Flux Creep Theory Research Articles

Flux migration across a closed HTS ring caused by the interaction of the current in the ring and a permanent magnet

By combining the Law of mass action, Arrhenius equation and the magnetic flux creep theory of Kim-Anderson, we proposed a model to depict the flux motion across a current-carrying high temperature superconductor (HTS) ring under an external magnetic field. In this model, the rate of flux motion is exponentially related to the thermal activation energy of trapped fluxes and the level of potential barriers in HTS material. The rate is also proportional to the number density of the flux lines enclosed by HTS ring. To qualitatively validate the rightness of the model, a test was carried out with a “double eye” shaped YBaCuO tape circuit and a permanent magnet at 77 K. The experimental results proved the validity of the model. This model may be helpful for understanding the flux relaxation in HTS loops under an external magnetic field and may account for the flux dynamics of HTS as well.

An inertial model of vortices to explain the extreme sensitivity of hexatic vortex fluid to low frequency ac excitation

Recently, it has been demonstrated that the Hexatic vortex fluid realized in 2-dimensional vortex state of a very weakly pinned amorphous MoGe thin film is extremely sensitive to external ac excitation. A large amplification of resistance is observed when the sample is exposed to external electromagnetic radiation or a small ac current is superimposed with the subcritical measuring dc current. The observed resistance strongly depends on both amplitude and frequency of the ac excitation. In this paper, we develop an inertial model of vortex lattice subjected to a small amplitude of ac current, by extending the flux creep theory. We show that the resistance increases exponentially with both amplitude and frequency of the ac current and explain quantitatively the variation of resistance with the amplitude and frequency of ac current using the presented model.

Vortex pinning and magnetic phase diagram of EuRbFe4As4 iron-based superconductor

We performed systematic AC susceptibility and magnetic moment measurements to investigate the vortex dynamics and pinning in single crystals as a function of temperature, frequency, and DC magnetic field. The vortex solid-liquid line was determined, and it can be fitted well with using β = 1.74 ± 0.1–1.91 ± 0.1, where Tp is the peak position on an imaginary part of the AC susceptibility plot (), for H ab. It indicates a rather high pinning strength of the vortex system. The activation energy U0 was determined from thermally activated flux creep theory and reached 6700 ± 1100 K at low fields, suggesting strong vortex pinning. A field dependence of U0(H ab) ∼ Ha with a = 0.47(4) suggests thermally activated plastic pinning or caused by planar defects. Magnetic moment measurements also confirmed strong pinning in the superconductor, and the superconducting response gives the main contribution to the M(H) hysteresis. Additionally, we show long-range ordering of the Eu2 + sublattice according to the AC susceptibility measurement data.

Flux-creep activation energy for a BaFe1.9Ni0.1As2 single crystal derived from alternating current susceptibility measurements

Systematic ac susceptibility measurements have been performed to investigate the vortex dynamics in a BaFe1.9Ni0.1As2 single crystal as a function of temperature, frequency, ac field amplitude, and dc magnetic field. The complex activation energy U(T,B,j) is derived in the framework of thermally activated flux creep theory and can be expressed in one simple formula. A power law dependence of U∼Bα with α = −0.46 is observed. The activation energy reaches 104 K at low fields, suggesting strong pinning in the material. The nonlinear function of the activation energy vs. the current density is determined, which has the expression of U∝j−0.1.

Comparison of Critical Current Density and Pinning Behaviour of Mono-core MgB2 Wires Prepared by Different Methods

Three series of mono-core MgB 2 wires with Nb sheath embedded in Cu subjected to different heat treatments (600 ∘C/300 min, 650 ∘C/30 min and 700 ∘C/30 min) were produced. For each series, three samples with different starting powder mixtures Mg + B (IS), MgH 2 + B (MH) and Mg + B ball milled (ML) were prepared. Hysteresis loops and magnetic relaxations were measured to calculate critical current density (via Bean’s critical state model) and mean effective activation energy (via Anderson’s flux creep theory). Thus, the highest current densities were obtained for IS and the worst superconducting properties were found for MH wires.

Critical current density and pinning behaviour of mono-core MgB2 wires prepared by internal magnesium diffusion and in-situ powder-in-tube method

Mono-core MgB2 wires were produced by internal magnesium diffusion (IMD) and in-situ powder-in-tube (PIT) technique. Hysteresis loops and magnetic relaxations were measured to calculate critical current density, Jcm (via Bean’s critical state model) and mean effective activation energy (via Anderson’s flux creep theory). To calculate Jcm of the IMD sample, the formulae for typical cylindrical sample geometry must have been modified properly with regard to IMD hollow cylinder geometry. Results for Jcm were compared to direct transport measurements. Also studied was the irreversibility field, Birr, and upper critical field, Bc2. It was found that the dominant difference between wires is in Jc. For the IMD sample, Jc was higher and less field-dependent than Jc of the PIT sample.

Dependence of the flux-creep activation energy on current density and magnetic field for a Ca10(Pt3As8)[(Fe1−xPtx)2As2]5 single crystal

We have performed detailed ac susceptibility measurements to investigate the vortex dynamics in a Ca10(Pt3As8)[(Fe1−xPtx)2As2]5 single crystal as a function of temperature, frequency, ac amplitude, and dc field. The field dependence of the activation energy U is derived in the framework of thermally activated flux creep theory, yielding a power law dependence of U ∼ Hα with α≈ −1.0 for H above 0.30 T, while below 0.3 T U is independent of the field. The activation energy reaches 104 K at low fields, suggesting strong pinning in the material. The nonlinear function of the activation energy vs. the current density is determined, which shows logarithmic dependence U(J)∝lnJ.

Vortex phase transition and isotropic flux dynamics in K0.8Fe2Se2 single crystal lightly doped with Mn

We have applied ac susceptibility measurements to study the vortex dynamics in a high quality K0.79Fe1.86Mn0.01Se2 single crystal with applied magnetic field both parallel and perpendicular to the c-axis. The irreversibility line has been determined in the frequency range of 133 Hz–9777 Hz which can be well fitted using Hirr=H0(1−T/Tc)β with β=1.49 for H∥c and β=1.63 for H∥ab. The field dependence of the activation energy U0 is derived in the framework of thermally activated flux creep theory, yielding a power law dependence ∼Hn with n≈−0.58 for H below 0.75 T and n≈−1 for H above 0.75 T. The derived activation energy U0 shows nearly isotropic behavior for both field directions and high values reaching 105 K at low fields. This observation points towards very strong intrinsic pinning in the investigated material, thus making KFeSe-systems promising for technical applications.

Effect of Packing Density on Critical Current Density at High Magnetic Fields in Polycrystalline MgB2 Superconductors

It is well understood that the critical current density in polycrystalline MgB2 superconductors is severely restricted by porosities and wet insulating layers that cover superconducting grains. The relationship between critical current density and electrical connectivity is well explained by the prediction of the percolation theory. Recently, it has been found that the irreversibility field that directly influences the high-field performance of the critical current density is also dependent on electrical connectivity. This behavior is explained by the finding that superconducting grains with the c-axis tilted by a small angle from the direction of applied magnetic field lose their superconductivity at relatively low magnetic fields owing to the low irreversibility field, resulting in a decrease in the effective packing density. This phenomenon is theoretically investigated using the percolation theory and the theory of flux creep and flow. The obtained result explains the experimental result well. This shows that the packing factor of MgB2 is also important for improving the critical current density at high magnetic fields.

The scaling analysis on effective activation energy in HgBa2Ca2Cu3O8+δ

We review the methods of calculating the effective energy Ueff(T,B,J) for both transport measurements and magnetic decay, and suggest a new resistivity expression that is compatible with both vortex glass theory and thermal assistant flux creep theory. Then we apply these methods in our HgBa2Ca2Cu3O8+δ single phase superconductor to obtain the activation energy. Transport results confirm that the magnetic field and temperature dependence of the Ueff(T,B) can be well described by our new model. Magnetic relaxation data shows that the current density dependence of Ueff(J) can be scaled onto a single curve following the vortex glass theory. The exponent obtained from the scaling law is 0.978 in the temperature range 4.2–60 K, close to the value of 7/9 in the regime of flux creep in large vortex bundles predicted by vortex glass theory.

Organization of flux line system and voltage oscillations in superconducting MgB2

The influence of bidirectional square wave (BSW) current on the evolution of the V–t curves was studied in a polycrystalline sample of MgB2. Regular sinusoidal-like voltage oscillations were observed at well-defined values of the amplitude (IBSW) and period (PI) of the BSW current, temperature, and external magnetic field. The voltage oscillations were interpreted mainly in terms of short- and long-range spatial correlations in a flux line system, relaxation effects, and the dynamic competition between pinning and depinning. The oscillating mode was also discussed in terms of sliding charge density waves associated with density fluctuations. Alternatively, the coupling between conventional thermally activated flux creep theory and annealing of the disordered states was considered as another possible mechanism in describing the voltage oscillations. Due to the complex interplay of pinning and driving forces, the oscillating mode is correlated to the drifting of flux lines, which are in motion, and it is assumed that the majority of flux lines try to traverse the sample, but do not leave it entirely. The symmetry in voltage oscillations was attributed to the equality between flux exit and entry along the sample edges. In this process, the majority of flux lines leave the sample and the direction of motion of flux lines reverses. During the oscillatory motion, we suggest that the interaction between flux lines and pinning centers may be elastic coupling in nature, because of rigidity of the flux line lattice in MgB2. Non-oscillatory behavior of V-t curves measured for BSW drive with low PI was attributed pre-dominantly to the effect of pinning on the distribution of the flux lines. The vortex capacitor model could be applied to explain the voltage decays in these V-t curves. However, the voltage decays associated with switching of IBSW to dc current (Idc) were correlated to current-induced quenched disorder and to the glassy state relaxation. Further, angular dependence of voltage oscillations reveals that the anisotropic effects are nearly negligible on the evolution of V-t curves. It was shown that the voltage oscillations can be described well by an empirical expression V(t) ∼ sin(wt + φ), where w is the frequency and φ is the phase angle. Finally, at well-defined values of IBSW and PI of BSW current, H, and T, it was argued that the MgB2 sample behaves like a double-integrator.

Suppression of dissipative flux-motion in a high-Tc (Bi,Pb)-2212 superconductor by Dy-doping

The temperature and magnetic field dependences of the activation energy and flux-pinning properties of Dy-doped (Bi,Pb)-2212 superconductor are systematically measured for a broad doping range. The behaviour of vortex dynamics close to a vortex-liquid to glass transition [ U o ( B , T g ) = k B T g ] is analysed by the modified thermally activated flux-creep theory. The results show that the temperature and field dependence of U o ( B , T ) is related to the strong thermal fluctuation at elevated temperatures and fields which can be suppressed by the introduction of the point defects due to Dy-doping. These point defects act as additional flux-pinning centers and the superconductor remains in the glassy-vortex-state.

Growth of YBa2(Cu,Co)4O8 Single Crystals Under Ambient Pressure and Their Superconducting Properties

We report the growth of superconducting YBa 2 (Cu,Co) 4 O 8 single crystals using KOH flux under ambient pressure and their superconducting properties. The average size of the YBa 2 (Cu,Co) 4 O 8 single crystals is 0.3 ×0.3 ×0.2 mm 3 . The superconducting transition temperature ( T c ) of the parent material is found to be 81 K, indicating a stoichiometric oxide superconductor. The T c and the c -axis length of YBa 2 (Cu,Co) 4 O 8 single crystals decrease systematically with increasing the Co-doping content. A comparison of the magnetic irreversibility with the flux-creep theory from the viewpoint of homogeneity/inhomogeneity is made.

Superconducting characteristics of (Bi, Pb)-2223 single crystals with controlled oxygen-content

Critical current density was measured for oxygen-controlled (Bi, Pb)-2223 single crystals before and after the irradiation with gold ions in a magnetic field parallel to the irradiation-induced defects along the c-axis. Eleven specimens prepared in different annealing conditions were measured. The condensation energy density of each specimen was evaluated from the observed critical current density by using the summation theory of pinning forces of columnar defects and the flux creep theory. It was found that the specimen heat-treated at 1 atm in oxygen atmosphere has the highest condensation energy density among all specimens. Hence, it is speculated that the optimum oxygen pressure for the anneal is around 1 atm.

Irreversibility line and flux pinning properties in iron-based high- T c superconductor SmFeAsO 0.85

The irreversibility line and flux pinning properties of high- T c superconductor SmFeAsO 0.85 were studied using DC magnetization data. Polycrystalline SmFeAsO 0.85 was prepared in a high pressure synthesis apparatus under the pressure of 6 GPa. The results of DC susceptibility showed the superconducting transition at about 55 K. A critical current density J c ( B) was calculated using Bean’s critical state model. At low temperatures (⩽20 K), J c ( B) showed a relatively high value with weak dependence on an applied magnetic field. At higher temperatures, a stronger dependence of the magnetic field was observed, which resulted from decrease in a critical current density probably due to the flux creep effect. The irreversibility line (IL) agreed well with the flux creep theory of Matsushita et al. A comparison of normalized pinning force density with the theoretical models showed that the irreversible behavior in SmFeAsO 0.85 is dominated mainly by normal point pinning (δ T c ) and surface pinning mechanisms.

Critical currents and pinning forces inNd2−xCexCuO4−δthin films

Critical current density, ${J}_{c}$, and flux-pinning force density, ${F}_{p}$, have been investigated at different temperatures in electron-doped ${\text{Nd}}_{2\ensuremath{-}x}{\text{Ce}}_{x}{\text{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ thin films for magnetic fields, $H$, applied parallel to the $c$ axis. The reduced pinning force density $f\ensuremath{\equiv}{F}_{p}/{F}_{p}^{\text{max}}$ shows a clear scaling behavior when $H$ is normalized to the irreversibility field ${H}^{\ensuremath{\ast}}$, indicating the presence of the same pinning mechanism in the investigated temperature range. Moreover the maximum of ${F}_{p}$ as function of the field at each temperature depends linearly on ${H}^{\ensuremath{\ast}}$. The experimental data, interpreted using a modified Anderson-Kim description of the flux-creep theory, imply a magnetic field dependence of the activation energy $U(H)\ensuremath{\sim}{H}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=0.8$. This value indicates that in ${\text{Nd}}_{2\ensuremath{-}x}{\text{Ce}}_{x}{\text{CuO}}_{4\ensuremath{-}\ensuremath{\delta}}$ a quasi-two-dimensional vortex system is present, intermediate between Bi-based and Y-based hole-doped compounds.

Relaxation properties of magnetic force between a magnet and superconductor in anunsymmetrical levitation system

We present an experimental study of the relaxation of vertical and horizontal forcecomponents in an unsymmetrical high-temperature superconducting levitation system, withdifferent initial cooling processes, after fixing the levitated body statically in agiven position. It was found that the values of the relaxation measurements of thelevitation force and lateral force remained constant or increased with time aftervertical and horizontal traverses. The phenomenon has been theoretically describedbased on the Bean model and the thermally activated flux creep theory. Thecriterion developed in the present work is considered to be suitable for providingqualitative predictions of the relaxation properties in the levitation force and lateralforce.

Limits to the critical current inBi2Sr2Ca2Cu3Oxtape conductors: The parallel path model

An extensive overview of a model that describes current flow and dissipation in high-quality ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{Ca}}_{2}{\text{Cu}}_{3}{\text{O}}_{x}$ superconducting tapes is provided. The parallel path model is based on a superconducting current running in two distinct parallel paths. One of the current paths is formed by grains that are connected at angles below $4\ifmmode^\circ\else\textdegree\fi{}$. Dissipation in this strongly linked backbone occurs within the grains and is well described by classical flux-creep theory. The other current path, the weakly linked network, is formed by superconducting grains that are connected at intermediate angles $(4\ifmmode^\circ\else\textdegree\fi{}--8\ifmmode^\circ\else\textdegree\fi{})$ where dissipation occurs at the grain boundaries. However, grain boundary dissipation in this weakly linked current path does not occur through Josephson weak links, but just as in the strongly linked backbone, is well described by classical flux creep. The results of several experiments on ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{Ca}}_{2}{\text{Cu}}_{3}{\text{O}}_{x}$ tapes and single-grained powders that strongly support the parallel path model are presented. The critical current density of ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{Ca}}_{2}{\text{Cu}}_{3}{\text{O}}_{x}$ tapes can be scaled as a function of magnetic field angle over the temperature range from 15 K to 77 K. Expressions based on classical flux creep are introduced to describe the dependence of the critical current density of ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{Ca}}_{2}{\text{Cu}}_{3}{\text{O}}_{x}$ tapes on the magnetic field and temperature.

Granular superconductivity in YBa 2Cu 3O 7−δ single crystals by divalent impurities doping: Possible role of valence and orbital symmetry

We have investigated the effect of divalent Ca, Sr and Zn atoms at the Y, Ba and Cu sites, respectively, of the YBa 2Cu 3O 7− δ single crystal on the magnetoconductivity and magnetic irreversibility properties for H|| c axis and J|| ab plane. The resistive transition is a clear two-step process. While the upper temperature step is only weakly affected by low applied fields, the lower temperature step is visibly broadened and shifted down to lower temperatures. Between upper and lower temperature steps lays the magnetic irreversibility line, T irr( H) which follows the power law predicted by the flux creep theories in most of the high field range. However, in a low field region, the T irr( H) exhibits two different regimes dominated by disorder and frustration and characterized by the de Almeida–Thouless and Gabay–Toulouse power law behaviors. We attribute the origin of the observed stepwise resistive transition and low field magnetic irreversibility regimes mainly to the granularity of the superconducting state of our doped samples and contrast our magnetic irreversibility present results with those of a pure YBa 2Cu 3O 7− δ single crystal. We suggest that the valance as well as the local breaking of the orbital symmetry by impurities plays an important role in the induction of this state. On the other hand, our results show that granular superconductivity can be induced in the YBa 2Cu 3O 7− δ system by divalent impurities doping in whatever site Y, Ba or Cu.

On the temperature dependence of the magnetic hysteresis widths observed in grain-alignedHg(Re)-1223 specimens

The magnetic field and temperature dependence of the magnetic hysteresis loop,ΔM, forgrain-aligned HgRe0.18Ba2Ca2Cu3O8+y specimens have been measured for two directions of field parallel (-axis) and perpendicular (-plane) to the c-axis of the crystal structure. The irreversibility field,Birr = μoHirr, for each field direction is well fitted by a flux creep theory from Matsushitaet al (1990 Appl. Phys. Lett. 56 2039). The magnetic field dependence of theΔM is fairly well described by using the resultant fitting parameters in the low-temperatureregion, but coincidence between experimental results and the theoretical curveis poor in the high-temperature region. The temperature dependence ofΔM in the low-temperature region is well described by the collective pinning theory ofFeigel’man et al (1989 Phys. Rev. Lett. 63 2303) or by the flux creep theory of Matsushitaet al. However, the dependence in the high-temperature region is far from thepredicted curves of these theories, so we tried to fit Burlachkov et al’ s theory(1994 Phys. Rev. B 50 16770) to the experimental results, which means that two-dimensional(2D) pancake vortices surmount the surface potential barrier. An exponential decay of theΔM with increasing temperature in the high-temperature region has been successfully explainedby the theory.