Flux Creep Rate Research Articles

Effect of External Nonuniform Magnetic Field on Flux Creep Process in Superconductor

The effect of an external nonuniform magnetic field on the flux creep rate in a high-temperature superconductor with trapped magnetic flux was studied. The magnetic relaxation was suppressed when the superconductor was put into a field of permanent magnets or when it approached a ferromagnet. The effect arises when the field sources (being magnetized, the ferromagnet produces its own field) are placed near the superconductor surface, where the flux line ends are located. For these cases, we carried out the calculations of vortex and current density distributions, which demonstrate that reverse currents flow in the near-surface regions of the sample. This verifies the hypothesis suggested earlier about the influence of counter Lorentz forces retarding the creep of the vortices. In the interpretation of the results, we also take into consideration the magnetic force acting on the vortex ends in the external nonuniform magnetic field that allows us to explain the experimental results, in which the current structure in the sample is unipolar.

Influence of Field Decrements on the Relaxation Behavior of Thin High- $T_{c}$ Superconductors Measured Using a Levitation Balance

Conventional relaxation measurements on various samples (a YBa2Cu3O7-δ thin film, a YBa2Cu3O7-δ-coated conductor, and a Bi2Sr2Ca2Cu3O10+δ tape) using a levitation balance are presented that are measured after a departure from the critical state by means of a small retraction Δd of the permanent magnet, which corresponds to a small field reduction ΔHα. In the case of YBa2Cu3O7-δ, flux creep rates S are found to decrease with increasing ΔHα until a small plateau is reached, where flux creep is effectively stopped. A further increase in ΔHα before the relaxation measurement leads to a change of sign of the creep rate. For the Bi2Sr2Ca2Cu3O10+δ tape, only a continuous decrease in S is obtained. An explanation of this effect is given based on calculations of flux density profiles and critical current densities in perpendicular geometry. The differences to the Bean model (i.e., longitudinal geometry) are discussed.

Critical currents, magnetic relaxation and pinning in NdBa2Cu3O7−δ films with BaZrO3-generated columnar defects

The critical current density Jc and the magnetic relaxation (‘creep’) properties have been studied for a set of NdBa2Cu3O7−δ (NdBCO) films doped with BaZrO3 (BZO) nanoparticles to form columnar defects. The dependence of Jc on the magnitude and orientation of the applied magnetic field Happ (0–6.5 T) and temperature T (5 K–Tc) was investigated. The normalized flux-creep rate S =− dln(J)/dln(t) was determined as a function of T. The current dependence of the effective activation energy Ueff(J) was derived using the formalism developed by Maley. The results are well described by an inverse power law type barrier of the form Ueff(J) ∼ U0(J0/J)μ with fitted values for the pinning energy scale U0 and the glassy exponent μ. When comparing values for these parameters in the BZO-doped samples with those for their undoped control counterparts, the most striking difference is the larger scale of current density J0 in the doped samples (a factor of 2.4 higher), while the other pinning parameters do not differ strongly. In the BZO-doped materials, the pinning energy scale U0 increases with vortex density and J0 decreases, with both following simple power law dependences on the field.

Strong pinning and elastic to plastic vortex crossover in Na-doped CaFe2As2single crystals

We study the vortex dynamics of NaxCa1-xFe2As2 single crystals with x = 0.5 (underdoped) and x = 0.75 (optimally doped), having T-c approximate to 19.4 and 33.4 K, respectively, by performing magnetization measurements of the critical current density J(c) and flux creep rate S. We find that the J(c) versus temperature, T, dependence is consistent with delta T-c pinning, indicating strong pinning associated with randomly distributed defects larger than the coherence length xi. The temperature dependence of S shows a crossover between glassy (elastic) and plastic creep regimes. The boundary T-cr(H) between both creep regimes coincides with the upper limit of the regime of strong pinning by nanoparticles. The glassy exponent mu in the optimally doped crystal is consistent with the thermal collective creep theory previously applied to cuprate superconductors, but in the underdoped sample the plateau in S(T) indicates that mu approximate to 3-3.3, a value larger than the existing theoretical predictions. We discuss the quantum creep contributions in both samples.

Mixed pinning landscape in nanoparticle-introduced YGdBa2Cu3Oyfilms grown by metal organic deposition

We study the field (H) and temperature ($T$) dependence of the critical current density (${J}_{c}$) and irreversibility field (${H}_{\mathrm{irr}}$) at different field orientations in ${\mathrm{Y}}_{0.77}$Gd${}_{0.23}$Ba${}_{2}$Cu${}_{3}$O${}_{y}$ with randomly distributed BaZrO${}_{3}$ nanoparticles (YGdBCO$+$BZO) and YBa${}_{2}$Cu${}_{3}$O${}_{y}$ (YBCO) films. Both MOD films have large RE${}_{2}$Cu${}_{2}$O${}_{5}$ (225) nanoparticles (\ensuremath{\sim}80 nm in diameter) and a high density of twin boundaries (TB). In addition, YGdBCO$+$BZO films have a high density of BZO nanoparticles (\ensuremath{\sim}25 nm in diameter). At high temperatures ($T$ g 40 K), the superconducting properties, such as ${J}_{c}$, ${H}_{\mathrm{irr}}$, and flux creep rates, are greatly affected by the BZO nanoparticles, while at low temperatures the superconducting properties of both the YBCO and YGdBCO$+$BZO films show similar field and temperature dependencies. In particular, while the ${J}_{c}$ of YBCO films follow a power-law dependence ($\ensuremath{\propto}{H}^{\ensuremath{-}\ensuremath{\alpha}}$) at all measured $T$, this dependence is only followed at low $T$ for YGdBCO$+$BZO films. As a function of $T$, the YGdBCO$+$BZO film shows ${J}_{c}(T,0.01T)~[1\ensuremath{-}(T/{T}_{c}){}^{2}]{}^{n}$ with $n$ \ensuremath{\sim} 1.24 \ifmmode\pm\else\textpm\fi{} 0.05, which points to ``$\ensuremath{\delta}{T}_{c}$ pinning.'' We analyze the role of different types of defects in the different temperature regimes and find that the strong pinning of the BZO nanoparticles yields a higher ${H}_{\mathrm{irr}}$ and improved ${J}_{c}$ along the $c$ axis and at intermediate orientations at high $T$. The mixed pinning landscapes due to the presence of disorder of various dimensionalities have an important role in the improvement of in-field properties.

Critical current densities and flux creep rate in Co-doped BaFe2As2 with columnar defects introduced by heavy-Ion irradiation

We report the formation of columnar defects in Co-doped BaFe2As2 single crystals with different heavy-ion irradiations. The formation of columnar defects by 200MeV Au ion irradiation is confirmed by transmission electron microscopy and their density is about 40% of the irradiation dose. Magneto-optical imaging and bulk magnetization measurements reveal that the critical current density Jc is enhanced in the 200MeV Au and 800MeV Xe ion irradiated samples while Jc is unchanged in the 200MeV Ni ion irradiated sample. We also find that vortex creep rates are strongly suppressed by the columnar defects. We compare the effect of heavy-ion irradiation into Co-doped BaFe2As2 and cuprate superconductors.

Critical Current Densities and Vortex Dynamics in Ba(Fe1−x Co x )2As2 Single Crystals

Superconducting properties are evaluated for high-quality single crystals of Ba(Fe1−xCox)2As2 in a wide range of doping levels. The critical current density, Jc, in an optimally-doped crystal (Tc∼24 K) shows a fishtail effect with its value over 105 A/cm2 even at 5 T below 10 K. Magneto-optical imaging has clarified rather homogeneous supercurrent flow in the crystal, in spite of a large amount of impurities. In the heavy-ion irradiated sample, the presence of columnar defects are confirmed and Jc has been enhanced by a factor of five at low temperatures, reaching 6×106 A/cm2 at 2 K under zero field. Flux creep rate in the heavy-ion irradiated sample has been reduced in accordance with the enhancement of Jc.

The Effect of a Ferromagnetic Medium on the Field of YBCO Trapped Field Magnets

Trapped field magnets (TFMs) are characterized by the maximum field they can retain when they are activated in air (~vacuum). In some applications however, TFMs are partially embedded in a ferromagnetic medium. We consider, experimentally and theoretically, some simple geometries involving contact between TFMs and ferromagnetic media. We find: an increase in maximum TFM field exceeding a factor of 2.53; a change in field profile from the well-known conical TFM field to a uniform field in the ferromagnetic material; and fields produced by present day TFMs capable of saturating Hyperco-50 alloy. The observed flux creep rate of the TFM field was found to be the same in air and in contact with ferromagnetic material.

Temperature dependence of pinning potentials in grain-aligned and Re-doped Hg-1223 superconductors

Effect of grain alignment and Re-doping on the flux-creep phenomena in Hg-1223 superconductors is investigated. Hg-based superconductors of HgBa 2Ca 2Cu 3Re x O y ( x = 0.15 and 0.18) were fabricated by high vacuum sealing and sintering method using a precursor. Grain alignment was formed magnetically under external magnetic field of 10 T. Connectivity between the superconducting CuO 2 layers is known to be enhanced with addition of Re. Flux creep characteristics and DC magnetizations were measured using a SQUID magnetometer at temperature range 5–150 K under magnetic fields up to 1 T. The pinning potentials U 0 ∗ estimated from the logarithmic time dependence of the magnetization for B∥ ab are generally larger than those for B∥ c. Non-linear relation of pinning barrier energy U( J) on current density J leads to apparently low energy in the high J region which is remarkable at low temperatures. Independence of the U 0 ∗ on the applied fields B∥ c in this region and increase of the U 0 ∗ with lowering B∥ ab indicate the difference of non-linearity. In addition, temperature dependence of the flux creep rate S is favorably compared with the Anderson–Kim model.

Temperature dependence of critical current density and flux creep of Hg(Re)-1223 powdered specimens

Magnetic hysteresis and flux creep phenomena of grain aligned HgRe 0.18Ba 2Ca 2Cu 3O y powder samples have been measured by SQUID and PPMS. The critical current densities for two field directions of B∥ c-axis and B∥ ab-plane showed J c( B∥ c-axis)> J c( B∥ ab-plane) in low temperature region. But the J c( B∥ c-axis) began to reduce abruptly at a certain temperature and became smaller than the J c( B∥ ab-plane) in higher temperature region. Such abrupt change was also measured in the flux creep phenomena, i.e. so called flux creep rate S=| d( lnΔM/ ΔM 0)/ d ln t| reduces at temperature which is approximately the same as the J c( B∥ c-axis) anomaly arises. Such anomaly is also observed in the temperature dependence of the magnetization itself at relevant magnetic field. Temperature dependence of the S is successfully analyzed by the Kim–Anderson model and the collective creep model.

Fishtail effect studied by ac susceptibility in ErBa2Cu3O7−δ single crystal

The second magnetization peak (SMP), also known as the fishtail effect, is studied by a scaling procedure for ac susceptibility measurements. From this scaling law the frequency dependence of the critical current J(ν) and the flux creep exponent n can be determined. A striking correlation between n and the SMP is observed, which indicates a clear change in the rate of flux creep around the peak position. This result points to the relevance of the dynamical contribution for the peak formation. However, we could not observe a transition between two different regimes of vortex motion at the SMP. The dependence of the SMP with sample dimensions is also discussed.

Anisotropic flux creep in Bi2212:Pb single crystal in crossed magnetic fields

An experimental study of magnetic flux penetration under crossed magnetic fields in Bi2212:Pb single crystals is performed by the magneto-optic technique. The anisotropy of the flux creep rate induced by the in-plane magnetic field is observed at T<54±2 K. This observation confirms the existence of the three-dimensional flux line structure in Bi2212:Pb at low temperatures. An asymmetry of the flux relaxation with respect to the direction of the in-plane field is found. This effect can be attributed to the influence of the laminar structure on the pinning in Bi2212:Pb single crystals.

Magnetic properties of Ag-added Gd–Ba–Cu–O superconductors

In order to obtain helpful guidelines for designing high- T c bulk superconductor magnet systems, the gap, temperature and time dependence of the trapped field for Y–Ba–Cu–O and Gd–Ba–Cu–O/Ag bulk superconductors were measured. For the gap dependence, we compared the experimental results and the analytical solution on the condition that J c is constant for the disk-shaped bulk superconductor, and we found that the analytical solution corresponds well with the experimental results. The peak value of the trapped field reached 4.6 T at 63 K for the Gd–Ba–Cu–O bulk superconductor, and the flux creep rate at 63 K was slower than that at 70 and 77 K. This indicates that cooling down to at least 63 K creates superior conditions for the bulk magnet in respect of the increasing trapped field and its stability.

Magnetic relaxation measurement of the infinite-layer superconductor Sr 0.9La 0.1CuO 2

The relaxation of the irreversible magnetization in the superconducting state for the grain-aligned electron-doped infinite-layer superconductor Sr 0.9La 0.1CuO 2 was measured. The normalized flux creep rate, S( T), and the current-dependent activation barrier, U( j), were obtained. Based on S( T) and U( j), three different magnetic relaxation behaviors were observed in the superconducting state, and this is quite different from what is seen in the highly anisotropic cuprate superconductors. Even compared to the absolute value of S( T) for the most isotropic superconductor YBa 2Cu 3O 7− δ among the cuprate superconductors, the absolute value of S( T) for Sr 0.9La 0.1CuO 2 is quite small. Along with the recent observation of a striking s-wave gap symmetry and the absence of any significant spin fluctuation in this electron-doped cuprate, which is quite different from the behavior seen in hole-doped cuprates, the magnetic properties of Sr 0.9La 0.1CuO 2 are not very similar to those of the hole-doped cuprates. U( j) has a H − α form with α≈0.2. This value is quite different from the predictions of the Yeshurun and Malozemoff model and the Tinkham model where α=1.

Critical currents, flux-creep activation energy, and potential barriers for the vortex motion from flux-creep experiments

We present an experimental study of thermally activated flux creep in a superconducting ring-shaped epitaxial YBCO film as well as a new way of analyzing the experimental data. The measurements were made in a wide range of temperatures between 10 and 83 K. The upper temperature limit was dictated by our experimental technique and at low temperatures we were limited by a crossover to quantum tunneling of vortices. It is shown that the experimental data can very well be described by assuming a simple thermally activated hopping of vortices or vortex bundles over potential barriers, whereby the hopping flux objects remain the same for all currents and temperatures. The new procedure of data analysis also allows to establish the current and temperature dependencies of the flux-creep activation energy U, as well as the temperature dependence of the critical current Ic, from the flux-creep rates measured at different temperatures. The variation of the activation energy with current, U(I/Ic), is then used to reconstruct the profile of the potential barriers in real space.

Flux creep in heavily lead doped Bi2212 single crystal

A comparative study of normalised flux creep rate S(T,H) for heavily lead doped Bi2212 single crystal and pure Bi2212 single crystal has been performed. A sharp anomaly in S(T) was observed at a temperature T = T CR, a cross over temperature below which collective pinning theory is valid for Bi2212 pure single crystal. Observed S(T) over a wide temperature range for the lead doped sample revealed a shift of T CR to a higher temperature. X-ray measurements showed a decrease of c-axis parameter with lead doping for this sample. The reduction of c-axis parameter improved the inter-layer coupling of the pancake vortices, enhancing the vortex pinning and causing the shift of the peak in S(T) towards a higher temperature. The critical current density J c as a function of field also indicated strong pinning in the lead doped sample, as compared to pure Bi2212 single crystals.

Magnetic relaxation in a commercial Bi:2223/Ag tape at 77 K

The evolution of the rate of flux creep along the major hysteresisenvelopes and along bridges between the envelopes in a commercial Bi:2223/Agtape at 77 K has been investigated. Magnetic relaxation rates depend stronglyon the prior magnetic history. It was found that the Bi:2223/Ag tape samplehas large flux creep along the hysteresis envelope. Flux creep activationenergy was calculated to be 0.12 eV from the rate of decay for the remanentmagnetization of 6 mT.

Flux-pinning enhancement in Ag-sheathed Bi-2223 tapes by nanometer-SiC addition

We have studied the influence of nanometer SiC particles on the flux pinning and the magnetization critical current density J cm of Ag-sheathed (Bi,Pb) 2Sr 2Ca 2Cu 3O x superconducting tapes. The results show that below 40 K SiC particles up to 0.5 wt.% introduce additional flux-pinning centres, and enhance J cm to different extent dependent on the temperature and applied magnetic field. For the tapes with SiC addition up to 0.5 wt.%, the magnetization critical current density J cm at 5 K in applied fields up to 50 kOe is twice that of the tape without SiC, for both H∥ c and H∥ ab. A study of the magnetization decay shows that tape with 0.15 wt.% nanometer SiC particles has a reduced flux-creep rate and increased pinning potential compared with the tape without SiC. The enhanced pinning properties can be attributed to the small SiC particles dispersed in the superconducting matrix and to the secondary defects at the interface between SiC particles and the superconducting matrix created by the introduction of the SiC particles.

Nonlinear flux diffusion in superimposed weak AC magnetic field

The influence of superimposed weak ac magnetic field on flux creep and relaxation phenomena is studied theoretically for a superconducting slab in superimposed dc and weak ac magnetic fields parallel to the slab surface. Nonlinear flux diffusion equations are solved with appropriate periodical boundary conditions, which describe the influence of the ac field component. The flux creep rate and magnetization decay are enhanced by the ac field as a result of rather strong nonlinearity of flux diffusion. The long-time relaxation profiles of electric field and shielding current change significantly as compared to the well-known stationary solutions in the absence of ac field. These results reflect rather general properties of nonlinear systems, namely the possibility of the large effect of small perturbations on the long-time behavior of a nonlinear system.

Flux creep and irreversibility line in superconducting Pb-Bi alloys

The critical current density, J/sub c/, in high-temperature superconductors becomes zero at irreversibility field, B/sub irr/, appreciably lower than the upper critical fields, B/sub c2/. The enhancement of J/sub c/ and B/sub irr/ is one of the crucial subjects to be attained. In high-temperature superconductors, conclusive result has not yet been presented because of the complexity of the material structure and in low-temperature superconductors scientific interest has not been paid because of the vanishingly small deviation of B/sub irr/ from B/sub c2/. In this study, we'll apply a simple system of low-temperature superconductor Pb-Bi, whose pinning characteristics were fully examined and controllable, to understand the relation of B/sub irr/ and the pinning mechanism. Observed irreversibility field, B/sub irr/, is discussed using the pinning characteristics and numerical calculation based on the flux creep theory. Magnetic relaxation caused by the flux creep was also observed by SQUID magnetometer. The relation of the apparent pinning potentials, U*/sub 0/, estimated from the flux creep rate and the irreversibility field, B/sub irr/, are studied.