Characterization of defects in amorphous type II superconductors using the collective flux pinning properties

As in crystalline materials, flux pinning in type II superconducting metallic glasses arises from the interaction of the flux-line lattice with defects that locally change the superconducting properties of the sample. The nature of these defects is still subject of numerous investigations. In this paper we demonstrate that the collective pinning properties of weak pinning, type II superconductors provide an ideal additional tool for probing defects of sizes comparable to the coherence length . Our results obtained from sputtered Nb _X Ge and Mo _X Si layers sketch a straightforward relation between the sputter conditions, the resulting defects, and the pinning behavior. A classification of the defects that provide the pinning is given and estimates on their sizes and densities are derived. They are in excellent agreement with other (direct) observations.     

Three-dimensional collective flux pinning in the layered superconductor 2H-NbSe2-xSx

The collective pinning theory was compared with the results of flux pinning in the layered superconductor 2H-NbSe _2–x S _x.The size effect on the flux-pinning force and the angular dependence of the peak effect were investigated. Our sample did not show the size effect. Even when a magnetic field was applied parallel to the crystal layers, the peak effect was observed far below the zero-field critical temperature. These results show that flux pinning is three-dimensional within the frame of the collective pinning theory and that the peak effect is not caused by the dimensional crossover. The peak effect can be qualitatively explained in terms of the dispersion of the tilt modulus of the flux-line lattice.     

Vortex Matter in Highly Strained Nb$$_{}$$Zr$$_{25}$$25: Analogy with Viscous Flow of Disordered Solids

We present the results of magnetization and magneto-transport measurements in the superconducting state of an as-cast Nb\(_{75}\)Zr\(_{25}\) alloy. We also report the microstructure of our sample at various length scales by using optical, scanning electron and transmission electron microscopies. The information of microstructure is used to understand the flux pinning properties in the superconducting state within the framework of collective pinning. The magneto-transport measurements show a non-Arrhenius behaviour of the temperature- and field-dependent resistivity across the resistive transition and is understood in terms of a model for viscous flow of disordered solids which is popularly known as the ‘shoving model’. The activation energy for flux flow is assumed to be mainly the elastic energy stored in the flux-line lattice. The scaling of pinning force density indicates the presence of two pinning mechanisms of different origins. The elastic constants of the flux-line lattice are used to estimate the length scale of vortex lattice movement, or the volume displaced by the flux-line lattice. It appears that the vortex lattice displacement estimated from elastic energy considerations is of the same order of magnitude as that of the flux bundle hopping length during flux flow. Our results could provide possible directions for establishing a framework where vortex matter and glass-forming liquids or amorphous solids can be treated in a similar manner for understanding the phenomenon of viscous flow in disordered solids or more generally the pinning and depinning properties of elastic manifolds in random media. It is likely that the vortex molasses scenario is more suited to explain the vortex dynamics in conventional low-T\(_C\) superconductors.     

Collective Pinning of a Flux-Line Lattice with Screw Dislocations

The energy of screw dislocations of a flux-line lattice in Type-II superconductors is calculated taking account of dispersion of the tilt modulus. On the basis of this calculation, the collective-pinning theory for the plastic case, proposed by Mullock and Evetts, leads to correlation lengths of a flux-line lattice much shorter than that for the elastic case leads, and much better theoretical fits to experimental results in Nb ₃ Ge and 2H-NbSe _2–x S _x are obtained. Furthermore, the intermediate state between three-dimensional disorder and two-dimensional disorder in a flux-line lattice is predicted when the screw dislocations trigger the dimensional crossover.     

The flux-line lattice in high-T c superconductors

The flux-line lattice in type-II superconductors has unusual nonlocal elastic properties which make it soft for short wavelengths of distortion. This softening is particularly pronounced in the highly anisotropic high-T _c superconductors (HTSC) where it leads to large thermal fluctuations and to thermally activated depinning of the Abrikosov vortices. Numerous transitions are predicted for these layered HTSC when the temperatureT, magnetic inductionB, or current densityJ are changed. In particular, the flux lines are now chains of two-dimensional (2D) “pancake vortices” which may “evaporate” by thermal fluctuations or may depin individually. At sufficiently highT, ohmic resistivityρ(T, B) is observed down toJ → 0. This indicates that the flux lines are in a “liquid state” with no shear stiffness and with small depinning energy or that the 2D vortices can move independently. At lowerT, ρ(T, B, J) is nonlinear since the pinning energy of an elastic vortex lattice or “vortex glass” increases with decreasingJ as predicted by theories of collective pinning and by “vortex glass” scaling.     

Collective mode dynamics of the vortex lattice in a highT c superconductor

Dispersion relations have been obtained numerically for the collective modes of the flux line lattice of a highT _c superconductor in the London limit and the effect of pinning forces is included. It is found that the waves propagating along the magnetic field the dispersion consists of two branches and that the low frequency branch may interact with other low-frequency excitations in the lattice.     

Comparison of Flux Pinning Mechanism in Laser Ablated YBCO and YBCO:BaZrO3 Nanocomposite Thin Films

Thin films of YBCO and YBCO:BaZrO₃ (BZO) nanocomposite have been deposited using the pulsed laser deposition technique. Substantial increase in critical current density (J _C ) and pinning force density (F _p ) of the nanocomposite thin films was observed. The possible pinning mechanism in YBCO:BZO nanocomposite thin films has been explored and compared with the pinning mechanism in pure YBCO thin film by studying the variation of J _C with magnetic field (B) and temperature. In the intermediate field regime (0.1–1 T), J _C follows B ^−α with nearly similar values of α for YBCO and YBCO:BZO nanocomposite thin films indicating similar pinning mechanism in both thin films. The variation of J _C with reduced temperature (t=T/T _C ) has been studied for both the films and it was observed that the mechanism of pinning in both YBCO and YBCO:BZO thin films is similar (δT _C pinning). The observed enhanced values of J _C and F _p of the nanocomposite thin film is attributed to the presence of BZO nanoparticles, which induces more defects due to lattice mismatch between YBCO and BZO leading to improved flux pinning properties of the nanocomposite thin film.     

The elastic Green's function for the pinned flux-line lattice in a type II superconductor

The elastic Green's function for the pinned flux-line lattice in the critical state is defined and evaluated in the coherent potential approximation. The presence of pinning sites contributes an additional restoring force, which must be calculated within a complete theory of the critical state, but which can be measured. Results are given for the dependence of the Green's function on the density of strong flux-line pins, and a criterion is derived for the applicability of the dilute-limit approximation. This criterion is never satisfied near the upper and lower critical fields. Assuming that the pins all interact sufficiently strongly with the flux-line lattice to exceed the threshold criterion, we find that the Green's function decreases (the flux-line lattice becomes more rigid) with increasing pin density.Research sponsored by the Division of Materials Science, U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.     

Longitudinal critical current in type II superconductors. II. Helical vortex instability near the surface

The calculation of the critical current for helical instability of the flux-line lattice, performed in a previous paper for a bulk superconductor, is extended to include the effect of a planar surface. The extension is of interest since an applied longitudinal current in general flows near the surface before the helical instability of the flux-line lattice triggers the transition to the flux-flow state. The magnetic stray field of the surface increases the critical current by a factor 1.41 (1.34) for weak (moderate) pinning, and it modifies the axis ratio of the helices. The pitch length and the extension of the helical mode into the specimen are decreased from their bulk values by surface pinning, but they are slightly increased if bulk pinning dominates.     

Flux pinning in high-Tc superconductive films

Magnetization measurements have been performed onc-axis oriented Y- and Gd-based superconductive films in a wide range of the temperaturesT (4.2–85 K) and magnetic fieldsH (0–8 T) withH c-axis. The influence of flux creep on both the temperature dependence of critical current densityJ _cm and the scaling behavior of flux pinning forceF _p has been discussed in detail. The experimental results show that Y and Gd films have different pinning mechanism. Flux pinning-force peaks in high fields are observed in Gd film at high temperatures and can be considered as evidence for collective pinning.     

Magnetic field density of perfect and imperfect flux line lattices in type II superconductors. I. Application of periodic solutions

The densityn(B) of the spatially varying magnetic fieldB inside a type II superconductor can be measured by nuclear magnetic resonance or muon-spin rotation (⁺SR). For a perfect flux-line latticen(B) exhibits van Hove singularities at the maximum, minimum, and saddle point values of the ideally periodicB(r). In a real superconductor, these singularities are smeared due to distortions of the flux-line lattice caused by, e.g., the interaction of flux lines with inhomogeneities in the material (pinning), structural defects in the flux-line lattice, the nonellipsoidal shape of the specimen, or fluctuations of the applied field and temperature. Such perturbations of the periodicity ofB(r) typically broaden the idealn(B) by convolution with a Gaussian whose width in general depends onB and which thus smears each singularity differently. Knowledge of the broadening is required for the interpretation of ⁺SR experiments in the new ceramic superconductors and also in pure niobium, where it competes with the broadening caused by the diffusion of the positive muons. In this paper (Part I), the broadening ofn(B) is discussed in detail and some of its features are derived from the periodic solutions of the Ginzburg-Landau and BCS-Gorkov theories. Forthcoming parts will deal with the application of nonperiodic solutions and with computer simulations.     

Statics and dynamics of the vortex lattice in high-T c superconductors

Some properties of the flux-line lattice in conventional and high-T_c supperconductors are reviewed, with particular stress on phenomenological theories, magnetization curves, vortex lattice in films, nonlocal elasticity, phase diagram of vortex arrangements, vortex dynamics, and geometry effects.     

Dynamic pinning model of electrical dissipation in the superconducting surface sheath

The dynamic pinning model of Yamafuji and Irie is adapted to the problem of electrical dissipation in the superconductive surface sheath. The free energy of the surface flux-spot lattice and its shear modulus—quantities required by the model—are calculated. The dc current-voltage characteristics of thick, Pb-In alloy films are analyzed in terms of an excess currentI _p due to pinning. The observed dependence ofI _p upon magnetic field is in good accord with the predictions of the model; the variations with temperature and alloy composition are made plausible as well.Work supported in part by Research Corporation.     

Statics and Dynamics of the Vortex Lattice in High-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Superconductors

No Heading Some properties of the flux-line lattice in conventional and high-T_c superconductors are reviewed, with particular stress on phenomenological theories, magnetization curves, vortex lattice in films, nonlocal elasticity, phase diagram of vortex arrangements, vortex dynamics, and geometry effects.PACS numbers: 74.25.Qt, 74.25.Ha, 74.20.De     

Flux pinning in superconducting amorphous Zr1−x Co x

The pinning force F_P in amorphous Zr_1–x Co _x (x=0.30; 0.35) is measured as a function of perpendicular field and temperature. The homogeneous samples exhibit a weak flux pinning force of about 10⁴ N/m ³ in the temperature range 2–3 K. The field dependence ofF _P at several temperatures can be explained by a collective pinning model in the Larkin-Ovchinnikov theory in three dimensions. Structural relaxation studies in amorphous ZrCo confirm that bothT _c andF _P are sensitive to a slight isothermal annealing treatment at 220°C for 1 h. The collective flux-pinning characteristics still remain after such a structural relaxation, which allows us to conjecture that these defects are stable against this thermal treatment.     

Superconducting properties of Nb3Ge thin films prepared by cosputtering

Nb₃Ge films with thicknesses between 0.5 and 1.5 m have been deposited on heated sapphire substrates by dc sputtering in a pure argon atmosphere. With a maximum superconducting onset temperature T _c= 22.7 K, these high-T _csamples crystallize in a single-phase A15 structure with lattice parameters down to 5.14 ». Critical current densities and upper critical magnetic inductions have been measured as a function of magnetic field orientation, temperature, and film thickness. The anisotropies of the critical currents and fields depend on the microstructure of the samples and show maxima for the field orientation normal to the sample surface in those films that exhibit columnar growth of the crystallites normal to the substrate. The temperature, field, and angular dependences of the pinning forces in these films are compared to existing pinning theories.Dedicated to Prof. Dr. B. T. Matthias on the occasion of his 60th birthday.Supported by Deutsche Forschungsgemeinschaft.     

Room-Tc Superconductivity on Whispering Mode in Quasi-1D Composite of Superconducting Nanotubes: Is It Possible?

Combining Little's and Ginzburg's ideas with recent progress in nanotubes research, a novel type of material is advanced as a perspective high-T _c superconductor on a base of a close-packed lattice of quasi-1D superconducting nanotubes. Idea is offered that superconducting coaxial multilayer nanotubes of the correlation length in diameter is an ideal and natural trap for pinning of Abrikosov vortex. Nanotube should be layered superconductor, such as LuNiBC. Mechanism of superconductivity was proposed and substantiated quantitatively on a base of a whispering mode, which is shown to be responsible for a strong enhancement of electron–phonon interaction and for an increase of critical temperature. Nanocomposite built from such quasi-1D nanotubes when coinciding with vortex lattice provides ideal conditions for the pinning, resonance, distortion, ordering, and Little–Parks effects, the joint action of which is suggested to result in synergetic effect increasing the superconductivity. Such quasi-1D or 2D nanotubular crystal is proposed to synthesize by template approach using zeolite-like membrane.     

Computations on the dimensional crossover in collective pinning

The displacement correlation function introduced by Larkin and Ovchinnikov for pinned flux lines in a superconducting layer is evaluated explicitly in order to study the thickness dependence. Expressions for the transverse and longitudinal correlation lengthsR _c andL _care derived and a criterion for the crossover from two- to three-dimensional collective pinning is obtained. Using these expressions, computations are carried out for amorphous superconductors.L _cturns out to drop exponentially fast in three dimensions, whileR _cchanges gradually through the crossover remaining close to its 2D value. The explicit thickness dependence is logarithmic, so that the pure 3D case is only accessible in a very limited experimental regime.     

On the threshold pinning force in type II superconducting films

The maximum pinning force of a two-dimensional vortex lattice in a random potential is calculated. A connection is established between this threshold pinning force and the potential energy discontinuities due to elastic and plastic instabilities of the vortex lattice. Inspired by recent computer simulations, we assume that the fluctuations in the commensurability between the random potential and the vortex potential breaks the vortex system up into a set of flowing channels in between trapped regions. Two instability mechanisms and their contribution to the threshold force are discussed within this channel-flow picture. We find that three different regimes exist depending on, w, the width of the channels;w=,a ₀w=a ₀ , wherea ₀ is the vortex lattice spacing. Weak pinning superconductors can pass through all three regimes as the reduced magnetic field is varied from 0 to 1, whereas strong pinning compounds can remain in the saturated region (w=a ₀ ) for all values of the field. We compare the expression for the threshold force with experimental results for both strong and weak pinning samples. A satisfactory qualitative agreement is obtained between theory and experiment.     

Vortex Dynamics in a Superconducting Film with a Kagome and?a?Honeycomb Pinning Landscape

The vortex dynamics in a superconducting thin Al film with a periodic Honeycomb or Kagome array of antidots has been investigated by electrical transport measurements. The large values of the superconducting coherence length and penetration depth of the Al films guarantee a maximum of one flux quantum trapped per pinning site. This allows us to directly compare the experimental results with previous theoretical investigations based on molecular dynamics simulations. For the Kagome lattice, two submatching features not anticipated theoretically at H/H ₁=1/3 and 2/3, where H ₁ is the field at which the number of vortices coincides with the number of pinning sites, are observed. Possible corresponding stable vortex patterns are suggested. For the Honeycomb pinning landscape, the commensurability effects are in agreement with the theoretical expectations. A preliminary analysis of the vortex mobility in this lattice shows the presence of a weak vortex guidance.