On the stability of the critical state with inhomogeneous temperature in composite superconductors

The problem of the thermal and magnetic destruction of the critical state in composite superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability. Received 11 October 2001 / Received in final form 30 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: taylanov@iaph.tkt.uz     

Ordering of the vortex lattice in Mo-Re films

We investigated the vortex lattice ordering induced by an applied current in thick (700-900 nm) Mo-Re films with strong pinning. Measurements of I-V characteristics as a function of field and at different temperatures were carried out. We found that, as in the case of weakly pinning amorphous samples, dynamic ordering can occur only if the size of the vortex correlated region is at least two times the intervortex distance. Received 20 July 2001     

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 YBa₂Cu₃O₇ 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 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. Received 21 December 1999     

Effects of crossed columnar defects on vortex pinning in Bi2Sr2CaCu2O8

To investigate the existence of a splay effect in Bi₂Sr₂CaCu₂O₈ (Bi-2212), vortex pinning has been studied in different configurations of strongly inclined columnar defects (75 from the c axis), installed by heavy-ion irradiation. It is shown that the symmetry of the track setting with respect to the field direction is a more influent parameter than the presence of a dispersion in the track directions. We claim that the enhanced pinning efficiency which is observed in some splayed configurations of columnar defects in Bi-2212 can be interpreted without invoking a splay effect. Received 27 December 1999     

Transition to plastic motion as a critical phenomenon and anomalous interface layer of a 2D driven vortex lattice

The dynamic transition between ordered flow and plastic flow is studied for a two-dimensional driven vortex lattice, in the presence of sharp and dense pinning centers, from numerical simulations. For this system, which does not show smectic ordering, the lattice exhibits a first order transition from a crystal to a liquid, shortly followed by the dynamical transition to plastic flow. The resistivity provides a critical order parameter for the latter, and critical exponents are determined in analogy with a percolation transition. At the boundary between a pinned region and an unpinned one, an anomalous layer is observed, where the vortices are more strongly pinned than in the bulk. Received 22 September 2001     

Van der Waals interaction between flux lines in high- superconductors

In anisotropic or layered superconductors thermal fluctuations as well as impurities induce a van der Waals (vdW) attraction between flux lines, as has recently been shown by Blatter and Geshkenbein in the thermal case [#!BlatterGeshkenbein!#] and by Mukherji and Nattermann in the disorder dominated case [#!NattermannMukherji!#]. This attraction together with the entropic or disorder induced repulsion has interesting consequences for the low field phase diagram. We present two derivations of the vdW attraction, one of which is based on an intuitive picture, the other one following from a systematic expansion of the free energy of two interacting flux lines. Both the thermal and the disorder dominated case are considered. In the thermal case in the absence of disorder, we use scaling arguments as well as a functional renormalization of the vortex-vortex interaction energy to calculate the effective Gibbs free energy on the scale of the mean flux line distance. We discuss the resulting low field phase diagram and make quantitative predictions for pure BiSCCO (Bi₂Sr₂CaCu₂O₈). In the case with impurities, the Gibbs free energy is calculated on the basis of scaling arguments, allowing for a semi-quantitative discussion of the low-field, low-temperature phase diagram in the presence of impurities. Received: 9 February 1998 / Accepted: 17 April 1998     

Absence of dynamical crossover in the vortex creep near by the second peak effect in superconducting Hg-1201 single crystals

DC magnetic relaxation measurements in HgBa₂CuO₄ single crystals are analyzed nearby the fishtail line. It is found that in this case, it is not necessary to introduce any crossover from plastic creep to elastic creep models at the fishtail line. This type of fishtail effect comes only from a competition between a critical current at low temperature which increases versus field and the activation energy, which decreases versus field. According to the doping level of the compound, the fishtail effect can be observed or not, without any correlation with a vortex phase transition. Moreover, in this type of fishtail effect, there is no history effects as recently observed in YBaCu₂O₃ by the partial magnetization loop technique, suggesting that the transition from plastic to elastic flow is here hidden by the disorder of these materials. Received 11 January 2000     

Nanosize patterns as reference structures for macroscopic transport properties and vortex phases in YBCO films

This paper reports on the striking correlation between nanosize mosaic domain walls in YBCO films and 1D rows of parallel Josephson junctions, determining the J _c vs.B curves. From X-ray data analysis, it results that the average “hidden" domain wall, faceted at a nanometric scale, is almost mimicking the Josephson Junction (JJ) 1D array. The assumption that the JJs and the domain-wall arrays are coincident, enables to find out the particular scaling field, making the J _c vs.B curves independent of temperature. This scaling field can be interpreted in terms of the Josephson nature of the transport current across these particular patterns in the intermediate temperature range. By means of our model it is also possible to calculate two asymptotic behaviors of the pinning force as a function of field, for low and high fields, respectively. These behaviors are punctually repeated by the experimental results in the same asymptotic limit, so that two corresponding vortex regimes are clearly pointed out. All results can be interpreted by concluding that in the intermediate temperature range, the strong pinning observed in high quality YBCO films is due to the Josephson Junctions average patterns. These patterns are the counterpart related to the transport mechanisms of “hidden" structural nano-domains. Received 16 October 2000 and Received in final form 28 November 2000     

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 T_c 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 . Received: 8 April 1998 / Revised: 15 July 1998 / Accepted: 2 September 1998     

Magnetothermal instabilities in an organic superconductor

We have studied the occurrence of magnetothermal instabilities in a single crystal during field sweep magnetization experiments, equivalent to short time relaxation studies. We find instability behaviour in good agreement with a recent model by Mints, for a non-linear E(J) characteristic. In particular, we find that a decrease of the dynamic relaxation rate, characterizing the effective activation energy, precedes the unstable regime. We point out formal analogies between such instabilities and the general predictions for flux avalanches. Received: 11 December 1997 / Revised: 15 January 1998 / Accepted: 31 March 1998     

Two-step flux penetration in classic antiferromagnetic superconductor

The influence of antiferromagnetic order on the mixed state of a superconductor may result in creation of spin-flop domains along vortices. This may happen when an external magnetic field is strong enough to flip over magnetic moments in the vortex core from their ground state configuration. The formation of domain structure causes modification of the surface energy barrier, and creation of the new state in which magnetic flux density is independent of the applied field. The modified surface energy barrier has been calculated for parameters of the antiferromagnetic superconductor DyMo₆S₈. The prediction of two-step flux penetration process has been verified by precise magnetization measurements performed on the single crystal of DyMo₆S₈ at milikelvin temperatures. A characteristic plateau on the virgin curve B(H ₀) has been found and attributed to the modified surface energy barrier. The end of the plateau determines the critical field, which we call the second critical field for flux penetration. Received 16 August 2002 / Received in final form 22 October 2002 Published online 29 November 2002     

Electrodynamics of the vortex lattice in untwinned YBaCuO by complex impedance measurements

We report complex impedance measurements in an untwinned YBaCuO crystal. Our broad frequency range covers both the quasi static response and the resistive response of the vortex lattice. It allow us to characterize the irreversibility line without the need of any frequency dependent pinning parameters. We confirm the validity of the two modes model of vortex dynamic, and extract both the surface critical current and the flux flow resistivity around the first order transition T_m. This latter is identified by the abrupt loss of pinning and by an unexpected step of (T) at T_m. Received 22 November 2002 / Received in final form 17 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: alain.pautrat@ismra.fr RID="b" ID="b"UMR 6508 associée au CNRS     

Influence of non-uniform J<Subscript>c</Subscript> distributions on flux jumps in high-temperature superconductors

The influence of non-uniform J_c distributions on flux jumps in high-temperature superconductors is investigated with the simplified models in the form of a composite superconducting slab consisting of different pinning regions. The magnetization loops and flux jumps for the simplified models are calculated with the modified recursion formulas which could predict the flux-jump fields. The valid ranges of the temperature and sweep rate for B_fj1 are specified and the fields of the subsequent jumps after the first flux jump of the inhomogeneous models are obviously lower than that of the homogeneous models. The results indicate that flux jump instability could be stimulated by non-uniform J_c distributions and with the increase of the discrepancy of J_c between different pinning regions the instability also increase.     

Vortex lattice accommodation on twin boundaries in studied by neutron diffraction

An extensive study of small angle neutron scattering was performed in twinned YBa₂Cu₃O₇ crystals in its superconducting state as a function of the angle between the c-axis of the crystal and the magnetic field. The half of the twin boundaries are oriented in the horizontal plane, which also contains the neutron beam and the magnetic field. Two different diffraction patterns are studied as a function of at 5 K and B = 0.5 T, one along the c-axis of the crystal, the other one along the applied field. These variations are interpreted in the model of accommodation of the vortices on the twin planes by zigzagging from these planes to the ab-planes of the crystal, in order to minimize their energy. Received: 9 March 1998 / Revised and Accepted: 12 June 1998     

Effect of changing microstructure of Y-Ba-Cu-O superconductors on the vortex motion under non-equilibrium thermal conditions

Repetition of cooling and heating of high-T_c superconductors is detected to be able to result in some change of their microstructure. A non-equilibrium experimental technique provides direct measurement of the velocity of vortex motion in high-T_c Y-Ba-Cu-O superconductors. Its value falls in the interval of mm/s depending on the number of the cooling or heating cycles, to which the samples are submitted. The thermal cycling created homogenization of the specimen's microstructure, and is presumed to cause this phenomenon, decreasing the number and strength of pinning centers. This supposition is proved by X-ray diffractography and transmission electron microscopy. A simple irreversible thermodynamic theory is elaborated to describe the reason, direction and dissipative character of the vortex motion. Received: 17 December 1997 / Accepted: 28 January 1998     

Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

We study the effect of an external field on (1 + 1) and (2 + 1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, “first order”-type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads ΔE ₁∼L ^θ[ln(L _z L ^{- ζ})]^-1/2, where ζ is the roughness exponent and θ is the energy fluctuation exponent of the manifold, L is the linear size of the manifold, and L_z is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds ∼L ^{2D + 1 - θ}[(1 - ζ)ln(L)]^1/2. We also present a mean field argument for the finite size scaling of the first jump field, h ₁∼L ^{d - θ}. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed. Received December 2000 and Received in final form April 2001     

Sudden critical current drops induced in S/F structures

In the search for new physical properties of S/F structures, we have found that the superconductor critical current can be controlled by the domain state of the neighboring ferromagnet. The superconductor is a thin wire of thickness d_s ≈2ξ_S. Nb/Co and Nb/Py (Permalloy Ni₈₀Fe₂₀) bilayer structures were grown with a significant magnetic anisotropy. Critical current measurements of Nb/Co structures with ferromagnet thickness d_F > 30 nm show sudden drops in two very defined steps when the measurements are made along the hard axes direction (i.e. current track parallel to hard anisotropy axes direction). These drops disappear when they are made along the easy axis direction or when the ferromagnet thickness is below 30 nm. The drops are accompanied by vortex flux flow. In addition magnetorestistance measurements close to T_C show a sharp increase near saturation fields of the ferromagnet. Similar results are reproduced in Nb/Py bilayer structure with the ferromagnet thickness d_F ~ 50 nm along the easy anisotropy axes. These results are explained as being due to spontaneous vortex formation and flow induced by Bloch domain walls of the ferromagnet underneath. We argue these Bloch domain walls produce a 2D vortex-antivortex lattice structure.     

Rotating superconductors: Ginzburg-Landau equations

Superconductors put into rotation develope a spontaneous internal magnetic field (the “London field”). In this paper Ginzburg Landau equations for order parameter, field, and current distributions for superconductors in rotation are derived. Two simple examples are discussed: the massive cylinder and the “Little and Parks geometry”: a thin film of superconducting material deposited on a cylinder of normal material. A dependence of T _c on rotational frequency is predicted. The magnitude of the effect is estimated and should be observable. Received 28 May 2001     

Relation between vortex excitation and thermal conductivity in superconductors

Thermal conductivity κ _xx(T) under a field is investigated in d _{x2 - y2}-wave superconductors and isotropic s-wave superconductors by the linear response theory, using a microscopic wave function of the vortex lattice states. To study the origin of the different field dependence of κ_xx(T) between higher and lower temperature regions, we analyze the spatially-resolved thermal conductivity around a vortex at each temperature, which is related to the spectrum of the local density of states. We also discuss the electric conductivity in the same formulation for a comparison. Received 8 December 2001 and Received in final form 20 March 2002 Published online 6 June 2002     

Nonlinear ac response of the vortex system in the cubic (K, Ba)BiO3 superconductor

We present ac susceptibility measurements performed on single crystals with different geometries: thick films, bars and hollow cylinders. We show that the dependence of the real () and imaginary () parts of the ac susceptibility is in very good agreement with Brandt's numerical calculations (Phys. Rev. B 58, 6523 (1998)) in the modified Bean critical state. Creep effects (at ) are investigated by studying the frequency dependence of the current density deduced from the temperature scans of the ac susceptibility over a large frequency range (). The relaxation rate is temperature independent and very similar to the one usually obtained in high cuprates. Received 17 March 1999