Vortex-glass Model Research Articles

Changing of the excess conductivity near the irreversibility temperature of the top seeded YBa2Cu3O7−x

A top seeded YBa2Cu3O7-x (YBCO) superconductor was grown using a bulk Nd123 seed crystal. Orientation peaks directed in the c-axis were observed from the X-ray diffraction measurement for the Y123 sample, indicating single crystal behavior. Magneto-resistivity measurements were carried out as a function of temperature under applied magnetic fields up to 4 T. The superconducting transition temperature (Tc) of the sample was obtained to be approximately 93 K and the excess conductivity curve was obtained experimentally from the resistivity measurement at zero magnetic field. The critical exponents were found to be λsfw = 2.26 ± 0.25, λ3D = 0.47 ± 0.03 and λ2D = 0.82 ± 0.07 for the short wave fluctuation (SWF) region and the mean field region characterized by 3D and 2D fluctuations, respectively. The crossover temperature determined from the crossover from 2D to 3D regime was found to be 96.37 K. The irreversible temperatures determined from the magneto-resistivity measurements and the irreversibility field line of the sample was obtained using the giant flux creep (gfc) model. The sample exhibits a behavior consistent with the gfc and the vortex glass model according to the n parameter calculated from the resistivity temperature measurements. The width enlarges with the applied magnetic field and was found to be approximately 4 K at 4 T for the Y123 sample. The sample was in the 3D regime below 96.37 K, while the sample was in the 2D regime between 96.37 K and 101.35 K. On the other hand, the reversible region was confined between 93.95 K and 93.33 K at 0 T. It was observed that 3D fluctuations are dominant in the reversible region, whereas 2D fluctuations are dominant in the irreversible region.

The activation energy U(T,B) in high temperature superconductor

It is reported in this paper on the thermally assisted flux flow in epitaxial YBa2Cu3O7-δ deposited by Laser ablation method on the SrTiO3 substrate. The resistivity measurements ρ (T, B) of the sample under various values of the magnetic field up to 14T in directions B∥ab-plane and B∥c-axis with a dc weak transport current density were investigated in order to determine the activation energy and then understand the vortex dynamic phenomena and therefore deduce the vortex phase diagram of this material. The apparent activation energy U0 (B) calculated using an Arrhenius relation. The measured results of the resistivity were then adjusted to the modified thermally assisted flux flow model in order to account for the temperature-field dependence of the activation energy U (T, B). The obtained values from the thermally assisted activation energy, exhibit a behavior similar to the one showed with the Arrhenius model, albeit larger than the apparent activation energy with ∼1.5 order on magnitude for both cases of the magnetic field directions. The vortex glass model was also used to obtain the vortex-glass transition temperature from the linear fitting of [d ln ρ/dT ] −1 plots. In the course of this work thanks to the resistivity measurements the upper critical magnetic field Hc2 (T), the irreversibility line Hirr (T) and the crossover field HCrossOver (T) were located. These three parameters allowed us to establish a phase diagram of the studied material where limits of each vortex phase are sketched in order to optimize its applicability as a practical high temperature superconductor used for diverse purposes.

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.

Thermally activated flux flow, vortex-glass phase transition and the mixed-state Hall effect in 112-type iron pnictide superconductors

The transport properties in the mixed state of high-quality Ca0.8La0.2Fe0.98Co0.02As2 single crystal, a newly discovered 112-type iron pnictide superconductor, are comprehensively studied by magneto-resistivity measurement. The field-dependent activation energy, U0, is derived in the framework of thermally activated flux flow (TAFF) theory, yielding a power law dependence U0~Hα with a crossover at a magnetic field around 2 T in both H⊥ab and H//ab, which is ascribed to the different pinning mechanisms. Moreover, we have clearly observed the vortex phase transition from vortex-glass to vortex-liquid according to the vortex-glass model, and vortex phase diagrams are constructed for both H⊥ab and H//ab. Finally, the results of mixed-state Hall effect show that no sign reversal of transverse resistivity ρxy(H) is detected, indicating that the Hall component arising from the vortex flow is also negative based on the time dependent Ginzburg-Landau (TDGL) theory. Meanwhile, the transverse resistivity ρxy(H) and the longitudinal resistivity ρxx(H) follow the relation |ρxy(H)|=Aρxx(H)β well with an exponent β~2.0, which is in line with the results in theories or experiments previously reported on some high-Tc cuprates.

The Effect of Using Different Y2O3 Layers on the Activation Energy and Irreversibility Line of MPMG YBCO Bulk at 1050 °C Growth Temperature

In this study, three kinds of YBCO samples which are named Y1, Y2 and Y3 were fabricated by a melt–powder–melt–growth (MPMG) method. The Y1 sample was placed into a platinum (Pt) crucible without Y2O3, the Y2 sample was located on a Al2O3 crucible with a freely poured Y2O3 powder and the Y3 sample was located on a Al2O3 crucible with a 1-mm-thick buffer layer of Y2O3. YBCO samples were investigated by magnetoresistivity (ρ–T) measurements in dc magnetic fields (parallel to the c-axis) up to 5 T. The effect of the Y2O3 layer on the activation energy and irreversible flux of the samples was studied. The activation energies (U) were determined using the Arrhenius activation energy law from ρ–T. The power law relationship for U with H−α was investigated. α was calculated to find out which defects were dominant in the samples. Irreversibility fields (Hirr) and upper critical fields (Hc2) were obtained using 10 and 90% criteria of the normal-state resistivity value from ρ–T curves. Irreversibility lines (ILs) were estimated from the equation Hirr ∼ (1 − Tirr(H)/Tirr(0))n. The fitting results to giant flux creep and vortex glass models were discussed.

Systematic Study of Vortex Pinning and a Liquid–Glass Phase Transition in BaFe2–xNixAs2 Single Crystals

The vortex pinning and liquid-glass transition have been studied in BaFe2–xNixAs2 single crystals with different doping levels (x = 0.065, 0.093, 0.1, 0.14, 0.18). We found that Ni-doped Ba-122 has rather narrow vortex-liquid state region. Our results show that the temperature dependence of the resistivity as well as I−V characteristics of Ni-doped Ba-122 is consistent with 3D vortex-glass model. It was found that -pinning gives the main contribution to overall pinning in 122 Ni-doped system. The vortex phase diagrams for different doping levels were built based on the obtained data of temperature of the vortex-glass transition Tg and the upper critical magnetic field Hc2.

The effect of growth temperature on the irreversibility line of MPMG YBCO bulk with Y2O3 layer

In this study, three kinds of YBCO samples which are named Y1040, Y1050 and Y1060 were fabricated by Melt–Powder–Melt–Growth (MPMG) method without a seed crystal. Samples seem to be single crystal. The compacted powders were located on a crucible with a buffer layer of Y2O3 to avoid liquid to spread on the furnace plate and also to support crystal growth. YBCO samples were investigated by magnetoresistivity (ρ–T) and magnetization (M–T) measurements in dc magnetic fields (parallel to c–axis) up to 5T. Irreversibility fields (Hirr) and upper critical fields (Hc2) were obtained using 10% and 90% criteria of the normal state resistivity value from ρ–T curves. M–T measurements were carried out using the zero field cooling (ZFC) and field cooling (FC) processes to get irreversible temperature (Tirr). Fitting of the irreversibility line results to giant flux creep and vortex glass models were discussed. The results were found to be consistent with the results of the samples fabricated using a seed crystal. At the fabrication of MPMG YBCO, optimized temperature for crystal growth was determined to be around 1050–1060°C.

Vortex–glass state in the isovalent optimally doped pnictide superconductor BaFe2(As0.68P0.32)2

We report on isochamp magneto-resistivity and ac susceptibility curves obtained in a high-quality single crystal of the isovalent optimally doped pnictide BaFe2(AsP)2 with superconducting temperature Tc = 27.8 K for H∥c-axis. Plots of the logarithmic derivative of the resistivity curves allowed the identification of a vortex–glass (VG) phase and to obtain the values of the critical glass temperature Tg, the temperature T* marking the transition to the liquid phase and of the critical exponent s. The presence of the VG phase is confirmed by detailed measurements of the third harmonic signal of the ac magnetic susceptibility. The modified VG model was successfully applied to the data allowing the obtention of the temperature independent VG activation energy Ub. The activation energy U0 obtained from the Arrhenius plots in the flux–flow region are compared with Ub and with U0 obtained from flux–creep measurements on a M(H) isothermal in the same sample. A phase diagram of the studied sample is constructed showing the Tg glass line, the T* line representing a transition (melting) to the liquid phase, the mean field temperature Tc(H) line and the Hp line obtained from the peaks in isothermal critical current, Jc(H) curves, which are explained in terms of a softening of the vortex lattice. The glass line was fitted by a theory presented in the literature which considers the effect of disorder.

Flux-flow and vortex-glass phase in iron pnictide single crystals with K

We analysed the flux-flow region of isofield magnetoresistivity data obtained on three crystals of NixAs2 with Tc ∼ 20 K for three different geometries relative to the angle formed between the applied magnetic field and the c-axis of the crystals. The field dependent activation energy, U0, was obtained from the thermal assisted flux-flow (TAFF) and modified vortex-glass models, which were compared with the values of U0 obtained from flux-creep available in the literature. We observed that the U0 obtained from the TAFF model show deviations among the different crystals, while the correspondent glass lines obtained from the vortex-glass model are virtually coincident. It is shown that the data is well explained by the modified vortex-glass model, allowing extract of values of Tg, the glass transition temperature, and , a temperature which scales with the mean field critical temperature . The resulting glass lines obey the anisotropic Ginzburg–Landau theory and are well fitted by a theory developed in the literature by considering the effect of disorder.

Effect of injected spins with different polarized orientations on the vortex phase transition in La0.7Sr0.3MnO3/La1.85Sr0.15CuO4 heterostructure

The current-voltage (I-V) characteristics with spin injection were investigated for the epitaxial La0.7Sr0.3MnO3/La1.85Sr0.15CuO4 heterostructure rotated from H//c to H//ab in magnetic fields up to 14 T. It is found that all the I-V curves in various magnetic fields can be scaled with a three dimensional (3D) vortex glass model, and the spin injection can induce a better 3D scaling behavior, which is closely related to the decrease of the anisotropy parameter. A vortex phase diagram for the evolution of vortex glass transition field (Hg) and upper critical field (Hc2) indicates that both Hg and Hc2 are suppressed by spin injection, and this effect becomes more obvious in the case of H//ab, which probably originates from the different suppression on the superconducting pairing strength by different injected spins' orientations.

Vortex Dynamics and Irreversibility Line in FeSe0.25Te0.75

AC multi-harmonic susceptibility measurements were performed in the FeSe0.25Te0.75 superconductor. A large frequency-magnetic field-temperature (f-H-T) region of the superconducting phase diagram was mapped under a wide range of the DC magnetic field. In particular the irreversibility line was accurately drawn up to 20 T as a function of both T and f. The frequency dependence of the irreversibility line was analyzed using the 3D vortex glass model, well describing the experimental behavior up to high magnetic field. The data evidence the evolution in time of the metastable critical state in a final stable vortex glass phase by decreasing the frequency. Moreover, from the Werthamer, Helfand and Hohenberg theory we estimated the upper critical field μ0Hc2(0K)∼ 62 T. The observed 3D flux-pinning response points out that this system is suitable for carrying quite high critical currents.

Applicability of the vortex-glass model for the single crystal Tl0.4K0.41Fe1.71Se2**Project supported by the National Natural Science Foundation of China (Grant Nos. 11404002, 11404003, and 11074001) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, and the “211 Project” of Anhui University, China (Grant No. J01001319-J10113190007).

We measure the current–voltage (I–V) characteristics for the single crystal of Tl0.4K0.41Fe1.71Se2 with the superconducting transition temperature (TC) around 30.5 K, under a 10 T magnetic field applied perpendicular and parallel to the ab plane. We find that the shapes of the I–V isotherms are very different from the description by the vortex-glass (VG) model. Combining theoretical calculations and analysis of the ρH⊥ab–T and ρH∥ab–T data, we give an explicit discussion over the suitability of the VG model for the A0.8Fe2Se2 superconductors, and point out the possibility of the material acting as a convenient platform for re-examination and further study of the complex vortex behaviors in the layered superconductors.

INFLUENCE OF INTRINSIC PINNING ON THE RESISTIVE PROPERTIES OF YBa2Cu3O7-δ SINGLE CRYSTALS

The dynamics of vortex matter in YBa 2 Cu 3 O 7-δ single crystal with unidirectional twin boundaries is studied experimentally in a wide range of velocities of the magnetic flux in a tilted magnetic field. It is determined that with the orientation of the magnetic field vector in the locality of the ab-plane, the dynamics of the magnetic flux near the melting temperature of the vortex lattice can be described by the Kim–Anderson model and as the temperature is lowered, by the theory of collective pinning on small-scale defects or by the vortex glass model. The intrinsic pinning caused by the layered crystal structure of the material has an impact on the dynamics of magnetic flux and this effect increases with the decreasing of the temperature.

A generalized method of estimation of critical exponents through an indigenous susceptometry setup for YBCO materials

The real and imaginary parts of complex susceptibility values of bulk ceramic YBCO materials have been extracted at different frequencies and temperatures by measuring impedances using a single-coil swept-ac method. From these susceptibility components, the ac conductivity and its loss angle have been derived numerically. The dynamic and static critical exponents, z and ν obtained from the scaling of conductivity loss angle based on FFH’s vortex glass (VG) model were found to be in agreement with the values obtained by other workers, in different methods characterizing a continuous phase transition and revealing a stronger correlation in HTS materials. To verify their universality, it has been shown that the exponent values support the scaling features of ac-conductivity (or resistivity) very well and can scale susceptibility also at the proximity of critical temperature. It is highly expected that this simpler and straight forward method of extraction and evaluation of these critical exponents discussed here may be applicable to any other High Temperature Superconductors or other complex materials in bulk form.

The applicability of the vortex glass model in the layered superconductorCu0.03TaS2

The vortex glass theory has been successfully employed to describe the vortex phase state of highTC superconductors (HTSCs). Its validity can be examined by scaling the current–voltageisotherms with appropriate exponents and a universal scaling function. However, thissecond order phase transition model is not applicable for the layered superconductorCu0.03TaS2 due to its weak pinning, which could be proved by the peak effect in theM–H loop. Finally, we give the different pinning mechanisms with and . Vortex strings and pancake vortices are formed under parallel and perpendicularmagnetic fields, respectively. The vortex strings are pinned by normal layers in layeredsuperconductors, while the pancake vortices are connected by Josephson coupling.

The electrical transport properties of high quality Bi-2223 crystal

We have studied electrical transport properties of a high qualityBi2Sr2Ca2Cu3O10 + x crystal below a superconducting critical temperature,Tc. In magneticfields B parallel to the c axis just above a voltage response onset resistance versus temperature data are well fittedto the vortex-glass model. Obtained from the vortex-glass analysis, a melting transitionboundary for Bi-2223 crystal is shifted towards lower temperatures compared to previouslyreported data for a (Bi, Pb)-2223 single crystal. The critical current density,Jc, of Bi-2223 crystalsis close to Jc values presented elsewhere for Bi-2223 tapes, suggesting a principal role ofweak intrinsic pinning properties of Bi-2223 as a main limiting factor ofJc of Bi-2223 conductors.

Effect of stripe order on the vortex phase transition inLa1.44Nd0.4Sr0.16CuO4 films

The vortex phase transition in La1.44Nd0.4Sr0.16CuO4 epitaxial films with different thicknesses under a compressive strainwere studied systematically by measuring the current–voltage (IV) characteristics in magnetic fields perpendicular to theCuO2 planes. For a strongly compressed thin film, in which the static stripe order is destroyed, theIV curves show a good three-dimensional (3D) vortex glass (VG) scaling collapsein various magnetic fields, indicating a 3D VG phase transition. By applyingthe standard scaling procedure to the data of a strain-released thick film withstatic stripe order, neither a 3D nor a quasi-2D VG model works well. Furtherinvestigation shows that, in order to achieve a good scaling collapse, theKosterlitz–Thouless correlation length should be used for the isothermals aboveTg. The scaling ofisothermals below Tg can also be optimized if the VG correlation length and adjusted static critical exponentν are usedwith D = 2 only, indicating that a quasi-2D VG phase might exist. Our findings reveal that the natureof the vortex phase transition is completely altered in the presence of the stripe order.

Solid–liquid transition in Nb powder determined by third harmonic susceptibility

Measurements of the third harmonic of the AC-susceptibility were employed to determine the boundaries of the linear regime of the magnetic response of Nb powder. Non-linear contributions to the magnetic response reveal the occurrence of a structured phase, disappearing as the vortex lattice melts to the liquid state. A systematic study of the third harmonic was conducted to determine how its onset temperature depends on experimental parameters, such as the frequency and amplitude of the excitation field. The melting line (ML) has been extracted from the onset temperature measured at low-frequencies and low-excitation fields in the presence of DC magnetic fields. The study indicates that the ML can be described by a 3D vortex-glass model, except at lower fields, where the system experiences a depinning crossover, and the best description of the experimental data is provided by a 3D Bose-glass model.

Angular-dependent I–V characteristics in borocarbide superconductorYNi2B2C

We present angular-dependent current–voltage(I–V) measurementsin borocarbide YNi2B2C single crystals near the vortex-glass irreversible line. External magnetic fields are applied along the angleθ with respectto the c-axis.The nonlinear I–V curves reveal scaling behaviour near the transition. Using the scaling analysis, therelevant critical exponents and vortex transition temperatures are determined for allorientations. The data agrees well with the vortex-glass (VG) model. No evidencewas found that supports the existence of a Bose-glass (BG) type of transition.

Flux-flow voltage noise and normal-state resistance fluctuations in epitaxial (Dy, Y)Ba 2Cu 3O 7 thin films

We have studied low-frequency noise in the normal and mixed states of high- T c thin films. In the normal state, resistance fluctuations with a 1/ f power spectrum are observed from 100 K up to 300 K. The normal state noise is largely attributable to hopping or reordering of oxygen vacancies which in turn lead to fluctuations in local carrier density in the copper oxygen planes. Analysis shows a substantial density of oxygen defect states with activation energies below 0.5 eV, followed by a rapid increase at higher energies. In the mixed state, we have measured the current-induced, vortex-motion voltage noise. When the current–voltage characteristics are nonlinear there exist two distinct regimes. The first is a low magnetic field regime where measurements of the variations of voltage noise with magnetic field reveal reproducible, microstructure-dependent noise magneto-fingerprints. Rapid variations of the noise as a function of magnetic field and ac current drive experiments indicated that the noise is associated with metastability of pinned vortex configurations. Above magnetic fields which roughly match vortex separation with the grain size in the films, the magnitude and fine structure of the noise magneto-fingerprints are suppressed, suggesting a crossover to a more weakly pinned vortex state. The second regime is a low bias voltage regime where the observed noise scales linearly with bias voltage and has a 1/ f-like spectrum. The linear voltage scaling is reminiscent of vortex shot noise although no characteristic transit time could be determined. At higher voltage biases, the noise power drops off rapidly. We attribute the sharp drop off to a loss of pinning at higher temperatures and fields which results in the absence of metastability in the vortex pinned states. The temperature and magnetic field dependence of the noise are discussed in the context of various models including vortex shot noise, channel, critical current fluctuation, and vortex-glass models.