Collective Flux Creep Model Research Articles

Effects of domain structures on vortex state of two-dimensional superconducting Mo2C crystals

Understanding of superconducting phase and vortex states in two-dimensional (2D) superconductors is fundamentally and technologically important. Here we report on low-temperature transport measurements on high-quality ultrathin superconducting Mo2C crystals containing well-defined line-shaped domain boundaries. We observe pronounced two-stage resistive transition accompanied by an appearance of kink structure well below the superconducting transition temperature, which is related to the development of one dimensional (1D) superconducting phase within the domain boundaries. The resistive transition under the magnetic fields is found to be well described by the thermally assisted collective flux creep model. The magnetic field dependence of activation energy barrier exhibits an enhancement at low fields, indicating a dimensional crossover from 2D to 1D vortex states in Mo2C crystals. We obtain the entire magnetic field-temperature phase diagram of ultrathin Mo2C crystals, revealing the existence of additional 1D vortex state induced by the domain boundaries. Our results demonstrate that the domain structures play an important role in determining the superconducting phase and vortex dynamics of 2D superconductors.

Voltage-current curves of high-temperature superconductor tapes measured at controlled current ramp rate compared with collective flux creep model

The voltage-current V(I) curve of high-temperature superconductor tapes as a function of current ramp rate R modelled by the collective flux creep model, with a power-law dependence of local electric field on current density, shows an approximate low-I relation V∝IR and a high-V relation V∝In. In order to compare experimental V(I) curves with the flux creep model prediction, a setup is designed with I provided by a dc power supply driven by an arbitrary waveform function generator and V and I data acquired synchronously by two nano-voltmeters. Some experimental results are given with their features discussed.

Magnetic relaxation measurements on a heavily Pb-dopedBi2Sr2CaCu2O8+δsingle crystal

The magnetic relaxation measurements on a heavily Pb-doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ single crystal were carried out in the vicinity of both the anomalous magnetization peak ${H}_{2p}$ and its onset field ${H}_{\mathrm{on}}$ at different temperatures. The results show that both the normalized magnetic relaxation rate $S(=\ensuremath{-}d\mathrm{ln}M/d\mathrm{ln}t)$ and the pinning potential ${U}_{0}$ exhibit remarkable changes near ${H}_{\mathrm{on}}$ and ${H}_{2p}$ in the temperature region where ${H}_{\mathrm{on}}(T)$ follows the relation of the disorder induced vortex lattice transition, ${H}_{\mathrm{on}}{(T)=H}_{\mathrm{on}}(0)[1\ensuremath{-}{(T/T}_{c}{)}^{4}{]}^{3/2}.$ For both $H<{H}_{\mathrm{on}}$ and $H>{H}_{2p},$ S increases and ${U}_{0}$ decreases, respectively, with increasing magnetic fields. A negative power law of ${U}_{0}(H)\ensuremath{\propto}{H}^{\ensuremath{-}\ensuremath{\alpha}}$ was observed for both $H<{H}_{\mathrm{on}}$ and for $H>{H}_{2p}.$ There exists a minimum in the magnetic-field dependence of $S(H)$ and a maximum in the pinning potential ${U}_{0}(H)$ in the field range between ${H}_{\mathrm{on}}$ and ${H}_{2p}.$ At lower temperature region where ${H}_{\mathrm{on}}(T)$ deviates from the above relation, ${U}_{0}(H)$ behaves differently. The results are discussed in terms of both collective flux creep model and plastic flux creep model.

Magnetic relaxation of Nd 1.85Ce 0.15CuO 4− δ single crystal

The vortex dynamics of a Nd 1.85Ce 0.15CuO 4− δ single crystal was investigated in terms of its magnetic relaxation process. The measurement of time dependent magnetization was carried out in a magnetic field of 750 Oe applied parallel to the c-axis with temperature varying from 5 to 17 K, covering the second peak region and extending below as well as above its temperature range. The normalized relaxation rates S determined from the FC and ZFC data generally exhibit asymmetrical behaviours, and both feature narrow and shallow valleys, interrupting the otherwise monotonic rise of the curve. In particular, the ZFC data for S( T) displays an additional maximum somewhat similar to those found in BSCCO and TBCCO. The data are further analyzed on the basis of collective flux creep model.

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.

Current-driven vortex dynamics in untwinned superconducting single crystals

Current-driven vortex dynamics of type-II superconductors in the weak-pinning limit is investigated by quantitatively studying the current-dependent vortex dissipation of an untwinned single crystal. For applied current densities (J) substantially larger than the critical current density , non-linear resistive peaks appear below the thermodynamic first-order vortex-lattice melting transition temperature , in contrast to the resistive hysteresis in the low-current limit . These resistive peaks are quantitatively analysed in terms of the current-driven coherent and plastic motion of vortex bundles in the vortex-solid phase, and the non-linear current - voltage characteristics are found to be consistent with the collective flux-creep model. The effects of high-density random point defects on the vortex dynamics are also investigated via proton irradiation of the same single crystal. Neither resistive hysteresis at low currents nor peak effects at high currents are found after the irradiation. Furthermore, the current - voltage characteristics within the instrumental resolution become completely ohmic over a wide range of currents and temperatures, despite theoretical predictions of much larger -values for the given experimental variables. This finding suggests that the vortex-glass phase, a theoretically proposed low-temperature vortex state which is stabilized by point disorder and has a vanishing resistivity, may become unstable under applied currents significantly smaller than the theoretically predicted . More investigation appears necessary in order to resolve this puzzling issue.

Dissipation mechanisms in granular high Tc superconductors

We have studied the magnetoresistance and I-V characteristics of polycrystalline La 2− x Sr x CuO 4− y Cl y samples as a function of temperature. Measurements were performed at temperatures near T c and results were modeled taking into account the effect of thermal fluctuations as proposed by the Ambegaokar-Halperin model, the Anderson-kim flux creep theory and the collective flux creep model (CFC). At low voltage, sub-ohmic results are better described by rhe CFC model. We found that the temperature dependence of the critical current density without thermal fluctuations indicates the presence of insulating barriers for non-chlorinated samples and metallic barriers for chlorinated samples. The obtained parameter μ ≅0.25 for both samples is, within the CFC model, in agreement with a picture where non-interacting vortices are pinned in a bidimensional defect array.

Dynamics of flux creep in high- Tc oxide superconductors

A macroscopic description of the magnetization has been carried out by solving the Maxwell equations to investigate the nonlinearity of electric field versus current density characteristics. It has been shown that the log E vs. log J curve has a concave curvature in the low-field region even at low temperature. This result disagrees with the vortex-glass model or the collective flux creep model.

Magnetic Relaxation Studies on Grain-Aligned HgBa2Ca2Cu3Oy Superconductor

Temperature dependent critical current density and flux-creep measurement were carried out in magnetically aligned HgBa2Ca2Cu3Oy . For 20 K<T<60 K, we observed quasi-exponential behavior of the critical current density J c. The normalized relaxation rate S vs T curve has an N-like shape with the minimum around T=15 K and the peak at 50 K. The theoretical U(J) given by the collective flux creep model describes the experimental result well.

Granularity, microstructure, and flux creep in TlBa 2Ca 2Cu 3O 9+δ superconducting powder and silver-sheated tapes

Silver-sheathed TlBa 2Ca 2Cu 3O 9+δ (Tl-1223) tapes, with a transport critical current density, J ct, of 6200 A/cm 2 at 75 K under zero magnetic field, were fabricated by the oxide-powder-in-tube (OPIT) method and characterized using an X-ray diffractometer (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), and superconducting quantum interference device (SQUID) magnetometer. The results of the magnetization and SEM study indicate that, in these tapes, individual grains are distributed randomly in orientation and weak links exist. However, strongly linked percolative current paths within the tape persisting in increasing fields, accompanied by strong intrinsic interplanar coupling, sustain a significant J ct at high fields and lead to the plateau in the J ct- H curve. Dislocation networks, which may act as effective pinning centers, are the common features observed in the tapes. To investigate the effects on flux pinning due to thermomechanical processing, magnetic relaxation at 1 and 2 T over 5–50 K was measured. The tape shows slightly lower normalized relaxation rates ( S=-(1/ M o)d M/ dln t) than the cauliflower-like precursor powder. Analyses of the relaxation data obtained from the tape, after incorporating temperature dependence and field scaling, yield an expression for the effective pinning energy U eff ( J, T, H) = ( U 1/ H 0.54)[1-( T/ 72.5) 2] 4( J/ J i ) μ . This result was compared with the prediction of the collective flux-creep model, which suggests that Tl-1223 has a three-dimension-like (3D-like) vortex lattice. Presumably, a more plate-like powder morphology may result in improved texturing by the OPIT process. Tl 0.5Bi 0.5Sr 2CaCu 2O 7+δ ((Tl,Bi)-1212) powder with this morphology was therefore synthesized for comparison.

Thermally activated coherent vortex motion in YBa2Cu3O7- delta thin film microbridges.

Microbridges with dimensions smaller than the London penetration depth \ensuremath{\lambda} have been prepared in epitaxial ${\mathrm{YBaCu}}_{2}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ thin films by means of electron beam lithography. Typical peaks and kinks are observed in their differential resistance versus current characteristics which can be attributed to coherent flux motion. A vortex activation energy proportional to the inverse current 1/I is obtained. Both the current and the temperature dependence of the activation energy are consistent with the collective flux creep model if the dimensionality of the elastic vortex lattice equals 2.