Bragg Glass Research Articles

Depinning and Creep Motion in Glass States of Flux Lines

Using dynamical computer simulation, we investigate vortex matter in glass states. A genuine continuous depinning transition is observed at zero temperature, which also governs the low-temperature creep motion. With the notion of scaling, we evaluate in high accuracy critical exponents and scaling functions; we observe a non-Arrhenius creep motion for weak collective pinning where the Bragg glass is stabilized at equilibrium, while for strong pinning, the well-known Arrhenius law is recovered. In both cases, a sharp crossover takes place between depinning and creep at low temperatures.

Influence of Grain Boundaries and Sn Distribution on the H-T Phase Diagram of ${\rm Nb}_{3}{\rm Sn}$

We measured the 1st and 3rd harmonics of the AC magnetic susceptibility as a function of the temperature and the DC magnetic field, on several Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn samples (single crystal, polycrystalline samples and multifilamentary wires), with different pinning properties. From these measurements, the Bragg phase, the disordered one and the irreversibility line have been identified in the H-T phase diagram of analysed samples. We observed that the presence of the pinning due to grain boundaries increases the region of the disordered phase in respect to the pinning due to point defects, and gives the possibility to detect an irreversibility line. Nevertheless it is possible to observe a phase transition between the Bragg and the disordered phase if the sample has an almost spatially uniform tin content. On the contrary, in a sample characterized by similar grain boundaries properties but where a tin gradient is present, the Bragg glass phase tends to disappear.

Influence of aluminum substitution on the vortex matter properties ofMgB2

The vortex matter phase diagrams of aluminum doped ${\mathrm{Mg}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}{\mathrm{B}}_{2}$ crystals, deduced from local Hall ac-susceptibility (for $\mathbf{H}\ensuremath{\parallel}c$ axis) and bulk dc-magnetization measurements (for $\mathbf{H}\ensuremath{\parallel}c$ axis and $ab$ plane) are reported. As in pristine and carbon doped $\mathrm{Mg}{\mathrm{B}}_{2}$, aluminum substituted crystals display the peak effect in the critical current. The peak effect is located very close to the ${H}_{c2}^{c}(T)$ line, while it disappears below a characteristic magnetic field ${H}^{*}$ that depends on Al content. The absence of significant bulk pinning below the onset of the peak effect implies that the Bragg glass phase is present there. In some of the crystals the peak effect is not present as a sharp negative peak of the real part of the local ac susceptibility, but it appears as a negative double-peak feature. This observation may be related with the miscibility gap that occurs for $0.05\ensuremath{\leqslant}x\ensuremath{\leqslant}0.5$. For low aluminum content the ${H}_{c2}^{c}(T)$ line lies slightly above the corresponding one of the pristine $\mathrm{Mg}{\mathrm{B}}_{2}$, but for higher aluminum content, ${T}_{c}$, ${H}_{c2}^{ab,c}(0)$, and anisotropy parameter $\ensuremath{\gamma}={H}_{c2}^{ab}(0)∕{H}_{c2}^{c}(0)$ take lower values when compared to pristine $\mathrm{Mg}{\mathrm{B}}_{2}$. Similarly with the pristine $\mathrm{Mg}{\mathrm{B}}_{2}$ crystals for the superconducting aluminum substituted crystals, the anisotropy parameter decreases monotonously as temperature increases as well. All the experimental observations could be qualitatively explained within the clean two-band approximation.

Vortex phase diagram and dynamics at low temperature in a thick a-MoxGe1−x film

We study the vortex phase diagram and dynamics in the low-temperature liquid phase of a thick amorphous a-MoxGe1−x film with weak pinning. The vortex solid state is ordered vortex lattice or Bragg glass, which is different from the disordered vortex glass of a-MoxSi1−x films with stronger pinning. We find, however, that the vortex liquid state is similar to that for the a-MoxSi1−x films, involving the quantum-vortex-liquid phase at low temperature, where we again detect the unusual vortex flow.

Magnetocaloric studies of the peak effect in Nb

We report a magnetocaloric study of the peak effect and Bragg glass transition in a Nb single crystal. The thermomagnetic effects due to vortex flow into and out of the sample are measured. The magnetocaloric signature of the peak effect anomaly is identified. It is found that the peak effect disappears in magnetocaloric measurements at fields significantly higher than those reported in previous ac-susceptometry measurements. Investigation of the superconducting to normal transition reveals that the disappearance of the bulk peak effect is related to inhomogeneity broadening of the superconducting transition. The emerging picture also explains the concurrent disappearance of the peak effect and surface superconductivity, which was reported previously in the sample under investigation. Based on our findings we discuss the possibilities of multicriticality associated with the disappearance of the peak effect.

Phase diagram of vortices in high-Tcsuperconductors from lattice defect model with pinning

The theory presented is based on a simple Hamiltonian for a vortex lattice in a weak impurity background which includes linear elasticity and plasticity, the latter in the form of integer valued fields accounting for defects. Within a quadratic approximation in the impurity potential, we find a first-order Bragg-glass, vortex-glass transition line showing a reentrant behavior for superconductors with a melting line near $ H_{c2} $. Going beyond the quadratic approximation by using the variational approach of M\'ezard and Parisi established for random manifolds, we obtain a phase diagram containing a third-order glass transition line. The glass transition line separates the vortex glass and the vortex liquid. Furthermore, we find a unified first-order line consisting of the melting transition between the Bragg glass and the vortex liquid phase as well as a disorder induced first-order line between the Bragg glass and the vortex glass phase. The reentrant behavior of this line within the quadratic approach mentioned above vanished. We calculate the entropy and magnetic induction jumps over the first-order line.

Vortex dynamics in (Tl,Pb)(Sr,Ba) 2Ca 2Cu 3O y single crystal

Magnetic moment measurements performed on a single crystal sample of (Tl,Pb)(Sr,Ba) 2Ca 2Cu 3O y reveal an increase in magnetic moment at intermediate fields. Magnetic hysteresis ( m– H) loops were taken at different constant temperatures using either a MPMS-5T SQUID magnetometer or a PPMS-9T magnetometer and within the temperature range 0.1 < T/ T c < 0.85. Vortex dynamics at fields below the peak in hysteresis loops for the sample is shown to be well explained by a quasi-lattice Bragg glass state and elastic collective vortex creep.

Vortex phase diagram near the lower critical point in untwinned YBa2Cu3Oy single crystals

In order to study the vortex phase diagram near the lower critical point Hlcp of the first-order melting transition, we have measured resistivity ρ(H,T) and magnetization M(H) in untwinned YBa2Cu3O7 single crystals. Below Hlcp, the resistive transition is described by the vortex glass theory and the relatively small value of the critical exponent can be explained by the recent theory of the vortex glass scaling which takes into account the pinning disorder strength. The partial loop measurements of M(H) with repeated field cycling provide evidence of the first-order transition at the onset of the peak effect H∗(T) between the Bragg glass and the vortex glass phases.

Smectic liquid crystals in an anisotropic random environment

We report a high-resolution x-ray scattering study of the smectic liquid crystal octylcyanobiphenyl (8CB) confined to aligned colloidal aerosil gels. The aligned gels introduce orientational fields that promote long-range nematic order while imposing positional random fields that couple to the smectic density wave and disrupt the formation of an ordered smectic phase. At low densities of aerosil, the low-temperature scattering intensity is consistent with the presence of a topologically ordered XY Bragg glass phase that is predicted to form in response to such anisotropic quenched disorder. The observed features of the phase include an algebraic decay of the smectic correlations, which is truncated at large length scales due to the imperfect nematic order, and a power-law exponent that agrees closely with the universal value predicted for the XY Bragg glass. At higher aerosil densities, deviations from the XY Bragg glass form are apparent. At high temperature, the scattering intensity displays pretransitional dynamic fluctuations associated with the destroyed nematic to smectic-A transition. The fluctuations obey quasicritical behavior over an extended range of reduced temperature. The effective critical exponents for the correlation lengths and smectic susceptibility differ systematically from those of pure 8CB, indicating that coupling of the nematic order to the gel suppresses its role in the smectic critical behavior.

Dynamic Order-to-Metastable-Disorder Vortex Matter Transition inBi2Sr2CaCu2O8+δ

Magneto-optical measurements of transient vortex states in Bi2Sr2CaCu2O8+delta show enhanced effects of metastability in prism-shaped as compared to platelet crystals including a significant shift of the second magnetization peak and qualitatively different dynamics. In contrast to platelets, where dislocations are generated only at the sample edges, we propose that in prism samples the dislocations are generated dynamically in the entire sample due to distributed surface barriers. As a result, a dynamic phase transition from a Bragg glass to a metastable disordered phase may occur well below the thermodynamic transition field.

Origin of the magnetization peak effect in theNb3Snsuperconductor

We report a pronounced peak effect in the magnetization and the magnetocaloric coefficient in a single crystal of the superconductor ${\mathrm{Nb}}_{3}\mathrm{Sn}$. As the origin of the magnetization peak effect in classical type-II superconductors is still strongly debated, we performed an investigation of its underlying thermodynamics. Calorimetric experiments performed during field sweeps at constant temperatures reveal that the sharp increase in the current density occurs concurrently with additional degrees of freedom in the specific heat due to thermal fluctuations and a liquid vortex phase. No latent heat due to a direct first-order melting of a Bragg glass phase into the liquid phase is found, which we take as evidence for an intermediate glass phase with enhanced flux pinning. The Bragg glass phase can, however, be restored by a small ac field. In this case, a first-order vortex melting transition with a clear hysteresis is found. In the absence of an ac field, the intermediate glass phase is located within the field range of this hysteresis. This indicates that the peak effect is associated with the metastability of an underlying first-order vortex melting transition.

Depinning of the Bragg Glass in a Point Disordered Model Superconductor

We perform simulations of the three-dimensional frustrated anisotropic XY model with point disorder as a model of a type-II superconductor with quenched point pinning in a magnetic field and a weak applied current. Using resistively shunted junction dynamics, we find a critical current I_{c} that separates a creep region with immeasurably low voltage from a region with a voltage V proportional, variant(I-I_{c}) and also identify the mechanism behind this behavior. It also turns out that data at fixed disorder strength may be collapsed by plotting V versus TI, where T is the temperature, though the reason for this behavior as yet not is fully understood.

Hierarchical Nature of the Vortex Matter in Type II Superconductors due to Competition Between Interactions, Thermal Fluctuations and Disorder

We describe quantitatively the combined effects of both the thermal fluctuations and of the quenched disorder via the replica trick applied to the Ginzburg–Landau (GL) theory. We show that the vortex state can appear in either of the three disordered phases: (i) unpinned vortex liquid, (ii) amorphous vortex glass (pinned), and (iii) the crystalline (pinned but not containing topological defects) Bragg glass. The formation of the vortex glass is associated with the continuous replica symmetry breaking (RSB) reflecting the hierarchial structure of the potential barriers in a vortex glass state. An earlier analysis in the framework of London approximation have established that activation barriers controlling vortex dynamics obey the extreme value statistics within roughly the same domain of the phase diagram. We show that the disordered GL model in which only the coefficient at the quadratic term |ψ |2 is random, first considered by Dorsey et al., exhibits, in the gaussian approximation, an additional non-hierarchical state possessing certain glassy properties like nonzero Edwards–Anderson order parameter. We associate this state with the “marginal glass phase” predicted in the earlier work of one of the authors; the marginal glass state being characterized by the marginally glassy dynamics. We show further that when the random component of the coefficient of the quartic term |ψ |4 in GL free energy is taken into account, RSB effects appear. Application of the obtained results to description of various disorder-generated phenomena in vortex matter are briefly considered. The location of the glass transition line is determined and compared to experiments. This line is clearly different from both the melting line and the second peak line describing the translational and rotational symmetry breaking at high and low temperatures respectively. The phase diagram is separated by these two lines into the four phases described above.

Phase diagram of vortex matter in layered high-temperature superconductors with random point pinning

We study the phase diagram of the superconducting vortex system in layered high-temperature superconductors in the presence of a magnetic field perpendicular to the layers and of random atomic scale point pinning centers. We consider the highly anisotropic limit where the pancake vortices on different layer are coupled only by their electromagnetic interaction. The free energy of the vortex system is then represented as a Ramakrishnan-Yussouff free energy functional of the time averaged vortex density. We numerically minimize this functional and examine the properties of the resulting phases. We find that, in the temperature ($T$) -- pinning strength ($s$) plane at constant magnetic induction, the equilibrium phase at low $T$ and $s$ is a Bragg glass. As one increases $s$ or $T$ a first order phase transition occurs to another phase that we characterize as a pinned vortex liquid. The weakly pinned vortex liquid obtained for high $T$ and small $s$ smoothly crosses over to the strongly pinned vortex liquid as $T$ is decreased or $s$ increased -- we do not find evidence for the existence, in thermodynamic equilibrium, of a distinct vortex glass phase in the range of pinning parameters considered here. %cdr We present results for the density correlation functions, the density and defect distributions, and the local field distribution accessible via $\mu$SR experiments. These results are compared with those of existing theoretical, numerical and experimental studies.

Effect of Planar Defects on the Stability of the Bragg Glass Phase of Type-II Superconductors

It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects as twin or grain boundaries. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher Miller index is irrelevant, even at large defect potentials. A finite density of parallel defects with random separations can be relevant even for larger Miller indices. Defects that are aligned with the applied field restore locally the flux density oscillations which decay algebraically with distance from the defect. The current-voltage relation is changed to lnV(J) approximately -J(-1). The theory exhibits striking similarities to the physics of Luttinger liquids with impurities.

Voltage noise of current-driven vortices in disordered Josephson junction arrays

Dynamical phenomena of moving vortices and voltage noise spectra are studied indisordered Josephson junction arrays (JJAs). The plastic motion of vortices, smectic flow,and moving Bragg glass phases are separated by two dynamic melting transitions driven bycurrent. From the voltage noise spectra of moving vortices, it is found that thedriving current plays an important role in the melting of pinning vortices glass andordering of moving vortices. The features of noise spectra obtained in the disorderedJJA model have been observed recently in the high-temperature superconductorBi2Sr2CaCu2Oy near the first-order melting transition, indicating that both of them are related to eachother.

Vortex regime crossover in the Bragg glass phase in a YBa 2Cu 3O 7− δ crystal

We have investigated the behavior of vortex lattice in a weakly pinned YBa 2Cu 2O 7− δ crystal using rotational magnetization measurements. At low applied magnetic fields parallel to the ab plane of the crystal, we have found that the vortex state undergoes a crossover from a relatively strongly pinned vortex regime to a weakly pinned vortex regime in the Bragg glass phase. In the weakly pinned vortex regime of the Bragg glass phase, vortices were described to be completely depinned and aligned parallel to the applied field.

Chaos and Residual Correlations in Pinned Disordered Systems

We study, using functional renormalization, two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depends on a nontrivial boundary layer regime with (possibly multiple) chaos exponents. Large scale mutual displacement correlations behave as [x - x'](2zeta-mu), mu proportional to the difference between Flory (or mean field) and exact roughness exponents zeta. For short range disorder mu>0 and small; e.g., for random bond interfaces mu=5zeta-epsilon, epsilon=4-d, and mu=epsilon{[(2pi)(2)/36]-1} for the one component Bragg glass. Random field (i.e., long range) disorder exhibits finite residual correlations (no chaos mu=0) described by new functional renormalization fixed points. Temperature and dynamic chaos (depinning) are discussed.

Investigations of Magnetic Behavior in Various&lt;tex&gt;$rm Nb_3rm Sn$&lt;/tex&gt;Multifilamentary Wires by Means of the 1st and 3rd Harmonics of the AC Magnetic Susceptibility

The 1st and 3rd harmonics of the AC magnetic susceptibility were measured as a function of the temperature on Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn multifilamentary wires, produced by different processes: bronze route (home made) and internal tin diffusion (Oxford) These measurements were performed both with and without a DC magnetic field, up to 19T. We observed that the magnetic response of the bronze route wire is mainly characterized by vortex dynamical phenomena, such as flux creep. This is in contrast with the internal tin wire, where the static hysteretic Bean model is sufficient to describe the magnetic behavior. Moreover, by using the 3rd harmonics measurements, it has been possible to get indication about the phase transition in the vortex lattice between the Bragg Glass phase and the disordered phase, which is absent in the bronze route multifilamentary wire. The H-T phase diagram has been obtained for both samples and has been compared with the previously analyzed one for the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn single crystals and polycrystalline samples

Nb3Sn single crystals, polycrystals and multifilamentary wires: common and different features in the magnetic response

The magnetic response of different Nb3Sn samples has been investigated studying the temperature dependence of both the 1st and 3rd harmonics of the AC magnetic susceptibility, in presence of a DC field up to 19 T. In single crystal and in polycrystalline samples, the occurrence of a Peak Effect was observed within DC magnetic fields ranging from 3 T to about 13 T. It corresponds to a transition in the vortex lattice between the Bragg Glass phase and a disordered phase. This transition has been also detected at higher magnetic fields in both the samples, thanks to the 3rd harmonics measurements. In contrast to single crystals and polycrystals, no Peak Effect and no indications about the Bragg/disordered phase transition have been detected in the analysed multifilamentary wires.