Vortex Glass-liquid Transition Research Articles

Study of vortex glass-liquid transition in superconducting Fe(Te, Se) thin films on LaAlO3 substrates

Superconducting thin films of two different thicknesses have been fabricated on (100) LaAlO3 substrates using a polycrystalline target of composition Fe1.05Te0.50Se0.50 by the pulsed laser deposition technique. The onset of superconducting transition temperatures (TConset) at 0 T magnetic field of the grown thin films of thickness of ∼74 nm and ∼185 nm are ∼12.65 and 13.15 K, respectively. The upper critical field BC2(0) values have been calculated by the Ginzburg–Landau theory as well as by the Werthamer–Helfand–Hohenberg model, and the corresponding coherence lengths have been estimated. In the present work, the thermally activated energy (TAE) has been obtained using the conventional Arrhenius law as well as by a modified thermally activated flux flow (TAFF) theory. For both models, the TAEs of vortices show a crossover at a magnetic field of ∼2 T corresponding to the transition from the single vortex pinning regime to the collective vortex pinning regime. Based on the analysis of the field dependence of TAE, the planer/point defect dominating magnetic field regions have been identified. The analysis of the magnetotransport data with the modified TAFF model reveals the dominating three dimensional behavior of vortices for both thin films. Moreover, in the vortex phase diagram, a narrow vortex melting region and a vortex glass-liquid phase transition below BC2 have been observed for both of the grown thin films. Furthermore, the X-ray photoelectron spectroscopy results show that Fe is present in Fe2+ and Fe3+ chemical states in both thin films.

Vortex glass-liquid transition and activated flux motion in an epitaxial, superconducting NdFeAs(O,F) thin film

An epitaxial NdFeAs(O,F) thin film of 90 nm thickness grown by molecular beam epitaxy on MgO single crystal with Tc = 44.2 K has been investigated regarding a possible vortex glass-liquid tran-sition. The voltage-current characteristics show excellent scalability according to the vortex-glass model with a static critical exponent {\nu} of around 1.35 and a temperature-dependent dynamic exponent z increasing from 7.8 to 9.0 for the investigated temperature range. The large and non-constant z values are discussed in the frame of 3D vortex glass, thermally activated flux motion, and inhomogeneity broadening.

Influence of crossing angles of columnar defects on vortex glass transition in YBCO thin films

To investigate the influence of the crossing angles of columnar defects (CDs) on the in-field properties of the critical current density Jc and the scaling parameter m derived from the isothermal current–voltage characteristics near the glass-liquid transition at B||c-axis, YBCO thin films were irradiated using the 200MeV Xe ions at two angles ±θi relative to the c-axis. For the thin films, the obvious effect of the crossing angle of CDs occurred on the vortex glass-liquid transition more than the Jc properties. On the glass-liquid transition line, two inflection points induced by the c-axis correlated pinning were confirmed even for the samples of θi=±45°. In the magnetic field dependence of m, the peak or kink appeared near B/Bϕ=1/3 for the smaller crossing angles, whereas that was slightly visible for the samples of θi=±45°. In addition, the values of m for the small crossing angle were larger than those for the parallel CD configuration, while those for the larger crossing angle became smaller. These results suggested that the morphologies of correlated pinning centers strongly affect the dynamics of flux lines even in the disordered system such as thin films.

Two-dimensional flux pinning in multilayered MgB 2/Ni thin films prepared by electron beam evaporation

Multilayered MgB 2/Ni thin films on Si substrates by electron beam evaporation were fabricated to enhance the critical current density J c in magnetic fields parallel to the surface. The magnetic field dependence of J c of the multilayered MgB 2/Ni thin films for B//surface shows a peak at the matching field. In the field angular dependence of J c, a sharp peak appears at B//surface. These results indicate that Ni layers which have ferromagnetism act as two-dimensional pinning centers in multilayered MgB 2/Ni thin films. The vortex glass–liquid transition temperature T g and the pinning parameter m were evaluated from the E– J characteristics. The slope of the magnetic field dependence of m in the multilayered MgB 2/Ni thin film under the matching field is larger than that over the matching field. In the T g/ T c– B phase diagram, the remarkable enhancement of T g for B//surface appears around the matching field. These features are characteristic behaviors for two-dimensional pinning centers.

Flux pinning properties of ErBa2Cu3Oy thin films with BaZrO3 nanorods

ErBa2Cu3Oy (ErBCO) thinfilms with BaZrO3 (BZO) nanorods were prepared by a PLD method for an enhancement of the critical current densityJc. Thevalues of Jc for the ErBCO thin film containing 1.5 wt% BZO (Er15) in magnetic fields are higher thanthose for the ErBCO thin film containing 0.5 wt% BZO (Er05). The peaks ofJc have been observed in the angular dependence ofJc in both the films when the magnetic field is applied parallel to thec-axis.It has been found that the peak is attributed to the flux pinning by BZO nanorods oriented parallel tothe c-axis. The vortex glass–liquid transition temperatureTg and the pinningparameter m were derived by fitting observed electric transport properties to thetheoretical expression based on the percolation transition model. The value ofTg of Er15 is higher than that of Er05. This result indicates that the vortex glass phaseextends to a higher temperature region on increasing the fraction of BZO. The peak ofm has been found in the magnetic field dependence. This fact is probably due to matching thedensity of BZO nanorods with that of fluxoids, which was confirmed by TEM observations.

Critical current density of MgB2 thin film with pinning centres introduced by deposition in oxygen atmosphere

Critical current densities Jc of MgB2 thin films have been measured; these were prepared by an electron beam evaporationmethod without any post-annealing. In order to improve the characteristics ofJc in high magneticfields, a MgB2 thin filmwas deposited in an O2 atmosphere. The values of Jc of the O2-doped film have exceeded those of the non-doped film inmagnetic fields applied perpendicular and also parallel to thec-axis. Thepeak of Jc caused by the c-axis correlated pinning centres has been observed in the angular dependence ofJc. The uppercritical field Bc2 and the vortex glass–liquid transition fieldBg have been estimated from temperature dependences of resistivity curves inboth directions of the magnetic fields perpendicular and parallel to thec-axis. It isfound that Bc2 andBg are increased bythe introduction of O2 in both the directions of the applied field. This fact indicates thateffective pinning centres have been introduced by the deposition of theMgB2 thinfilm in an O2 atmosphere.

Dose effect of heavy-ion irradiation on the critical exponents in YBa 2Cu 3O 7− x thin films

We investigated the influence of densities of columnar defects on the critical exponents estimated from the critical scaling analysis of current–voltage characteristics in YBa 2C 3O 7− x thin films. To avoid the difference of background pinning between samples, the densities of columnar defects were controlled in one sample successively. The dynamic critical exponent z increased with increasing the densities of columnar defects from B φ=0.5–1.0 T. It was also found that the installed defects led to the appearance of peak in the magnetic field dependence of z, while such peak did not appear before irradiation. These results are explained by the percolation model considering the statistical distribution of the pinning strength rather than the vortex glass–liquid transition model. The various changes of z due to the heavy-ion irradiation are related to the change of the pinning strength distribution due to the introduction of columnar defects, which act as the strong pinning centers.

Observation of flux flow based on vortex-glass scaling analysis for single phase HgBa 2Ca 2Cu 3O 8+ δ superconductor

A single phase HgBa 2Ca 2Cu 3O 8+ δ superconductor, having a T c of 133 K, was successfully synthesized. Electrical resistivity and critical current density measurements were performed. With the experiments of flux motion, it became clear that there is actually a more subtle shape to the I– V curve, or the ρ– T curve: separate regions of flux creep and flux flow can be identified according to the two universal curves, indicating a vortex-glass transition. This paper reports the ρ– T curves collapse on to the positive curvature line, associating with flux flow. The phase diagram in H– T space for the vortex-lattice can also show a vortex-glass–liquid transition at temperature T g.

A theory of the thermal depinning transition in type-2 superconductors

Abstract It is pointed out theoretically that the electric field, E , vs. current density, J , characteristic of the vortex glass state is different from that predicted by M.P.A. Fisher; that is, the electric resistivity, ρ = E / J has a finite value even at J →0, while the Fisher theory predicts ρ →0 with J →0. It is also pointed out that the vortex glass–liquid transition is merely a kind of the bifurcation transition in the mixed state of type-2 superconductors containing pinning centers, which may be called the thermal depinning transition between the pinning state and the depinning state of fluxoids resulting from the thermal agitation on fluxoids. Furthermore, it is shown theoretically that only the flux flow resistivity obeys the scaling law near the thermal depinning transition temperature, T dp , while the flux creep resistivity approaches a finite value as J is decreased to zero, even in the pinning state below T dp . When ρ is measured down to a very small level of E , therefore, the noticeable deviation from the scaling law of ρ against J that was predicted by Fisher is expected to appear due to the above-mentioned behavior of the flux creep resistivity. The above theoretical conclusion that is contrary to the theoretical prediction by Fisher, however, seems to be supported by the recently observed data over a very wide range of the electric field, E provided by Kodama et al., because the present theoretical expression for the E vs. J , characteristics agrees quantitatively with these observed data.

Irreversibility field of Bi-2223 silver-sheathed tape determined with different electric field criteria

Dependence of the irreversibility field ( B i) on the electric field criterion ( E c) was measured for a Bi-2223 silver-sheathed tape wire using various measuring methods. It was found that B i increased monotonically with the electric field criterion. A good agreement was obtained for B i between experiments and the theoretical analysis using the flux creep-flow model. This implies that the resistive property of superconducting wires can be well described by the mechanism of flux creep and flow. The vortex glass–liquid transition field ( B g) was also determined from E– J curves which measured in the low and high electric field regions. It was found that B g also depends on the ranges of electric field. This is incompatible with the prediction of the vortex glass–liquid transition theory.

Current-voltage characteristics in a superconducting Bi-2223 tape in the range of very low electric field

Current-voltage characteristics in the range of very low electric field were analyzed from a relaxation of the magnetization using a SQUID magnetometer in a superconducting Bi-2223 tape. It was found that the observed current-voltage characteristics in this range were scaled well as predicted by the vortex glass-liquid transition theory. However, the obtained transition field was much lower than that obtained from a scaling in the higher electric field range. At the same time, the dynamic critical index, z, was much larger than usual values. Hence, it is concluded that these parameters are not uniquely determined independently of the level of electric field. The experimental result was compared with the theoretical analysis using the flux creep-flow theory in which the distribution of the effective flux pinning strength was taken into account. It was found that the theoretical result explains approximately the observed result. This shows that the essential mechanism which governs the transport property in the superconducting tape is the flux pinning.

Theoretical study on vortex glass-liquid transition in pinned superconductors

The vortex glass-liquid transition in pinned superconductors is studied theoretically from the viewpoint of thermal depinning of flux lines. It is clarified that this depinning phenomenon is a transition of the second order. This result is consistent with the fact that the scaling of the current-voltage curves is well explained by the theoretical model of flux creep and flow. It is also found that the degree of disorder of the flux line lattice decreases abruptly with elevating temperature above the transition temperature. This agrees qualitatively with the observation of flux lines using a Lorentz microscope.

Inhomogeneous distribution of flux pinning strength and its effect on irreversibility line and vortex glass-liquid transition line in Bi-2212 tapes

The irreversibility line and the vortex glass-liquid transition line under a magnetic field parallel to the c-axis are investigated for silver-sheathed and dip-coated Bi-2212 tape wires. It is found that the two characteristic lines for silver-sheathed tape is well explained by the flux creep-flow model assuming the distribution of pinning strength with a single peak. On the other hand, general agreements are obtained for these characteristic lines and the critical current density between experiments and theory only when two peaks are assumed in the distribution of flux pinning strength for the dip-coated tape. The causative structure in the dip-coated tape for the peak at small strength in the distribution is discussed.

The vortex glass to liquid transition in Bi2212 whisker

Through scaling the dc I– V isotherms of Bi2212 whisker in magnetic field H‖ c, the vortex glass–liquid transition is found in Bi2212 whisker whereas it does not appear in Bi2212 crystal slab [R. Behr, J. Kotzler, G. Nakielski, M. Baumann, M. Kaufmann, J. Kowalewski, Physica C 235 (1994) 2669]. The critical exponents are ν=0.5, z=4.0. We found that the critical exponents are influenced by the planar defects of the sample. The result was compared to those of single crystals and films [Behr et al., 1994; H. Yamasaki, K. Endo, S. Kosaka, M. Umeda, S. Yoshida, K. Kajimura, Phys. Rev. B 50 (17) (1994) 12959].

Thermal depinning of flux lines in superconductors

The thermal depinning of flux lines on the irreversibility line is investigated from a viewpoint of thermodynamics using the coherent potential approximation theory, a kind of statistical theory for flux pinning. The effect of thermal activation is approximately introduced by making the pinning potential shallow following the theoretical scheme by Yamafuji et al. It is shown that the thermal depinning is the transition of the second order. Since the vortex glass–liquid transition, which is considered to be identical with the thermal depinning, is originally predicted to be the second-order transition, the present theoretical result is reasonable. The present result also suggests that the irreversibility line observed at higher temperatures and at lower fields than the critical point for weakly pinned superconductors is also the transition line of the second order. In addition, it is shown that the degree of disorder of the flux line lattice decreases fast, suggesting a quick recovery of the order of the lattice with elevating temperature above the critical temperature.

Effect of distribution of flux pinning strength on irreversibility line and vortex glass–liquid transition line in a Bi-2212 tape wire

The irreversibility line and the vortex glass–liquid transition line are investigated for a dip-coated Bi-2212 superconducting tape. These two characteristic lines are also analyzed using the flux creep-flow model in which the distribution of the flux pinning strength is assumed. These results are compared with the previous results for a silver-sheathed Bi-2212 tape. Good agreements were not obtained simultaneously between the experiment and the theory for the two characteristic lines in the dip-coated tape, although the theory explained the experimental results well in the silver-sheathed tape. This seems to be ascribed to the peculiar distribution of the flux pinning strength with two peaks due to a percipitation of an impurity phase in the present dip-coated tape specimen.

Correlation length of flux lines in the vicinity of the vortex glass-liquid transition in high-temperature superconductors

The correlation length of flux lines responsible for the scaling of current-voltage curves in the transition region between the glass and liquid states in high temperature superconductors is argued based on experimental results on various specimens of Bi-based superconductors. From the correspondence between the temperature dependence of the pinning correlation length and the static critical index, v, it is concluded that the responsible correlation length is the pinning correlation length. This insists that the pinning interaction governs the flux lines in the glass state. This hypothesis is supported by the fact that the transition line depends on the flux pinning strength and the dynamic critical index, z, is appreciably influenced by the width of the distribution of flux pinning strength. It is concluded that the so-called vortex glas-liquid transition is a kind of transition of flux lines between the glass state governed by the pinning and the depinned melt state due to the thermal activation.

Scaling of current-voltage curves of Bi-2212 tape wire

The current-voltage curves are measured for a dip-coated Bi-2212 tape wire at various temperatures under the magnetic field parallel to the c-axis. It is found that the current-voltage curves are approximately scaled on two master curves by normalizing as predicted in the vortex glass-liquid transition theory. However, the obtained dynamic critical index was about 3 and too small in spite of the two-dimensional flux line system. These results are compared with the theoretical analysis based on the flux creep-flow model taking account of the distribution of pinning strength. It is found that the theoretical result approximately explains the experimental result on the scaling behavior, the critical indices and the transition line.

Scaling of current-voltage curves in superconducting Bi-2223 silver-sheathed tape wires

The current-voltage characteristics are measured for two Bi-2223 tape specimens with different critical current densities at various temperatures under the magnetic field parallel to the c-axis. It is found that the current-voltage curves are scaled on two master curves by normalizing as predicted in the vortex glass-liquid transition theory. However, the obtained dynamic critical indices increased, and the static critical indices decreased appreciably with increasing magnetic field. These experimental results are compared with the numerical calculation based on the flux creep and flow model, taking the distribution of the flux pinning strength into account. Agreement is obtained between the experimental and theoretical results not only on the scaling curve but also on the critical indices and the transition line. The static critical index showing a divergence of the correlation length near the transition temperature can also be explained from the temperature dependence of the pinning correlation length. These results suggest that the scaling behavior is not correlated to the phase transition of fluxoids assumed in the vortex glass-liquid transition theory but seems to be correlated to a kind of transition governed by the flux pinning.

Irreversibility and transport in the high Tc superconductor HgBa2Ca2Cu3O8 + δ

A HgBa2Ca2Cu3O8 + δ superconductor, having a Tc of 133 K (oxygen-annealed sample), was successfully synthesized. A.c. susceptibility, electrical resistivity and critical current density measurements were performed. The irreversibility line (IL) was obtained and a new feature of 1 − t ∝ H1/4 (t = Tirr/Tc is the reduced temperature, where irr is the irreversibility temperature) was found and explained in terms of T. Matsushita's theory. The results of the transport measurements can be looked upon as evidence that there also might be a vortex glass-liquid transition in Hg-based systems. The dimensions of the superconducting CuO2 layer for different compounds was used to explain the observed transition in the IL.