Collective Creep Research Articles

Low-field flux creep behavior near second peak H 2p in Pr-doped Bi-2212 single crystal

Magnetic hysteresis M( H) and magnetic relaxation M( t) results on Pr-doped single-crystal Bi 2Sr 2Ca 0.89-Pr 0.11Cu 2O 8+ δ with optimum T c=88 K are reported. Superconducting H– T phase diagram with applied field parallel to single-crystal c-axis indicates that in the mixed state the anomalous second peak field and its onset field H 2p/ H on varies from 900/800 G at 15 K to 210/85 G at 40 K with a plateau around 20–30 K. Low-field magnetic relaxation M( t) data near H 2p/ H on indicates a distinct change of flux creep behavior. For H< H on, the relaxation mechanism follows the collective creep model M( t)= M 0[1+( μk B T/ U 0)ln( t/ t 0)] −1/ μ and crosses to the vortex glass model M( t)= M 0( t/ t 0) 1/[1−( Uo/ k B T)] when H> H on. Such a crossover behavior implies a change in vortex coupling mechanism from vortex quasi-lattice to entangled vortex glass.

Dynamic response of Ag–Bi2223 tapes in applied fields by electric transport measurement

Electric transport measurement of Ag-sheathed Bi 2−x Pb x Sr 2 Ca 2 Cu 3 O y tapes in magnetic fields H was conducted by the four-probe method to study the effect of H and sweeping rate of applied current dI/ dt on critical current. It is found that H and dI/ dt apparently affect the critical current and the V–I characteristic curve. To understand the experimental result, numerical simulation was carried out based on the collective creep model of the vortex glass. The numerical result is in agreement qualitatively with the experiment. It is shown that the influence of the applied field, temperature and vortex pinning on the normalized critical current can be reduced to a single critical current parameter n.

Voltage Relaxation and Its Influence on Critical Current Measurements

Based on the collective creep model, we numerically studied evolution of electric field and current density in superconductors and its influence on transport measurements of critical current. It is shown that many experimental facts, such as the dependence of V-I curves on sweeping rate of applied current and voltage relaxation are the results of this evolution. The simulation results are confirmed by electric transport measurements on Ag-sheathed Bi2−xPbxSr2Ca2Cu3Oy tapes. Discussions on influences of the voltage relaxation on electric transport measurements including superconducting critical current are made.

Temporally ordered collective creep in NbSe3 : A new window on low-temperature charge-density-wave dynamics

We have observed a new form of collective creep in the CDW conductor NbSe 3 . This creep provides fundamental insight into the relation between local and collective pinning and the mechanism of CDW dissipation, and has broad implications for understanding the CDW response at low temperatures.

Flux flow of La-Sr-Cu-O single crystals

We measured voltages across micro-bridges fabricated along the c-axis of La/sub 2-x/Sr/sub x/CuO/sub 4/ single crystals under an external magnetic field. A sharp voltage peak appears when the magnetic field was aligned to the ab plane within a few degrees. The vortex velocity estimated from the maximum voltage is much lower than the velocity that was measured in Bi/sub 2/Sr/sub 2/CaCu/sub 2/O/sub x/ single crystals. If many weak point-like pinning centers are assumed to be in the sample, the angular dependence of the voltage is explained by the collective flux creep model.

Dimensional crossover in flux dynamics in YBa 2Cu 3O 7− δ/PrBa 2(Cu 3− xGa x)O 7− δ superlattices

Magnetic measurements were performed on a ring patterned [YBa 2Cu 3O 7− δ ] 56 Å/[PrBa 2(Cu 3− x Ga x )O 7− δ ] 125 Å superlattice with a transition temperature to superconductivity of T c=69 K. In this way, the critical current density j c( T), current–voltage characteristics E( j) and hysteresis M( H) were obtained. The normalized relaxation rate S( T) shows an anomalous drop for T≥65 K pointing to a reduced dissipation. An additional scaling analysis according to the vortex-glass theory reveals a crossover from 3D to quasi-2D behavior. A related anomaly was also observed in j c( T) behavior showing an unusual kink, from which a corresponding H– T borderline can be constructed, which is suggested to be due to a crossover from 3D to 2D collective pinning in accordance with the collective creep theory.

Anomalous magnetic behavior of superconducting thin films in small magnetic fields [4] close to the transition temperature

Using a specially designed SQUID magnetometer we measured the temperature dependence of the critical current density in a ring patterned thin film for magnetic fields parallel to the c-axis. In addition, the temporal relaxation of the remanent state as prepared by field cooling in an external field of 100 Oe at different temperatures is determined. The j c ( T ) data show a field-dependent anomalous kink close to Tc pointing to reduced dissipation with increasing temperature allowing to construct a corresponding H-T borderline. A similar behavior is observed for the normalized relaxation rate S ( T ) as extracted from the temporal behavior of the remanent state, which, at low temperatures, exhibits the expected increase for increasing T-values, while an anomalous decrease of S ( T ) is found for temperatures above 85 K. While the low-T regime is attributed to creep of 2D pinned single vortex lines, the high-T behavior is suggested to be dominated by collective motion with a more sluggish dynamics. This change in dynamics is also reflected by the activation barriers for flux creep U ( j ), which show a corresponding crossover in μ from 0.06 to 0.99. An additional scaling analysis of the E-j characteristics for according to vortex glass theory reveals quasi-2D collective creep behavior with .

Temperature dependence of the distribution of the thermally activatedenergy barriers in Tl2Ba2CaCu2O8 film

The effects of frequency and ac amplitude on ac susceptibility have been measured for a thin Tl2Ba2CaCu2O8 film in the range 100 Hz-100 kHz in magnetic field 0.52 T. A phenomenological equation with an asymmetrical distribution of thermally activated energy barriers has been used to analyse these frequency and amplitude dependences of the ac susceptibility (,hac) in the vicinity of the peak temperature of ´´. We obtain the effective energy barrier U against amplitude hac (current density j): U hac-0.38. This U(j) relationship shows that the flux lines are in the 3D collective creep regime. Therefore, we conclude that the effective energy barrier is in fact an average of the barrier's distribution, and the distribution function is a distinguished asymmetrical one in this 3D collective creep regime.

Collective flux creep: Beyond the logarithmic solution

Numerical studies of the flux creep in superconductors show that the distribution of the magnetic field at any stage of the creep process can be well described by the condition of spatial constancy of the activation energy U independently on the particular dependence of U on the field B and current j. This results from a self-organization of the creep process in the undercritical state $j&lt;{j}_{c}$ related to a strong nonlinearity of the flux motion. Using the spatial constancy of U, one can find the field profiles $B(x),$ formulate a semianalytical approach to the creep problem and generalize the logarithmic solution for flux creep, obtained for $U=U(j),$ to the case of essential dependence of U on B. This approach is useful for the analysis of dynamic formation of an anomalous magnetization curve (``fishtail''). We analyze the quality of the logarithmic and generalized logarithmic approximations and show that the latter predicts a maximum in the creep rate at short times, which has been observed experimentally. The vortex annihilation lines (or the sample edge for the case of remanent state relaxation), where $B=0,$ cause instabilities (flux-flow regions) and modify or even destroy the self-organization of flux creep in the whole sample.

Low-temperature magnetic relaxation inHgBa2Ca2Cu3O8+δsingle crystals with columnar defects

Micrometer-sized Hall probes are used to measure the low-temperature magnetic properties of ${\mathrm{HgBa}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals with and without columnar defects. Introduction of columnar defects by heavy-ion irradiation suppresses the quasiexponential temperature dependence of the critical current, but only when the density of flux lines is less than the density of defects. The current-dependent creep activation energy $U(J)$ is found to be best described by the power law: ${U(J)=U}_{0}[{(J}_{c}{/J)}^{\ensuremath{\mu}}\ensuremath{-}1].$ At high current densities J, and low fields, there is a crossover to a quantum vortex creep process with a temperature-independent magnetic relaxation rate. On the low-J side of this crossover in the unirradiated sample, $\ensuremath{\mu}g~1,$ indicating that the thermally activated vortex creep process is consistent with collective creep. When the flux-line density exceeds the columnar defect density in the irradiated sample, the vortex creep process is characterized by $\ensuremath{\mu}\ensuremath{\sim}1.$ For flux-line densities less than the defect density, an anomalously large exponent is found $(\ensuremath{\mu}g~2),$ which is inconsistent with vortex transport occurring either by the nucleation and expansion of half-loop excitations or by variable-range hopping of vortex lines as described by the Bose-glass theory.

Vortex plastic creep in a superconducting crystal of Tl-2223

The dissipation in the mixed state of a Tl 2Ba 2Ca 2Cu 3O 10 (Tl-2223) crystal was studied by an analysis of the DC relaxation and that of the frequency dependence of the AC susceptibility. Near the irreversibility line, the field dependence of the activation energy at zero current limit evidences the plastic nature of the vortex movement mediated by individual vortex loops. At lower temperatures, the data are analysed in a current dependent activation energy U( J) framework. The data are analysed in the model proposed by Abulafia et al. in U 0(1−( J/ J 0) 1/2) which predicts a non divergent energy barrier at zero current. The analysis of the magnetic field dependence of U 0 has shown that the plastic model used in the region of the irreversibility line can account for the observations. In this system, no elastic collective creep was observed in the domain that we have explored.

Temperature dependence of the critical current determined from magnetic relaxation in HgBa 2Ca 2Cu 3O 8+ δ

Based on the U( j) relation of the collective pinning theory, U( j)=[ U c/ μ][( j c/ j) μ −1], we introduce a direct method to derive the temperature dependence of the characteristic exponent μ, the collective pinning energy U c and the critical current density j c from magnetic relaxation measurement. By utilizing a linear relation between 1/ R≡1/|∂ ln j/∂ ln t| and ln t at a fixed temperature, μ and U c are easily obtained. Inserting these parameters into U( j) we can extract j c. So μ( T), U c( T) and j c( T) are able to be derived from relaxation measurements at different temperatures. This method was applied to a HgBa 2Ca 2Cu 3O 8+ δ superconductor. The results were discussed within the collective pinning and creep theory.

Effect of Nd4Ba2Cu2O10 addition on the pinning properties of Nd-Ba-Cu-O crystals

Abstract We have studied the effects of Nd 4 Ba 2 Cu 2 O 10 (Nd422) on the pinning characteristics of NdBa 2 Cu 3 O 7− δ (Nd123) crystals. Like Y 2 BaCuO 5 particles in the Y–Ba–Cu–O system, the addition of Nd422 could enhance critical current density J c at lower fields. The peak field ( B pk ) and the J c value at B pk were almost independent of Nd422 contents although a slight decrease in J c at B pk was observed with increasing Nd422 contents. The normalized relaxation rate ( S ) increased for all the samples when the field exceeded B pk . The addition of Nd422 was effective in preventing a rapid increase in S above B pk . The exponent μ , defined in the collective creep model, was deduced by fitting the experimental data and was found to show strong field dependence. We found that μ changes from positive to negative at around B pk , suggesting that the flux creep mechanism is different below and above B pk .

Characteristic exponents near vortex-glass temperature in GdBa 2Ca 3Cu 7− δ film

The I– V curves of GdBa 2Ca 3Cu 7− δ film were measured at temperatures near the vortex-glass transition temperature T g. For T < T g the temperature dependence of the glassy exponent μ, the collective pinning energy U c and the critical current density J c are derived from I– V curves. It is found that μ changes with temperature and field. The experimental results can be described with vortex-glass or collective pinning and creep theory. For T > T g, we determined the critical exponents by scaling the nonlinear I– V curves. These exponents are consistent with values expected for freezing into a superconducting vortex-glass phase.

Relation between the second peak in the magnetization curves and magnetic relaxation ofLa2−xSrxCuO4single crystals

A large distinct second peak in magnetization has been observed in La{sub 2{minus}x}Sr{sub x}CuO{sub 4} single crystals with x=0.14, 0.15, and 0.18, while a small second peak has been observed in the samples with x=0.115, 0.12, and 0.13. The large second peak has been observed only in the overdoped region (x{ge}0.14). To clarify the flux-pinning mechanism associated with these second peaks, magnetic relaxation has been investigated for x=0.115 and x=0.15. We have evaluated the flux-pinning energy U{sub 0} based on the Anderson-Kim model and a glassy exponent {mu} based on the collective creep model. In the sample having the large second peak, U{sub 0} showed a maximum at a little lower field than the field where the second peak was observed and {mu} changed from positive to negative values with increasing applied field around the field where U{sub 0} took the maximum. On the other hand, the exponent {mu} indicated negative values for the sample having a small second peak. The field dependence of the flux-pinning force above the second peak was found to fit very well to that of a catastrophic depinning model. The maximum in U{sub 0} appears at the field where the pinning character changes from collectivemore » creep to catastrophic depinning; the second peak is related to a crossover in flux dynamics from elastic to plastic behavior. Since both the collective creep and the catastrophic depinning models assume weak inhomogeneous pinning centers, there is a possibility that the pinning centers originate from oxygen-deficient regions which change into efficient pinning centers with increasing field and/or normal metallic states which fluctuatingly appear in the overdoped superconducting region. {copyright} {ital 1997} {ital The American Physical Society}« less

Comparison of results of different methods for the analysis of flux creep behavior in a melt-texturedYBa2Cu3O7−xsample showing a fishtail effect

Magnetic investigations of the flux creep behavior of a melt-textured ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ sample with a pronounced fishtail effect are reported. To get information about the influence of oxygen on the pinning behavior, the sample was measured before and after a change in oxygen content by annealing. From the time dependence of the magnetic moment measured at fields of 1, 3, and 5 T and at temperatures between 4 and 72 K, the current density dependence of the effective activation energy was determined and interpreted in terms of collective pinning theory. The results are compared with those obtained from the simpler analysis within Anderson's flux creep theory, as well as with the results of an analysis in terms of activation energy distributions. Finally, measurements of the hysteresis loops recorded with different field sweep rates were analyzed using the ``generalized inversion scheme.'' The nature of the fishtail is discussed in comparison with existing models, which try to explain this effect. From all these analyses, a phase diagram for the pinning in the investigated sample is proposed, which is based on the assumption that two different types of pinning centers exist, which behave in different ways. Those that dominate in the field and temperature regime where no fishtail appears may be denoted as ``background'' pinning centers. They show a three-dimensional behavior with a change from small-flux-bundle pinning to large-flux-bundle pinning at higher temperatures. The pinning behavior in this field and temperature regime is not influenced by a change in the oxygen content. In contrast, the pinning centers that dominate in the field and temperature regime where the fishtail appears have higher activation energies and show a two-dimensional pinning behavior with a change from single vortex creep to collective vortex creep with increasing field and temperature. These pinning centers are strongly influenced by the oxygen content.

Collective creep near the second peak of magnetization curve in LaBa2Cu3O7 and La2−xSrxCuO4 single crystals

For LaBa2Cu3O7 and La2−xSrxCuO4 single crystals, the second peak depending on temperature in magnetization curves was observed. From measurements of the magnetic relaxation, it was found that the second peak for both samples was related to a crossover from the collective creep in elastic regime to the catastrophic depinning in plastic one.

Magnetic relaxation and collective creep in a grain aligned sample of YBa2Cu3O7−δ

Measurements of creep of magnetic flux lines are conducted in a c axis grain-aligned sample of YBa2Cu3O7−δ within the temperature region from 4.2 to 90K, for fields ranging from 0 to 6K. The effective pinning energy U0 and the power μ are obtained.

Diamagnetic peaks in magnetization versus temperature curves caused by flux trapped relaxation observed in YBa2Cu3O7−δ samples

We present the results and interpretations for two types of diamagnetic peaks observed in magnetization versus temperature curves, taken for field cooled on warming (FCW) experiments in YBa2Cu3O7−δ samples. The high field data (2.0 <H < 4.5 T), for a high quality twinned crystal, presents a universal behavior described by the collective flux creep theory.

The effect of oxygenation and annealing on the peak effect of the magnetization of melt-grown YBa/sub 2/CU/sub 3/O/sub 7-δ/

The influence of oxygenation and high temperature annealing on the peak effect of the magnetization of melt-grown YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// (0</spl delta/<1) material has been studied. A control sample was prepared using a normal melt-growth procedure and oxygenated during cooling. A single grain cut from the control sample was annealed in the temperature region of the crystal growth (1030/spl deg/C-900/spl deg/C) followed by a standard oxygenation. Some of the control sample was powdered and oxygenated for different lengths of time. The peak of the magnetization shifted to a higher field for the sample oxygenated for longer times. Compared with the control sample, the peak of the magnetization of the sample annealed in the higher temperature region shifted to a lower field. The results are discussed within the framework of the collective pinning and collective creep model.