The activation energy of these samples has proved to take the form given above. This common behavior of single crystals and thin films is interpreted in the framework of a critical state model according to which the vortices move along the sample twin boundaries that behave as arrays of weak links.

Self-oscillations in electric circuits with high-temperature superconductors

The paper presents the experimental results showing a specific behavior of high-temperature superconductors in various electric circuits. Self-oscillations of temperature and current in the superconductor manifest themselves as sharp peaks of voltage across the superconductor on the background of a basic signal. It is shown that these oscillations can also appear when a superconductor is in flux creep regime. In inhomogeneous superconducting samples, the oscillations are associated with cyclic movement of normal or resistive zones.