Two-dimensional Pancake Vortices Research Articles

Contribution of vanadium particles to thermal movement of correlated two-dimensional pancake Abrikosov vortices in Bi-2223 superconducting system

This article breaks new ground in understanding of variation in the magnetic strength performance, flux pinning and energy dissipation mechanism of polycrystalline bulk Bi1.8Sr2.0Ca2.2Cu3.0Oy (Bi-2223) superconducting materials added with the different vanadium concentration level (0.0≤x≤0.30) under the magnetic field strengths applied up to 5T for the first time. We provide the sophisticated and phenomenological discussions on the magnetoresistivity measurement results in three main sections along the paper. All the findings show that the increase of both the vanadium concentration in the crystal structure and external magnetic field strength damages significantly the magnetic strength performance, vortex dynamics, flux pinning ability and vortex lattice elasticity of bulk Bi-2223 superconducting ceramics. The vanadium addition promotes thermally the movement of correlated two-dimensional (2D) pancake Abrikosov vortices between the in-plane Cu–O2 layers in the valance band, vortex lattice elasticity, vortex dynamics, distance for interlayer Josephson couplings and flux pinning centers and the theoretical computations confirm the remarkable degradation in the formation of super-electrons in the Bi-2223 crystal system. Thus, the vanadium addition is anticipated to be one of the best selectable materials to examine the differentiation in the thermal movement of correlated 2D Pancake Abrikosov vortices in the bulk Bi-2223 superconducting system.

Degradation in fundamental characteristic features of Bi-2212 superconducting ceramic material with Sr/Ti partial substitution

The present work investigates the vital differentiations in some basic characteristic properties including the crystallinity quality, flux pinning mechanism, superconducting, dc electrical features, grain boundary coupling problems and strength of connection between the superconducting grains in the poly-crystallized Bi2.1Sr2.0−xTixCa1.1Cu2.0Oy cuprate ceramic materials with the partial aliovalent substitution of Sr2+ impurities for the Ti4+ foreign additives in the crystal system. All the materials are prepared by the standard solid-state reaction method, and the characterization of samples produced is thoroughly performed by the typical experimental measurements such as dc electrical resistivity over the temperature, critical current density and powder X-ray diffraction investigations. It is obvious that all characteristic properties tend to diminish constantly with the augmentation of the aliovalent Sr/Ti partial replacement level, and in case of x = 0.10 they reach the global minimum values. To illustrate, the low Bi-2212 superconducting phase diverges from the stabilization because of new induced permanent crystal structure (crystallinity) problems such as the voids, porosity, defects, texturing, cracks, grain boundary coupling problems, grain alignment distributions, stress raisers, omnipresent flaws and crack initiation sites in the crystal system. Besides, the presence of Ti impurities leads to the formation of new impurity phases related to very low superconducting and characteristic TiO2 phase, being favored by either the decrement of c lattice cell parameter or increment of a-axis length. The similar findings are observed in the temperature dependent electrical resistivity measurements. Namely, the electrical resistivities at the normal state are found to increase dramatically from about 74.75–180.47 mΩcm whereas the offset and onset critical temperature values are recorded to diminish from 82.11 K (for the pure sample) to 50.52 K (for the sample prepared with x = 0.10 substitution level) and 84.03–75.14 K, respectively, with the enhancement in the substitution level. Likewise, the Sr/Ti partial replacement affects negatively not only the thermal fluxon motions of correlated two-dimensional pancake vortices but also the ability and strength of vortex lattice period, elasticity, effective and active energy barriers for the flux pinning centers in the Bi-2212 superconducting crystal lattice. In this respect, the Sr/Ti partial substitution mechanism is ploughed to improve the fundamental characteristic features.

Formation of artificial flux pinning centers in Bi-2223 cuprate superconductor with Ni impurities and enhanced resistant to thermal fluxon motions of correlated 2D pancake vortices in new matrix

This comprehensive study attempts to find out the evaluation of magnetoresistivity performance and flux pinning centers in the Bi-2223 superconductor with nickel impurities and diffusion annealing temperature interval 650 °C–850 °C by means of magnetotransport measurements (0–5T). It is found that the cooper-pair probabilities as well as pinning of thermal fluxon motions of two-dimensional (2D) pancake vortices and interlayer Josephson coupling between the isolated grains considerably improve with the annealing temperature up to 700 °C as a result of enhancement in the effective flux pinning regions. However, from 700 °C onwards the potential energy barriers decrease significantly due to the increment of permanent structural problems in the crystal system. Namely, the presence of excess Ni impurities develops the recoupling linelike/discrete pancakelike nature. In this respect, the bulk sample exposed to the diffusion annealing temperature of 850 °C exhibits the worst magnetic performance characteristics. The flux lines in the material more easily jump to neighboring states due to the cooper pair-breaking mechanism, and thus the thermal fluxon motions of 2D pancake vortices lead to the energy dissipation. We also discuss the differentiation of vortex lattice elasticity for the materials with the aid of the theoretically calculated quantities such as the thermodynamic critical field (μ0Hc), irreversibility field (μ0Hirr), lower critical field (μ0Hc1), upper critical field (μ0Hc2), penetration depth (λ), coherence length (ξ) and Ginzburg Landau parameter (κ). According to the computational values, the optimum annealing temperature of 700 °C strengthens the pinning of 2D pancake vortices, vortex lattice period and elasticity as a result of the decrease in the inter-plane interaction energy. To sum up, 700 °C favors the applications of bulk Ni surface-layered Bi-2223 compounds in rather higher magnetic fields for a major innovation.

Effect of MgB2 addition on thermal fluxon motions of two-dimensional pancake vortices in Bi-2223 superconducting ceramics

This study reports the variations of magnetoresistivity performance and pinning ability for the bulk Bi1.8Pb0.4Sr2(MgB2)xCa2.2Cu3.0Oy ceramic materials with the MgB2 addition (0 ≤ x ≤ 0.5) in the crystal structure by magnetotransport measurements performed in the applied magnetic fields (0–7T). According to the results, the maximum critical transition temperature values (Tcoffset and Tconset) are about 114.1 K and 121.3 K for the best sample exposed to x = 0.05 content level of MgB2 addition while the minimum Tcoffset and Tconset are obtained to be 109.4 K and 118.6 K for the pure sample at zero applied magnetic field, respectively. Besides, the highest Tcoffset value of 69.6 K is observed for the former sample at 7 T external field strength. This is attributed to the fact that the existence of optimum MgB2 in the Bi-2223 crystal structure results in the increased nucleation center formations so that the binding between the dopants and adjacent layers can pin the fluxon motions of two-dimensional (2D) pancake vortices at higher magnetic field such a value of 7 T. On the other hand, the main reason of decrement in the Tcoffset parameters stems from the pair-breaking mechanism based on the changed spin states of cooper-pair electrons. Moreover, the flux pinning energy parameters estimated from thermally activated flux creep model tend to augment considerably with the increment of MgB2 content level up to x = 0.05. Additionally, the coherence length and penetration depth parameters as well as the irreversibility and upper critical fields confirm the positive effect of optimum MgB2 addition on the elastic moduli of vortex lattice, Josephson coupling length, magnetic performance and especially pinning ability throughout the Bi-2223 crystal structure.

Significant development on pinning of vortices in Y-123 superconductor with homovalent Ba/Nd substitution

In this study, the magnetotransport measurements are performed in the field range of 0–7 T to determine the effect of Nd nanoparticles inserted in the Y-123 crystal structure on the superconducting characteristics and flux pinning mechanism of the YBa2−yNdyCu3O7 materials (0.000 ≤ y ≤ 0.500). Moreover, the experimental measurement results enable us to evaluate the crucial parameters as regards critical transition temperatures (\(T_{c}^{onset}\) and \(T_{c}^{offset}\)), room temperature resistivities (ρ300), residual resistivity ratios (RRR), thermodynamic critical fields (μ0Hc), lower critical fields (μ0Hc1), upper critical fields (μ0Hc2), critical fields (μ0Hc3), irreversibility fields (μ0Hirr), coherence lengths (ξ), penetration depths (λ) and Ginzburg–Landau (\(\kappa\)) parameters. All the values obtained show the considerable improvement with the increment of the Nd nanoparticles in the Y-123 crystal system up to the critical value of y = 0.250 beyond which the prompt degradation begins in the crystal structure due to new induced artificial dislocations and permanent disorders in the Cu–O2 consecutively stacked layers. Hence, the excess Nd inclusions lead to the thermal motion of the vortices easily. This fact is completely confirmed by the magnetotransport measurements performed in the external magnetic fields. Namely, the optimum level of Nd dopant seriously increases the coupled regions as a result of the degradation of pancake positional fluctuations, and pinning of two-dimensional pancake vortices enhances with the recoupling of the adjacent layers. However in case of the maximum Nd inclusions, the flattened pancakes with more interplane interaction energy never travel from layer to layer due to the alteration of the coupled vortices into the discrete pancakelike (recoupling linelike) nature. In other words, the excess Nd nanoparticles inserted in the Y-123 crystal system reduce significantly the interlayer Josephson coupling length, elastic moduli of the vortex lattice and magnetic field carrying capacity. Furthermore, the flux pinning energy (U0) is calculated from thermally activated flux flow model. The activation energy computed increases regularly with the increment of Nd decorations until y = 0.250 after which the value significantly decreases towards to the global minimum point. However, the pinning energy values always decrease with the increase of the external magnetic field strength. In case of external magnetic fields of 7 T the maximum activation energy is found to be about 477 K. As for the Y-123 material doped with maximum Nd additives of y = 0.500, the flux pinning energy values are not calculated at any applied magnetic field which is >0.1 T due to the cooper pair-breaking in Ba-site Nd substituted Y-123 systems. At the same time, the evaluated parameters follow the same trend: firstly enhancement up to the critical Nd dopant value of y = 0.250 and then the rapid regression towards the global minimum point. Finally, the optimum Nd impurity level is found to be y = 0.250 in the Y-123 system at even higher applied magnetic field strengths.

Evidence for decoupled two-dimensional vortex behavior of YBa2Cu3O7−δ in La0.7Sr0.3MnO3/YBa2Cu3O7−δ/La0.7Sr0.3MnO3 trilayer

We investigate the vortex behavior of YBa2Cu3O7−δ thin films sandwiched between two ferromagnetic layers (La0.7Sr0.3MnO3/YBa2Cu3O7−δ/La0.7Sr0.3MnO3). The magnetization study on La0.7Sr0.3MnO3/YBa2Cu3O7−δ/La0.7Sr0.3MnO3 trilayers conspicuously shows the presence of both ferromagnetic and diamagnetic phases. The magnetotransport study on the trilayers reveals a significant reduction in the activation energy (U) for the vortex motion in YBa2Cu3O7−δ. Besides, the “U” exhibits a logarithmic dependence on the applied magnetic field which directly indicates the existence of decoupled two-dimensional (2D) pancake vortices present in the CuO2 layers. The evidence of 2D decoupled vortex behavior in La0.7Sr0.3MnO3/YBa2Cu3O7−δ/La0.7Sr0.3MnO3 is believed to arise from (a) the weakening of superconducting coherence length along the c-axis and (b) enhanced intraplane vortex–vortex interaction due to the presence of ferromagnetic layers.

Observation of reduced activation energy and the possible existence of decoupled pancakevortices in superconductor/ferromagnet bilayers

Investigations of different superconducting (S)/ferromagnetic (F) heterostructuresgrown by pulsed laser deposition reveal that the activation energy (U) for the vortexmotion in a high Tc superconductor is reduced remarkably by the presence of F layers. TheU exhibits a logarithmic dependence on the applied magnetic field in the S/F bilayerssuggesting the existence of decoupled two-dimensional (2D) pancake vortices. This resultis discussed in terms of the reduction in the effective S layer thickness and theweakening of the S coherence length due to the presence of F layers. In addition, theU and thesuperconducting Tc in Y Ba2Cu3O7 − δ/La0.5Sr0.5CoO3 bilayers are observed to be much lower than in theY Ba2Cu3O7 − δ/La0.7Sr0.3MnO3 ones. This in turn suggests that the degree of spin polarization of the F layer might notplay a crucial role for the suppression of superconductivity due to a spin polarized inducedpair-breaking effect in S/F bilayers.

Biot-Savart correlations in layered superconductors

We discuss the superconductor-to-normal phase transition in an infinite-layered, type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally excited pancake vortices and assume that the dominant interlayer coupling is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group (RG) flow, is that the phase transition in this model is a Kosterlitz-Thouless transition despite being a three-dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence is that the jump in the measured in-plane superfluid stiffness, a universal quantity in $2d$ Kosterlitz-Thouless theory, receives a small nonuniversal correction (of order 1% in ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+x}$). This overall picture places some claims expressed in the literature on a more secure analytical footing and resolves some conflicting views.

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.

Pancake Vortices

I describe the magnetic-field and current-density distributions generated by two-dimensional (2D) pancake vortices in infinite, semi-infinite, and finite-thickness stacks of Josephson-decoupled superconducting layers. Arrays of such vortices have been used to model the magnetic structure in highly anisotropic layered cuprate high-temperature superconductors. I show how the electromagnetic forces between pancake vortices can be calculatated, and I briefly discuss the effects of interlayer Josephson coupling.

Defect-unbinding and the Bose-glass transition in layered superconductors.

The low-field Bose-glass transition temperature in heavy-ion irradiated Bi(2)Sr(2)CaCu(2)O(8+delta) increases progressively with increasing density n(d) of irradiation-induced columnar defects, but saturates for n(d) greater or = 1.5 x 10(9) cm(-2). The maximum Bose-glass temperature corresponds to that above which diffusion of two-dimensional pancake vortices between vortex lines becomes possible, and the "linelike" character of vortices is lost. We develop a description of the Bose-glass line that quantitatively describes experiments on crystals with widely different track densities and material parameters.

Vortex melting and decoupling transitions inYBa2Cu4O8single crystals

The vortex correlation along the c axis in high quality single crystals of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ has been investigated as a function of temperature T in different magnetic fields, using the flux transformer configuration. A simultaneous sharp drop associated with the vortex lattice melting is observed in both the primary and secondary voltages ${(V}_{\mathrm{top}}$ and ${V}_{\mathrm{bot}}).$ Just above the melting temperature, the vortices form three-dimensional line liquid with the correlation length along the c direction ${L}_{c}<~t,$ the sample thickness. The temperature where a resistive peak in ${R}_{\mathrm{bot}}$ develops corresponds to the decoupling temperature ${T}_{d}$ at which the vortices lose their correlation along the c direction and they dissolve into the two-dimensional pancake vortices. The $H\ensuremath{-}T$ phase diagram for the ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ single crystal is obtained.

Anisotropy and two-dimensional behaviour in the high-temperature superconductors

The electrodynamic behaviour of the high-temperature cuprate superconductors is strongly affected by the anisotropy of these layered materials. Their transport, magnetic and pinning properties are determined by the properties of vortices, which can be regarded as stacks of two-dimensional (2D) pancake vortices (with cores localized in the layers, bilayers or trilayers) connected by Josephson vortices (with cores localized in the nonsuperconducting charge-reservoir layers). When the Josephson coupling between the superconducting layers is strong, as in YBCO, the line energy associated with the Josephson vortices is large, the 2D pancake vortices in adjacent layers are strongly coupled and the magnetic anisotropy of the superconductor is relatively weak. When the Josephson coupling is weak, as in BSCCO, the line energy associated with the Josephson vortices is small, the 2D pancake vortices in adjacent layers are weakly coupled and the magnetic properties are highly anisotropic and nearly 2D. The transport properties for currents flowing parallel to the layers are dominated by 2D pancake vortex motion, while those for currents flowing perpendicular to the layers are dominated by Josephson vortex motion. In this paper, I review these effects and discuss a number of consequences for vortex-lattice melting, flux pinning, flux creep and the critical current density.

Effect of Dissipation on Quantum Tunneling of Vortices in Tl 2 Ba 2 Ca 2 Cu 3 O 10+δ Superconductors

The temperature and magnetic field dependence of the magnetic relaxation rate has been investigated at low temperatures (1.8 < T < 10 K) on two Tl2Ba2Ca2Cu3O10+δ samples (epitaxial thin film and sintered pellet). The temperature dependence gives evidence of a crossover in the mechanism of vortex motion, from classical thermal activation to quantum tunneling as temperature decreases. The field dependence of the relaxation rate indicates a crossover in the dimensionality of vortices, from three-dimensional flux lines to two-dimensional pancake vortices as field increases. For the thin film, the temperature dependence of the rate has been fitted to the theoretically predicted expressions for finite-temperature enhancement of the quantum rate in different regimes of dissipation. In spite of the similarity of the fits, the estimate of the ratio of Hall to viscous drag terms in the equation of motion indicates that quantum tunneling in this system occurs in an intermediate dissipative regime, where both terms contribute to the motion of vortices.

Field penetration and surface barriers in superconductingBi2Sr2CaCu2O8+δwhiskers

We have used an array of Hall probes to investigate the spatial dependence of the local magnetic induction of individual superconducting Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} whiskers. At low temperatures ({le}50K) the exponential temperature dependence of the field of first flux penetration, H{sub P}(T), is consistent with recent theories of flux penetration by two-dimensional pancake vortices. A power-law dependence at higher temperatures suggests that flux penetrates as three-dimensional lines nearer T{sub c}. We also show directly that at high temperatures the flux distribution is dominated by a surface barrier, whereas at low temperatures bulk pinning appears to dominate. {copyright} {ital 1997} {ital The American Physical Society}

Dissipation anisotropy of highly c-axis-oriented(Bi,Pb)2Sr2Ca2Cu3Ox silver sheathed tapes

Dissipation anisotropy of a highly c-axis-oriented (Bi,Pb)2Sr2Ca2Cu3Ox silver-sheathed tape in the vicinity of Tc(T/Tc&amp;gt;0.9) has been investigated by measuring the dependence of the magnetoresistance on the applied field, the temperature and the angle (θ) between the magnetic field direction and the tape surface. The results show that the dissipation anisotropy increases with the increase of the field and the temperature. It is found that the dissipation is only related to the magnetic field component perpendicular to the tape surface (c-axis component), i.e., R(H,θ)=R(Hsinθ). The experimental results can be accounted for in terms of the easy motion of two-dimensional (2D) pancake vortices along the CuO2 planes.

Magnetic coupling of two-dimensional pancake vortex lattices in a finite stack of thin superconducting films with transport currents in the two outermost layers

We give a detailed study of the magnetic coupling between two-dimensional (2D) pancake vortices in a stack of N Josephson-decoupled superconducting thin films. The problem of a single pancake vortex in a finite stack of layers is first considered. We then investigate the magnetic interaction between 2D pancake lattices residing in different layers. It is assumed that all these 2D lattices have the same structure and orientation, although it is not required that they be in perfect registry. We derive an analytical solution for the coupling force on a pancake in a lattice arising from its interaction with a vortex lattice in another layer. As a direct application of this solution, we consider the case wherein a magnetic field is applied perpendicular to the layers and equal but oppositely directed surface current densities are introduced into the top and bottom layers, respectively. For weak currents, force-balanced configurations of pancake vortices are obtained. We then show the existence of a decoupling surface current density. Above this critical value, slippage occurs between 2D pancake lattices in different layers. This decoupling surface current density is then calculated for different magnetic fields and for different values of N.

Anomalous magnetic behavior in the grain aligned HgBa2Ca2Cu3O8+δ superconductor

For magnetic fields parallel to the c-axis configuration for a layered structure Hg-1223 compound, the M–H curves displayed the wrong sign of hysteresis (virgin curve lies above the reverse curve) within a certain temperature regime ≥96 K. For the temperature region below 96 K, the magnetic response was caused by a one-component (three-dimensional) system. For 96 K&amp;lt;T&amp;lt;108 K, the interunit cell coupling of CuO2 plane pairs is broken, but the coupling of CuO2 planes inside the unit cell is effective. At the temperature region above 108 K, the magnetic response was caused by the fluctuation of two-dimensional pancake vortices in a decoupled CuO2 plane inside the unit cell.

Flux-line dynamics in YBa2Cu4O8 from 89Y NMR.

Measurements of the $^{89}\mathrm{Y}$ NMR linewidth \ensuremath{\Delta}\ensuremath{\nu} and spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ have been performed in an oriented powder sample of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ (${\mathit{T}}_{\mathit{c}}$ = 81 K) for both ${\mathbf{H}}_{0}$\ensuremath{\parallel}c and ${\mathbf{H}}_{0}$\ensuremath{\perp}c at ${\mathit{H}}_{0}$ = 9.4 and 5.9 T. Evidence for the effects of thermal motion of flux lines (FL's) below ${\mathit{T}}_{\mathit{c}}$ is presented and the microscopic correlation times of the FL motion are derived by using a simple model. From the temperature and field dependence of ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ an effective correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{e}}$ describing the pseudodiffusion of two-dimensional (2D) pancake vortices is extracted. The effective activation energy of the FL motion is found to be inversely proportional to the magnetic field, supporting the similar conclusion recently obtained in ${\mathrm{HgBa}}_{2}$${\mathrm{CuO}}_{4+\mathrm{\ensuremath{\delta}}}$. From the temperature dependence of \ensuremath{\Delta}\ensuremath{\nu} another correlation time \ensuremath{\tau}, different from ${\mathrm{\ensuremath{\tau}}}_{\mathit{e}}$, is obtained. It is argued that the correlation times derived from \ensuremath{\Delta}\ensuremath{\nu} and ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$, respectively, refer to different motional regimes below and above the irreversibility temperature ${\mathit{T}}_{\mathrm{irr}}$. \textcopyright{} 1996 The American Physical Society.

Instability of a tilted vortex line in magnetically coupled layered superconductors.

We calculate the line tension of a tilted stack of magnetically coupled two-dimensional pancake vortices held at the ends and show that the line tension becomes negative at an angle of 52\ifmmode^\circ\else\textdegree\fi{}. We further calculate the tilt modulus at arbitrary angle \ensuremath{\theta} and show that it becomes negative starting at the same angle 52\ifmmode^\circ\else\textdegree\fi{} for long wavelengths. A structure for the vortex line is given, which is shown to have a lower energy. \textcopyright{} 1996 The American Physical Society.