Direct observation of magnetic flux lattice melting and decomposition in the high-Tc superconductor Bi2.15Sr1.95CaCu2O8+x

Graphical reduction and analysis small-angle neutron scattering program: GRASP

GRASP is a scientific software application designed for the graphical inspection, reduction and analysis of multidetector data produced by the small-angle neutron scattering (SANS) instruments at the Institut Laue-Langevin and other neutron sources around the world. The first developments of GRASP began more than 20 years ago and were written in MATLAB, allowing rapid development of scientific code, with much of the data handling, matrix manipulation, mathematical tools, user interface and graphical tools integrated at a high level in the underlying MATLAB platform. By their very nature, multidimensional data are often best appreciated in graphical form. GRASP deals with many of the diverse requirements for data reduction and analysis of SANS data using a general set of tools and reduction algorithms suited to 2D multidetector data. A further fundamental architectural inclusion is a third dimension of data manipulation, thereby easily allowing parametric analysis and cross referencing of series data such as composition, kinetic measurements, temperature, magnetic field, angle or time of flight, often considered as a single 'measurement'. This article serves as a reference document for users of the software, and outlines the architecture and strategy of the program. An overview of some of the features, capabilities, peripheral user modules and neutron scattering tools is presented.

Decomposing the Bragg glass and the peak effect in a Type-II superconductor

Adding impurities or defects destroys crystalline order. Occasionally, however, extraordinary behaviour emerges that cannot be explained by perturbing the ordered state. One example is the Kondo effect, where magnetic impurities in metals drastically alter the temperature dependence of resistivity. In Type-II superconductors, disorder generally works to pin vortices, giving zero resistivity below a critical current j_c. However, peaks have been observed in the temperature and field dependences of j_c. This peak effect is difficult to explain in terms of an ordered Abrikosov vortex lattice. Here we test the widespread paradigm that an order-disorder transition of the vortex ensemble drives the peak effect. Using neutron scattering to probe the vortex order in superconducting vanadium, we uncover an order-disorder transition from a quasi-long-range-ordered phase to a vortex glass. The peak effect, however, is found to lie at higher fields and temperatures, in a region where thermal fluctuations of individual vortices become significant.

The disordering of the vortex lattice in a type-II superconductor is widely perceived to underpin unusual peaks in the temperature and field dependence of critical current. By contrast, here Toft-Petersen et al. find an order-disorder transition in a superconducting vanadium sample that is unconnected with peaks observed in critical current.

Moving Sofas and Exhuming Woodchucks

Continuing concerns about the relevance and impact of management research deserve reflection and response. In this article, the author considers ways to increase management research relevance, including rewards for relevance and mechanisms for inreach. The author argues, however, that management research is already quite relevant and that basic research and research that appears somehow "artificial" should not be sacrificed on the altar of relevance. Conversely, the author argues that seeking relevance by following fads creates an unfortunate and dangerous illusion of responsiveness. To enhance impact, the author suggests seeking channels for better communication of the relevance and applicability of management research as well as the presentation of management research to potential users in intrinsically appealing ways. This might require using more concrete examples and metaphors and telling better stories. It should not involve "dummying down" research reports or debasing the nature of the research process.

Muon-spin rotation measurements of an unusual vortex-glass phase in the layered superconductor Bi2.15Sr1.85CaCu2O8+δ

Muon-spin rotation measurements, performed on the mixed state of the classic anisotropic superconductor Bi(2.15)Sr(1.85)CaCu(2)O(8+δ), obtain quantities directly related to two- and three-body correlations of vortices in space. A novel phase diagram emerges from such local probe measurements of the bulk, revealing an unusual glassy state at intermediate fields which appears to freeze continuously from the equilibrium vortex liquid but differs both from the lattice and the conventional high-field vortex glass state in its structure.

First-order reorientation transition of the flux-line lattice in CaAlSi

The flux-line lattice in CaAlSi has been studied by small-angle neutron scattering. A well-defined hexagonal flux-line lattice is seen just above H(c1) in an applied field of only 54 Oe. A 30° reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be first-order and could be explained by nonlocal effects. The magnetic field dependence of the form factor is well-described by a single penetration depth of λ=1496(1) Å and a single coherence length of ξ=307(1) Å at 2 K. At 1.5 K, the penetration depth anisotropy is γ(λ)=2.7(1), with the field applied perpendicular to the c axis, and agrees with the coherence length anisotropy determined from critical field measurements.

Interplay of anisotropy and disorder in the doping-dependent melting and glass transitions of vortices in Bi2Sr2CaCu2O 8+delta

We study the oxygen doping dependence of the equilibrium first-order melting and second-order glass transitions of vortices in Bi2Sr2CaCu2O 8+delta. Doping affects both anisotropy and disorder. Anisotropy scaling is shown to collapse the melting lines only where thermal fluctuations are dominant. Yet, in the region where disorder breaks that scaling, the glass lines are still collapsed. A quantitative fit to melting and replica symmetry-breaking lines of a 2D Ginzburg-Landau model further reveals that disorder amplitude weakens with doping, but to a lesser degree than thermal fluctuations, enhancing the relative role of disorder.

Square vortex lattice at anomalously low magnetic fields in electron-doped Nd1.85Ce0.15CuO4

We report here on the first direct observations of the vortex lattice in the bulk of electron-doped Nd1.85Ce0.15CuO4 single crystals. Using small-angle neutron scattering, we have observed a square vortex lattice with the nearest neighbors oriented at 45 degrees from the Cu-O bond direction, which is consistent with theories based on the d-wave superconducting gap. However, the square symmetry persists down to unusually low magnetic fields. Moreover, the diffracted intensity from the vortex lattice is found to decrease rapidly with increasing magnetic field.

Direct observation of the flux-line vortex glass phase in a type II superconductor

The order of the vortex state in La1.9Sr0.1CuO4 is probed using muon-spin rotation and small-angle neutron scattering. A transition from a Bragg glass to a vortex glass is observed, where the latter is composed of disordered vortex lines. In the vicinity of the transition the microscopic behavior reflects a delicate interplay of thermally induced and pinning-induced disorder.

Critical currents at the bragg glass to vortex glass transition

We present simulations of the transport properties of superconductors at the transition from the Bragg glass (BG) to the vortex glass (VG) phase. We study the frustrated anisotropic 3D XY model with point disorder, which has been shown to have a first-order transition as a function of the intensity of disorder. We add an external current to the model, and we obtain current-voltage curves as a function of disorder at a low temperature. We find that the in-plane critical current has a steep increase at the BG-VG transition, while the c-axis critical current has a discontinuous jump down, this later result in agreement with the first-order character of the transition.

Effects of two-band superconductivity on the flux-line lattice in magnesium diboride

We present neutron scattering from the flux line lattice (FLL) in MgB2. Between 0.5 and 0.9 T the FLL undergoes a 30 degrees reorientation, and simultaneously the scattered intensity falls sharply consistent with the weaker superconducting pi band being suppressed with increasing field. We speculate that the pi and sigma bands favor different FLL orientations, and that the reorientation is driven by the suppression of the pi band. When the c axis of the crystal is rotated 45 degrees to the applied field the penetration depth anisotropy could be measured, and rises both as a function of applied field and temperature.

Experimental evidence for anisotropic double-gap behavior in MgB2

The behavior of a type II superconductor in the presence of a magnetic field is governed by two characteristic length scales, the London penetration depth and the coherence length. We present magnetization measurements on MgB2 powder showing an anisotropy in the upper critical field and hence the coherence length of 6. Using the technique of small angle neutron scattering we show that this anisotropy is not mirrored in the London penetration depth, which is almost isotropic. This result can be explained by the superconductivity residing in two distinct electronic bands of the material, only one of which is highly anisotropic.

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.

Peak effect in a driven lattice gas model

We study the peak effect (PE), i.e., a sharp peak observed in the critical current as a function of the particle density, discovered in transport properties of a driven lattice gas model. We show that the PE corresponds to a first-order phase transition found in the undriven system at equilibrium, which in turn gives rise to an "anomalous" second peak in magnetic hysteresis loops. We also explain the "history" dependent phenomena observed in the PE region by investigating the system characteristic time scales, which diverge at low T and have a broad maximum as a function of the external field around the PE. The model we consider can be related to a coarse grained description of vortex lines in superconductors and we discuss the relations of the PE described here and the one experimentally observed in these systems.

Direct evidence for an intrinsic square vortex lattice in the overdoped high- T(c) superconductor La(1.83)Sr(0.17)CuO(4+delta)

We report here the first direct observations of a well ordered vortex lattice in the bulk of a La(2-x)Sr(x)CuO(4+delta) single crystal (slightly overdoped, x = 0.17). Our small angle neutron scattering investigation of the mixed phase reveals a crossover from triangular to square coordination with increasing magnetic field. The existence of an intrinsic square vortex lattice has never been observed in high-temperature superconductors and is indicative of the coupling of the vortex lattice to a source of anisotropy, such as those provided by a d-wave order parameter or the presence of stripes.

Intrinsic behavior of flux lines in pure niobium near the upper critical field

We report small-angle neutron-scattering (SANS) measurements of flux line properties near H(c2) in an ultrapure sample of niobium with weak pinning of flux in the bulk. These confirm in detail the Abrikosov picture of the flux line lattice to within 20 mK of the upper critical field line. However, it has recently been claimed [X. S. Ling et al., Phys. Rev. Lett. 86, 712 (2001)], on the basis of SANS observations of a disordering of flux lines in niobium, that the flux lattice melts at temperatures clearly separated from the upper critical field line. This discrepancy may possibly arise from differences in sample purity and pinning.

A Bragg glass phase in the vortex lattice of a type II superconductor

Although crystals are usually quite stable, they are sensitive to a disordered environment: even an infinitesimal amount of impurities can lead to the destruction of crystalline order. The resulting state of matter has been a long-standing puzzle. Until recently it was believed to be an amorphous state in which the crystal would break into 'crystallites'. But a different theory predicts the existence of a novel phase of matter: the so-called Bragg glass, which is a glass and yet nearly as ordered as a perfect crystal. The 'lattice' of vortices that contain magnetic flux in type II superconductors provide a good system to investigate these ideas. Here we show that neutron-diffraction data of the vortex lattice provides unambiguous evidence for a weak, power-law decay of the crystalline order characteristic of a Bragg glass. The theory also predicts accurately the electrical transport properties of superconductors; it naturally explains the observed phase transitions and the dramatic jumps in the critical current associated with the melting of the Bragg glass. Moreover, the model explains experiments as diverse as X-ray scattering in disordered liquid crystals and the conductivity of electronic crystals.

Disorder driven melting of the vortex line lattice

The 3D XY model with random in-plane couplings is simulated to model the phase diagram of a disordered type II superconductor as a function of temperature T and randomness strength p for fixed applied magnetic field. As p increases to a critical p(c), the first order vortex lattice melting line turns parallel to the T axis, continuing down to low temperatures, rather than ending at a critical point. Above p(c) preliminary results suggest the absence of a phase coherent vortex glass.

'Inverse' melting of a vortex lattice

Inverse melting is the process in which a crystal reversibly transforms into a liquid or amorphous phase when its temperature is decreased. Such a process is considered to be very rare, and the search for it is often hampered by the formation of non-equilibrium states or intermediate phases. Here we report the discovery of first-order inverse melting of the lattice formed by magnetic flux lines in a high-temperature superconductor. At low temperatures, disorder in the material pins the vortices, preventing the observation of their equilibrium properties and therefore the determination of whether a phase transition occurs. But by using a technique to 'dither' the vortices, we were able to equilibrate the lattice, which enabled us to obtain direct thermodynamic evidence of inverse melting of the ordered lattice into a disordered vortex phase as the temperature is decreased. The ordered lattice has larger entropy than the low-temperature disordered phase. The mechanism of the first-order phase transition changes gradually from thermally induced melting at high temperatures to a disorder-induced transition at low temperatures.

Effects of point defects on the phase diagram of vortex states in high- T(c) superconductors in the B parallel to c axis

The phase diagram for the vortex states of high- T(c) superconductors with point defects in the B--> parallel to c axis is drawn by large-scale Monte Carlo simulations. The vortex slush (VS) phase is found between the vortex glass (VG) and vortex liquid (VL) phases. The first-order transition between this novel normal phase and the VL phase is characterized by a sharp jump of the density of dislocations. The first-order transition between the Bragg glass (BG) and VG or VS phases is also clarified. These two transitions are compared with the melting transition between the BG and VL phases.

An unusual phase transition to a second liquid vortex phase in the superconductor YBa2Cu3O7

A magnetic field penetrates a superconductor through an array of 'vortices', each of which carries one quantum of flux that is surrounded by a circulating supercurrent. In this vortex state, the resistivity is determined by the dynamical properties of the vortex 'matter'. For the high-temperature copper oxide superconductors (see ref.1 for a theoretical review), the vortex phase can be a 'solid', in which the vortices are pinned, but the solid can 'melt' into a 'liquid' phase, in which their mobility gives rise to a finite resistance. (This melting phenomenon is also believed to occur in conventional superconductors, but in an experimentally inaccessible part of the phase diagram.) For the case of YBa2Cu3O7, there are indications of the existence of a critical point, at which the character of the melting changes. But neither the thermodynamic nature of the melting, nor the phase diagram in the vicinity of the critical point, has been well established. Here we report measurements of specific heat and magnetization that determine the phase diagram in this material to 26 T, well above the critical point. Our results reveal the presence of a reversible second-order transition above the critical point. An unusual feature of this transition-namely, that the high-temperature phase is the less symmetric in the sense of the Landau theory-is in accord with theoretical predictions of a transition to a second vortex-liquid phase.

Simulation of flux lines with columnar pins: bose glass and entangled liquids

Using path integral Monte Carlo we simulate a 3D system of up to 1000 magnetic flux lines by mapping it onto interacting bosons in (2+1)D. With increasing temperatures we find first order melting from an ordered solid to an entangled liquid signaled by a finite entropy jump and sharp discontinuities of the defect density and the structure factor S(G). For a particular density of strong columnar pins the crystal is transformed into a Bose glass phase with patches of crystalline order disrupted by the trapped vortices at the pinning sites but with no overall positional or orientational order. This glassy phase melts into a defected entangled liquid through a continuous transition.

New vortex-matter size effect observed in Bi(2)Sr(2)CaCu(2)O(8 + delta)

The vortex-matter 3D to 2D phase transition is studied in micron-sized Bi(2)Sr(2)CaCu(2)O(8 + delta) single crystals using local Hall magnetization measurements. At a given temperature, the second magnetization peak, the signature of a possible 3D--2D vortex phase transition, disappears for samples smaller than a critical length. We suggest that this critical length should be equated with the 2D vortex lattice ab-plane correlation length R(2D)(c). The magnitude and temperature dependence of R(2D)(c) agree well with Larkin-Ovchinnikov collective pinning theory.

Superheating and supercooling of vortex matter in a Nb single crystal: direct evidence for a phase transition at the peak effect from neutron diffraction

We report the first observation of a striking history dependence of the structure function of vortex matter in the peak effect regime in a Nb single crystal by using small angle neutron scattering combined with in situ magnetic susceptibility measurements. Metastable phases of vortex matter, supercooled vortex liquid and superheated vortex solid, have been identified. We interpret our results as direct structural evidence for a first-order vortex solid-liquid transition at the peak effect.

Static and dynamic coupling transitions of vortex lattices in disordered anisotropic superconductors

We use three-dimensional molecular dynamics simulations of magnetically interacting pancake vortices to study vortex matter in disordered, highly anisotropic materials such as BSCCO. We observe a sharp 3D-2D transition from vortex lines to decoupled pancakes as a function of relative interlayer coupling strength, with an accompanying large increase in the critical current reminiscent of a second peak effect. We find that decoupled pancakes, when driven, simultaneously recouple and order into a crystalline-like state at high drives. We construct a dynamic phase diagram and show that the dynamic recoupling transition is associated with a double peak in dV/dI.

Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

Supercooling of the disordered vortex lattice in Bi(2)Sr(2)CaCu(2)O(8+delta)

Time-resolved local induction measurements near the vortex lattice order-disorder transition in optimally doped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals show that the high-field, disordered phase can be quenched to fields as low as half the transition field. Over an important range of fields, the electrodynamical behavior of the vortex system is governed by the coexistence of ordered and disordered vortex phases in the sample. We interpret the results as supercooling of the high-field phase and the possible first-order nature of the order-disorder transition at the "second magnetization peak."

Transient vortex states in Bi2Sr2CaCu2O(8+delta) crystals

A high temporal resolution magneto-optical system is employed to observe the time evolution of the vortex structure in Bi(2)Sr(2)CaCu(2)O(8+delta) crystals after a sudden application of a magnetic field. The magneto-optical images reveal dynamic coexistence of two vortex phases: a quasiordered phase in the sample interior and a transient disordered phase near the sample edges. The border between these two phases, marked by an abrupt change in the gradient of the local induction, moves with time. This motion enables tracing the decay of the transient state and the concurrent growth of the thermodynamic vortex phases. The growth rate is sensitive to the location in the field-temperature phase diagram.

Abrupt change of josephson plasma frequency at the phase boundary of the bragg glass in Bi(2)Sr(2)CaCu(2)O(8+delta)

We report the first detailed and quantitative study of the Josephson coupling energy in the vortex liquid, Bragg glass, and vortex glass phases of Bi(2)Sr(2)CaCu(2)O(8+delta) by the Josephson plasma resonance. The measurements revealed distinct features in the T and H dependencies of the plasma frequency omega(pl) for each of these three vortex phases. When going across either the Bragg-to-vortex glass or the Bragg-to-liquid transition line, omega(pl) shows a dramatic change. We provide a quantitative discussion on the properties of these phase transitions, including the first order nature of the Bragg-to-vortex glass transition.

Vortices freeze like window glass: the vortex molasses scenario

We overview several recent experimental and numerical observations, which are at odds with the vortex glass theory of the freezing of disordered vortex matter. To reinvestigate the issue, we performed numerical simulations of the overdamped London-Langevin model, and use finite size scaling to analyze the data. Upon approaching the transition the initial vortex-glass-type criticality is arrested at some crossover temperature. Below this temperature the time scales continue growing very quickly, consistent with the Vogel-Fulcher form, while the spatial correlation length xi stops exhibiting any observable divergence. We call this mode of freezing the vortex molasses scenario.

Interlayer quasiparticle transport in the vortex state of josephson coupled superconductors

We calculate the dependence of the interlayer quasiparticle conductivity, sigma(q), in a Josephson coupled d-wave superconductor on the magnetic field B parallelc and the temperature T. We consider a clean superconductor with resonant impurity scattering and a dominant coherent interlayer tunneling. When pancake vortices in adjacent layers are weakly correlated, at low T the conductivity increases sharply with B over a field scale determined by the impurity scattering, before reaching an extended region of slow linear growth. At high T the conductivity initially decreases and then reaches the same linear regime. For correlated pancakes, sigma(q) increases much more strongly with the applied field.