Labusch Parameter Research Articles

The Labusch parameter of a driven flux line lattice in YBa Cu O superconducting films

We have investigated the influence of a driving force on the elastic coupling (Labusch parameter) of the field-cooled state of the flux line lattice (FLL) in 400 nm thick YBa$_2$Cu$_3$O$_7$ superconducting films. We found that the FLL of a field-cooled state without driving forces is not in an equilibrium state. Results obtained for magnetic fields applied at $0^\circ$ and 30$^\circ$ relative to CuO$_2$ planes, show an enhancement of the elastic coupling of the films at driving current densities several orders of magnitude smaller than the critical one. Our results indicate that the FLL appears to be in a relatively ordered, metastable state after field cooling without driving forces.

The Labusch Parameter of a Driven Flux Line Lattice in YBa2Cu3O7Superconducting Films

We have investigated the influence of a driving force on the elastic coupling (Labusch parameter) of the field-cooled state of the flux line lattice (FLL) in 400 nm thick YBa2Cu3O7superconducting films. We found that the FLL of a field-cooled state without driving forces is not in an equilibrium state. Results obtained for magnetic fields applied at 0° and 30° relative to CuO2 planes, show an enhancement of the elastic coupling of the films at driving current densities several orders of magnitude smaller than the critical one. Our results indicate that the FLL appears to be in a relatively ordered, metastable state after field cooling without driving forces.

Peak effect of critical current in an untwinned Y-123 superconducting single crystal

Broad double peaks of the critical current density were observed in an untwinned Y-123 single crystal prepared by a pulling technique. Force-displacement characteristics of flux lines were measured using the Campbell method in the vicinity of the peak fields. It was found that the interaction distance decreased monotonically in a wide range of the field, while the increasing rate of the Labusch parameter changed appreciably at the magnetic field at which the critical current density started to increase. These results are completely different from those in the case of Bi-2212. This fact seems to suggest that the peak effect is ascribed to the change in the flux-pinning mechanism but not to the change in the property of flux lines. Field-induced pinning by weakly superconducting regions seems to be a candidate for the responsible pinning mechanism. However, the characteristic field at which the critical current density starts to increase increases with elevating temperature. Hence, this temperature dependence cannot be explained by such a simple mechanism. The synchronization mechanism known in metallic superconductors may also work in Y-123.

Peak effect of critical current in a Bi-2212 superconducting single crystal

Force-displacement characteristics of flux lines were measured using the Campbell method in the vicinity of the peak effect for an overdoped Bi-2212 single crystal. It was revealed that there are two quasi-stable states with different critical current densities, suggesting a phase transition of the first order. It was also found that the interaction distance increased discontinuously around the peak field, while the Labusch parameter showed no anomaly. This shows that the flux-pinning mechanism does not change across the peak field and that the peak effect is caused by the change in the property of flux lines. It is considered that the dimensional crossover of flux lines brings about the first-order transition and such characteristics. The elastic correlation length of flux lines along the c-axis was of the order of and agreed with the theoretical prediction. This shows that the flux lines are not in the complete two-dimensional state even above the peak field.

Force-displacement characteristic of fluxoids along the c-axis in superconducting Bi-2212 single crystal near the peak field

Force-displacement characteristic of fluxoids in a superconducting Bi-2212 single crystal was measured by using the Campbell method at low temperatures and low magnetic fields where the peak effect of critical current density was observed. It is found that the interaction distance, d i, has a peak around the peak field while the Labusch parameter, α L, increases monotonously with increasing magnetic field. The peak of d i means an increment of flexibility of fluxoids to randomly distributed pins and this is considered to be brought about by some deformation of fluxoid cores along the length. Although this may be associated with the cross-over from three-dimensional flux lines to two-dimensional pancakes, the characteristic length of deformation is considered to be much longer than the distance between the CuO 2 planes.

Linear response in the AC susceptibility of vortices in YBa 2Cu 3O 7 crystals with columnar defects

We explore the AC magnetic susceptibility of YBa 2Cu 3O 7 single crystals with columnar defects. For vortices parallel to the defects the linear response is mainly determined by the Campbell penetration depth with a field independent Labusch parameter indicating that vortices are individually pinned. The small dissipation in this limit is likely to arise from thermal fluctuations of vortex segments between pairs of metastable states (two-level systems) in the Bose glass phase. Tilting vortices away from the tracks results in a reduction of the Bose glass temperature and an increase of the dissipation due to the reduction of the pinning forces. We discuss the onset of nonlinear response as the AC field increases.

Relaxation effects in HTc-Superconducting Thin Films

Mechanical relaxation experiments have been widely applied to bulk high temperature (HT C ) superconducting materials. In contrast to that only few results obtained on HT C superconducting thin films were reported. None dealt with stress driven phenomena due to the high background damping from the substrate materials used. In applied magnetic fields, however, a host reed technique can be used and the measured damping then gives information about the superconducting properties of the sample. We will discuss some experimental aspects and describe the basic information which was obtained on YBa 2 CU 3 O 7-X and Bi 2 Sr 2 CaCu 2 O 8+X thin films. This includes the lower critical field, the Labusch parameter, pinning energies related to the model of thermally assisted flux flow (TAFF), and a matching effect of the flux line lattice (FLL) to the thickness of the films.

Numerical calculation of elastic pinning parameters by point pins

One-dimensional numerical simulations of the pinned vortex lattice have been carried out using an inverted model in which widely spaced and weak point pinning centres are distorted by a rigid lattice. This allows us to simulate a much larger array than if we had to find the position of each vortex separately. Using steepest descent and molecular dynamics methods, the Labusch parameter is found to have similar power law dependencies on the density of pins and elementary pinning force to the bulk pinning force. This implies that the maximum reversible displacement is a constant and it is found to be roughly 0.2 of a vortex spacing. The results are in agreement with the Larkin-Ovchinnikov theory of collective pinning. Quasi-static shifting of the pins over the rigid vortex lattice allowed the size of avalanches in the flow state to be measured. The distribution of avalanche sizes displays power law behaviour over several decades.

Flux line lattice states and pinning in niobium wire networks in high magnetic fields

The properties of the flux line lattice in the thin strands of superconducting niobium wire networks with thickness and width comparable to the penetration depth are investigated in the limit of very few flux lines. An angle dependent upper critical field is observed that is consistent with the existence of surface superconductivity. Our results indicate the existence of a flux line lattice in the complete field range Bc1 ⩽ B ⩽ Bc∥ ≃ 1.4 Bc2. The flux line lattice undergoes a dimensional crossover when the transversal correlation length Rc is of the order of the strand width. The field dependence of the Labusch parameter due to surface pinning is determined and compared to a model for surface pinning by Bean-Livingston barriers.

Pinning lengthscales by magnetic force-displacement in single-crystal YBCO

Magnetic flux-profiling experiments have been used to obtain force-displacement responses from the vortex lattice in a single-crystal of YBCO, extending earlier measurements to a wider range of applied fields and temperatures. In contradiction to previous experiments performed on aligned YBCO powders, the interaction distance and Labusch parameter obtained from these appear to agree with those obtained from transport techniques in thin-film specimens. This suggests that there is in fact no fundamental difference in pinning between these sample forms. A strong dependence of d0 on temperature is observed, and fits to simple collective pinning theory suggest this model is inappropriate at the higher temperatures.

Determination of pinning strength of YBa2Cu3O7−δ from magnetic stiffness measurements

A method is presented to determine the Labusch parameter α from the measurement of magnetic stiffness η. Quantitative results on various YBa2Cu3O7−δ samples are reported. For all samples η is a function of the external magnetic field and does not depend on magnetic history. For small magnetic fields η obeys a B1.5 behavior. At fields above 120 mT the melt grown material and the thin film turn over to a B2 dependence. The results can be understood in terms of a crossover from nearly single vortex characteristics to the elastic interaction of vortices in the flux line lattice.

Frequency, field, and temperature dependence of the AC penetration depth of a GdBa 2Cu 3O 7−δ film in the mixed state

We report on a systematic mutual induction measurement of the complex AC penetration depth λ of a sputtered high-quality GdBa 2Cu 3O 7−δ film in the mixed state by a very small coil system arranged near the sample surface. The complex penetration depth λ( B, T, ω) for DC inductions B ⩽ 0.65 T (perpendicular to the film), for temperatures 36 K ⩽ T ⩽ 81 K, and for frequencies 1 kHz ⩽ ω/2 π ⩽ 500 kHz was determined from the measured signal by a novel inversion scheme. The results are consistent with theoretical predictions based upon single vortex pinning. The Labusch parameter α, the flux creep relaxation time τ, as well as the effective activation energy U are simulateneously determined.

Pinning force density in strongly pinned superconductors

Pinning force density in strongly pinned superconductors is theoretically estimated in terms of the coherent potential approximation in which the Labusch parameter is assumed as a single parameter representing the strength of interference among individual pinning potentials through the elasticity of the fluxoid lattice. From the statistical average the pinning force density is shown to have a nonzero value only when the elementary pinning force is larger than some threshold value. At the same time the threshold value is also obtained as a function of the elementary pinning force. When the solution of the pinning force density is obtained consistently, the threshold value is found to be always smaller than the elementary pinning force. This means that the pinning loss is of the hysteresis type, as is well recognized. The obtained pinning force density obeys the linear summation and qualitatively agrees with many experimental results on strongly pinned superconductors. The theoretical result is compared quantitatively with the experimental result on the pinning force density in superconducting NbTa with normal Nb 2N precipitates as strong pinning centers.

The elastic regime of vortices in superconducting YBCO and multilayer YBCO/PrBCO films

A sensitive AC transport technique is used to determine the force-displacement response in the elastic regime of vortices pinned in YBCO and multilayer YBCO/PrBCO films. The dependences of the elastic limit of displacement and the Labusch parameter are presented as a function of temperature, magnetic-field amplitude and orientation. Results are presented for DC sputtered and laser-ablated epitaxial c-axis YBCO films as well as a DC sputtered multilayer YBCO/PrBCO film with a unit-cell ratio of 4:6. The elastic parameters enable the effective energy of the pinning wells to be determined, and comparisons of these values are made with activation energies extracted from thermally activated flux-flow analyses of magneto-resistance data. The force-displacement values show better agreement with magnetic-relaxation measurements than those from Arrhenius analyses.

RF field penetration into a Bi 2Sr 2CaCu 2O 8 single crystal in the mixed state

The magnetic-field dependence of the effective RF field penetration depth of a Bi 2Sr 2CaCu 2O 8 single crystal has been measured in the mixed state under magnetic fields H up to 5T. A crossover from the pinning dominated region at low fields to the dissipative region at high fields has been clearly observed in the intermediate temperature range 0.5 < T/ T c < 0.75. In the pinning dominated region, the field dependence of the elastic pinning force constant (Labusch parameter α p ) has been estimated to be α p ∝ H 1.5. This behavior is similar to that of conventional superconductors.

Linear ac magnetic response near the vortex-glass transition in single-crystalline YBa2Cu3O7.

By using a miniature two-coil mutual-inductance method and an exact inversion scheme, the ac penetration depth ${\ensuremath{\lambda}}_{\mathrm{ac}}$ was measured in a twinned ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ crystal in dc fields parallel to the c axis. The Ohmic dc resistance was also measured on the same crystal. The behavior of these quantities was altogether consistent with the vortex-glass-transition scaling. However, if we calculate the Labusch parameter and the pinning relaxation time from ${\ensuremath{\lambda}}_{\mathrm{ac}}$, they show unexpectedly large frequency dependencies, which can hardly be explained by the standard theory of the linear ac response of pinned vortices.

Two dimensional aspects of pinning in high temperature superconductors

A summary of computer simulations of flux pinning and flux creep in two dimensional systems is given. A softening of the shear modulus due to the random potential is observed. This phenomenon is treated in weak disorder perturbation theory. One can calculate the Labusch parameter directly from the disordered Hamiltonian. However, the perturbation theory turns out to be ill behaved. This probably indicates that the perturbed lattice configuration is non reachable within perturbation theory. This point is also supported by recent simulations which find that the displacements of the vortices change discontinuously as function of the strength of the random potential.

Similar shifts of the depinning and irreversibility lines of oxygen irradiation of melt-processed Bi 2Sr 2CaCu 2O 8

With the vibrating reed technique and DC magnetization we have measured the depinning and irreversibility lines, the Labusch parameter and the dissipation caused by the flux line movement, before and after irradiation of a dense melt-processed Bi 2Sr 2CaCu 2O 8 superconductor. The sample was irradiated with 1.5x10 15 cm -2 400 MeV oxygen ions. After irradiation, the shift of the depinning line to higher reduced temperatures measured with the vibrating reed is similar to the shift of the irreversibility line. This result and the changes observed in the Labusch parameter and damping of the reed indicated unambiguously an increase in the pinning strength after irradition. The observed changes provide evidence supporting the thermally activated depinning interpretation and the diffusion character of the flux motion. The estimated average activation barrier follows a field dependence close to B -0.25 for fields larger than ∼0.2 T.

Nonsaturated pinning characteristics by normal precipitates in superconducting NbTa

Nonsaturated pinning characteristics and elastic and plastic properties of a fluxoid lattice were measured by an a.c. inductive method for superconducting NbTa tapes with normal Nb 2N precipitates. The Labusch parameter characterizing an elastic constant of the pinned fluxoid lattice decreased fairly linearly with increasing magnetic field, and increased with increasing volume fraction of normal precipitates. The interaction distance, the maximum reversible displacement at the yield point, was kept nearly constant or increased up to a vicinity of the upper critical field for strongly pinned specimens. This behaviour in the interaction distance, which is quite different from the case of saturation, suggests that the defective fluxoid lattice is stabilized by strong pinning interactions. The dependence of the macroscopic pinning force on the pinning parameters estimated from electron micrographs was also investigated. It seems to agree with the linear summation theory better than the Larkin-Ovchinnikov theory.

Vibrating-reed studies of flux pinning in the superconducting metallic glass Zr70Cu

With the vibrating-reed technique we have measured the resonance frequency and damping of superconducting ribbons of a ${\mathrm{Zr}}_{70}$${\mathrm{Cu}}_{30}$ amorphous alloy as a function of magnetic field and temperature for different heat treatments of the same sample. Through these measurements we obtain the Labusch parameter \ensuremath{\alpha} in the reduced-field (b) range 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$0.2. At b=0.1, \ensuremath{\alpha}=(3.8\ifmmode\times\else\texttimes\fi{}${10}^{11}$)${\mathit{B}}_{\mathit{c}2}$(T${)}^{2.15}$ N ${\mathrm{m}}^{\mathrm{\ensuremath{-}}4}$ ${\mathrm{T}}^{\mathrm{\ensuremath{-}}2.15}$, a result which is in agreement with the absolute value and temperature dependence of the pinning force obtained from critical-current measurements. The effect of annealing below the glass transition temperature is to produce changes in \ensuremath{\alpha} which depend on field and temperature in a complicated fashion. There are indications that surface pinning could be important in these samples.