Flux Creep Theory Research Articles

On the flux bundle size in weakly pinned superconductors

Recently it was found that the transverse flux bundle size estimated from the observed irreversibility field in terms of the flux creep theory takes much smaller values than the prediction from the elastic correlation length of the fluxoid lattice. This is more remarkable for the case of larger correlation length, i.e., for superconductors with a weaker flux pinning strength. It is assumed that the flux bundle size is determined so that the critical current density under the flux creep is maximized. This assumption is analogous to the irreversible thermodynamic principle for the linear dissipation systems that the energy dissipation is minimized. The obtained flux bundle size is proportional to the one-third power of the value derived from the elastic correlation length. Qualitative and quantitative agreements are obtained between the prediction and the experiments. The theoretical result also explains the observed finite relaxation rates at ultra-low temperatures which have been believed to be explained only by the quantum tunneling mechanism.

Intergrain flux creep in high-Tc superconductors.

Equations describing the intergrain flux creep of ceramic superconductors are derived. They are based on the behavior of small superconducting loops closed by overdamped Josephson junctions. The elementary loops are formed around nonsuperconducting regions between the grains, the loops acting as pinning centers. Despite different pinning mechanisms the equations for the relaxation of the intergrain current density in a static and a slowly varying external magnetic field are formally similar to those of the classical flux-creep theory based on volume pinning.

Dissipative flux motion in YBa2Cu3O7?? films ? Investigation by means of transport I-V curves

The nature of dissipative flux motion in epitaxial YBa2Cu3O7−δ thin films has been investigated by means of resistivity ϱ(T, B) and transport current-voltage characteristicsE(j, T, B) covering up to 5 orders of magnitude in voltage for a wide range of temperatures (4.2–85 K) and magnetic fields (0.5–7.0 T). Activation energiesU(T, B, j) have been determined in the framework of the collective flux creep theory. It is shown thatU(T, B, j) decreases with increasing temperature, magnetic field and current density. In order to study the influence of a well-defined defect structure, columnar defects have been generated by irradiation with 340 MeV Xe-ions. From a scaling law relating theI–V curves after irradiation with the curves before irradiation it is found that vortices pinned by the columnar defects do not contribute to dissipation. Due to irradiation the irreversibility line is shifted to higher magnetic fields, indicating its connection to the pinning mechanisms present in the samples.

Scaling of the flux pinning force in epitaxial Bi2Sr2Ca2Cu3Ox thin films.

Magnetic-field and temperature dependence of the critical current density ${\mathit{J}}_{\mathit{c}}$ is investigated in epitaxial ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ thin films. For the magnetic field H applied parallel to the c axis, the flux pinning force density ${\mathit{E}}_{\mathit{p}}$ (=${\mathit{J}}_{\mathit{c}}$B) exhibits clear scaling behavior when H is normalized by the irreversibility field ${\mathit{H}}^{\mathrm{*}}$. The maximum pinning force density scales linearly with ${\mathit{H}}^{\mathrm{*}}$. This is the first observed scaling of ${\mathit{E}}_{\mathit{p}}$ in high-quality thin films of Bi oxides, which we can reasonably explain with flux-creep theory by assuming that the activation energy is proportional to the flux line spacing.

Exactly solvable model of flux creep in high-Tc superconductors.

An exactly solvable model of flux creep in high-[ital T][sub [ital c]] superconductors within the framework of both thermally activated and quantum-tunneling flux-creep theory is presented in this paper. The activation energy and crossover temperature between activated creep and quantum tunneling are explicitly expressed for an elastic flux line in a typical weakly periodical or quartic pinning potential involving a viscous medium. The exact analytic expression of magnetic relaxation rate is derived for the full parameter range. These expressions are somewhat better because several superconducting mechanism-sensitive parameters have been included. The present results are in reasonable agreement with the experimental data obtained in high-[ital T][sub [ital c]] superconductors.

Flux line pinning by point defects in single crystalline high-T c superconductors

The temperature and time dependence of the magnetization M of single crystalline high- T c YBa 2Cu 3O 7−δ and Bi 2Sr 2Ca Cu 2O 8+δ samples is analysed in order to determine critical magnetization currents j c as well as pinning potentials U. The evaluation of the experimental data within the framework of critical state and flux creep theories is performed under the assumption of a distribution of activation energies. These energy spectra, as well as the temperature dependence of the critical current density, turn out not to depend significantly on crystal orientations relative to the applied magnetic field. Flux bundle volumes V that are coherently moved in an activation process seem to be much smaller than the volume of a single flux line. From these results we conclude that the dominant pinning process in as-grown single crystalline high- T c superconductors is given by the interaction of flux line segments with point defects, located in the CuO planes. Furthermore, the energy spectra, resulting from evaluations considering first-order kinetics, are temperature independent and give a natural explanation for the increase of the effective potential U with temperature, if the barrier heights U are determined within a single barrier model.

Magnetization and relaxation curves of TlBaCaCuO: Measurements and simulation

In this publication, experimental curves from torque magnetometry will be compared with curves which are generated by numerical simulation. The experimental results refer to steady and to relaxation torque measurements of a film of the HTSC TlBaCaCuP. For simulation, a differential equation was solved. This equation is derived from a simple dynamic model which contains implicity the flux creep theory with logarithmic barrier and describes steady curves as well as relaxation curves. This method overcomes some problems which occur if experimental curves are fitted to analytical solutions. It is a promising attempt to extract material parameters from measurements of ring shaped samples. With out simulated curves we try to reproduce the shape of the measured curves as a first step. A detailed quantitative analysis is not yet the aim of this work.

Assessment of thick film YBCO for flux transformer and magnetic screening applications

Measurements on the flux creep properties of a series of thick-film YBCO tubes and rings that have been processed at a range of different temperatures are reported, and their potential for use in large-area flux transformers and shields for superconducting quantum interference device (SQUID) magnetometers is considered. It is found that films showing flux creep rates adequate for flux transformer or low-field ( approximately 100- mu T) magnetic shielding applications can be made without recourse to special doping or heat treatment techniques. Application of flux creep theory to the data and observations of the microstructure in similar films implies that the scale over which the supercurrents are flowing is on the order of tens of mm and that this would place a lower limit on fabrication accuracy. For screening the earth's magnetic field, the films reported here would be adequate; for higher fields, thicker or multiple shields may by required. >

Effect of short coherence length along the c-axis on the irreversibility line in high- Tc superconductors

It has been empirically known that the irreversibility line in quasi-two-dimensional high- T c superconductors is farther from the phase boundary, B c2( T), than in three-dimensional ones. Such a difference was investigated in terms of the flux creep theory from the viewpoint of the coherence length along the c-axis, ξ⊥. For superconductors with short ξ⊥ in the field normal to the c-axis, the flux bundle size is small due to the small shear modulus C 66 of the fluxoid lattice, resulting in small pinning potential depth. Hence, even if strong pinning centers such as fine non-superconducting particles are successfully introduced into the materials, their effect on the irreversibility line is not as large as that in three-dimensional superconductors. However, this inherent inferiority can be overcome up to a sufficient level for practical applications by improvement of the flux pinning characteristics. The case is also treated where the magnetic field is applied parallel to the c-axis. In this case, the irreversibility line is restricted to a low level because of the small B c2 value.

Irreversibility line in superconducting Bi-2212 single grain with fine normal particles

The irreversibility line was obtained in terms of the imaginary a.c. susceptibility measurement for a melt-processed superconducting Bi-2212 single grain with fine non-superconducting particles. This line showed different temperature dependences in high and low temperature regions. The one in the low temperature region agrees approximately with the prediction from the flux creep theory with experimentally observed pinning parameters. On the other hand, the one in the high temperature region is close to the well known characteristics in Y-based superconductors, suggesting flux pinning by boundaries such as the surfaces of non-superconducting particles. A quantitative discussion is also given on flux bundle size.

Low-temperature current-voltage characteristics of YBa 2Cu 3O 7− δ films in a magnetic field: direct evidence for a vortex-glass phase

Evidence for a vortex-glass phase is found from nonlinear current-voltage ( I- V) characteristics measured on YBa 2Cu 3O 7− δ thin films in high magnetic fields and at low temperatures. Well below the superconducting transition temperature the I- V curves are well described by E/ J = ϱ 0 exp[−( J 0/ J) μ ], with E the electric field and J the current density. The exponent μ is 0.19 ± 0.05 for low values of current density and μ = 0.94 ± 0.1 at high values. The results at low J are characteristic of a vortex glass and constitute the first direct evidence that the low-temperature state of a disordered superconductor is a vortex glass. The results are at variance with predictions from the theory of collective flux creep. Near the phase transition, both ϱ 0 and J 0 exhibit critical behaviour.

The study of AC susceptibility of MTG YBCO sample under high magnetic fields

AC susceptibility measurements were carried on the Melt-Textured-Growth (MTG) YBa 2Cu 3O y sample in external magnetic field up to 7T. The results reveal that the MTG sample is strong anisotropic for magnetic field oriented parallel and perpendicular to c-axis. The linear relation between the transition temperature Tc(H) and magnetic field is obtained for H⊥C orientation. The upper critical field H c2(0) is estimated to be 183.4T. In addition, no transition temperature T c dependence of frequency is observed. For H∥C orientation, the data of Ton(H) and Tm(H) as the functions of magnetic field H can be fitted to relations: Ton(H) proportional to H 2 3 and Tm(H) proportional to H 2 3 . The relations are understood in terms of the flux creep theory of Anderson and Kim.

Thermally activated flux motion in high- T c superconductors

Using the modified Anderson-Kim theory of flux creep and the Bean model, we derive an analytical expression for magnetic relaxation of high-Tc superconductors, which is applicable in the whole flux creep region. The high driving force limit of the expression gives the usual logarithmic decay law and its low driving force limit takes the exponential form. Theoretical analysis is in agreement with the existing experimental results.

Study of magnetic relaxation processes in ceramic Tl-2223 high- Tc superconductors

The magnetic relaxation of polycrystalline Tl 2Ba 2Ca 2Cu 3O χ was studied in the temperature range 4–100 K. The results were compared with the predictions of the conventional flux creep theory, collective pinning model and vortex glass-vortex liquid phase transition theory. In the chosen time window ( t⩽2500 s) the magnetization decay at low ( T⩽10 K) and high temperatures ( T⩾40 K) can excellently be described by a simple logarithmic relation M ≈ In( t). Deviations from the In( t)-decay occuring in the intermediate temperature range can be explained by the collective pinning model as well as by the vortex glass picture. Considering the conventional flux creep model as a first approximation to our measurement data, the distributions of the pinning potentials were obtained with peaks at U 0≊60 meV. This low value of most of the activation barriers might be responsible for the drastic decrease of the remanent magnetization and critical current density at temperatures T⩾30 K.

Non-logarithmic relaxation in flux-grown YBa2Cu3O7−δ single crystal

Abstract Magnetic relaxations have been measured for up to 20 h for a flux-grown YBa 2 Cu 3 O 7- δ single crystal, with the applied field (up to 7 T) parallel to the c -axis. A ln( t ) relaxation of the magnetisation, found from the Anderson-Kim flux creep model, only describes our data for low temperatures and low fields. However, we have found that a power-law relaxation ( M )( t )∝ t -α ), which points to a logarithmic current-dependence of the effective activation energy [ U ( J )= U 0 ln ( J 0 / J )], fits the data well for a wide range of temperatures and applied fields. Values for U 0 ( B, T ) have been obtained from the power-law relation, and compared with the values derived from the logarithmic relaxation rates. Discrepancies between them are discussed. Possible connections between our experimental data and Feigel'man's collective flux creep theory are also discussed.

Dissipative flux motion in epitaxial YBa 2Cu 3O 7−δ and Bi 2Sr 2CaCu 2O 8+ x films

We have performed a comparative study of the dissipative flux motion in the anisotropic and the very anisotropic high temperature superconductors YBa 2Cu 3O 7−δ and Bi 2Sr 2CaCu 2O 8+x, respectively, by AC susceptibility measurements in an applied DC magnetic field between 0.01 and 7 T. The limit of small current densities (10 −8< J<1 A cm 2) was invesvestigated by using small amplitudes of the driving AC field. For the very anisotropic Bi 2Sr 2 CaCu 2 O 8+ x superconductor the thermally activated motion of two-dimensional vortex lattice defects, which we refer to as plastic flux creep, is found to prevail over the motion of elastically correlated flux bundles, or elastic creep. The magnetic field dependence of the activation barrier and the irreversibility lines are found in good agreement with plastic flux creep theory. For the less anisotropic superconductor YBa 2Cu 3O 7−δ the flux motion is dominated by elastic flux creep. For this material the detailed measurement of the frequency and amplitude dependence of the AC susceptibility transition gives clear evidence for a finite temperature phase transition to a vortex glass state. The relevant critical exponents and the magnetic field dependent glass temperature are derived. Our results demonstrate the influence of the anisotropy of the superconducting material on the dissipative flux motion.

CRITICAL CURRENT DENSITY AND ITS RELATED PROBLEMS IN CVD-Y1Ba2Cu3O7

High performance of the critical current density Jc in Y1Ba2Cu3O7 films prepared by chemical vapor deposition has been demonstrated. The pinning mechanism in high-Tc superconducting oxides was explored from a viewpoint of the anisotropic behavior of Jc, and the global pinning force Fp was investigated in terms of the flux creep. It was found that the global pinning force on the basis of the flux creep theory well describes the Jc properties in CVD-Y1Ba2Cu3O7 films. The scaling in the form Fp∝(B/Bc2)1/2(1-B/Bc2)3/2 of the unrelaxed state which is not limited by the flux creep was presented.

Pinning, creep and possible melting in the mixed state of NbZr films

Current-Voltage (I–V) characteristics and resistivity measurements on Nb xZr 1−x (x ∼ 0.15) thin films are reported over a broad range of temperature and magnetic field. In the vicinity of the critical temperature (field) the I–V curves show a transition from the Ohmic to a strongly non-linear behavior on increasing the excitation current density. The linear resistivity is thermally activated with a field dependent barrier height. Although the Ohmic and non-linear data can be described in the framework of the glass model for the mixed state in hard superconductors, it does not yield a universal set of exponents for the glass to fluid transition. The overall response of the mixed state can be understood in the framework of the standard flux-creep theory with inter-vortex interaction.

Dissipative behavior due to flux motion in ultrathin YBaCuO films

The resistive transition of ultrathin YBCO films in a field has been measured to study the dissipative behavior due to flux motion. The thickness of the films is in the order of 30 – 40 nm. The broadening of the resistive transition is compared with that of thick films. The results are discussed in the framework of the flux creep theory.

Analysis of the hysteresis curves of a laser-ablated YBCO thin film via an exponential critical state model

Our experimental data show that the magnetization of a laser-ablated YBCO thin film can be properly devided into reversible and irreversible parts. The time dependent irreversible magnetization follows flux-creep theory. By using the exponential critical state model, the irreversible magnetization of the hysteresis curves are perfectly quantitatively analyzed.