Search

We present the results of a study of the vortex lattice (VL) of the nickel chalcogenide superconductor ${\mathrm{TlNi}}_{2}{\mathrm{Se}}_{2}$, using small angle neutron scattering. This superconductor has the same crystal symmetry as the iron arsenide materials. Previous work points to it being a two-gap superconductor, with an unknown pairing mechanism. No structural transitions in the vortex lattice are seen in the phase diagram, arguing against $d$-wave gap symmetry. Empirical fits of the temperature dependence of the form factor and penetration depth rule out a simple $s$-wave model, supporting the presence of nodes in the gap function. The variation of the VL opening angle with field is consistent with earlier reports of multiple gaps.

Despite numerous studies the exact nature of the order parameter in superconducting ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ remains unresolved. We have extended previous small-angle neutron scattering studies of the vortex lattice in this material to a wider field range, higher temperatures, and with the field applied close to both the $\ensuremath{\langle}100\ensuremath{\rangle}$ and $\ensuremath{\langle}110\ensuremath{\rangle}$ basal plane directions. Measurements at high field were made possible by the use of both spin polarization and analysis to improve the signal-to-noise ratio. Rotating the field towards the basal plane causes a distortion of the square vortex lattice observed for $\mathbit{H}\ensuremath{\parallel}\ensuremath{\langle}001\ensuremath{\rangle}$ and also a symmetry change to a distorted triangular symmetry for fields close to $\ensuremath{\langle}100\ensuremath{\rangle}$.The vortex lattice distortion allows us to determine the intrinsic superconducting anisotropy between the $c$ axis and the Ru-O basal plane, yielding a value of $\ensuremath{\sim}60$ at low temperature and low to intermediate fields. This greatly exceeds the upper critical field anisotropy of $\ensuremath{\sim}20$ at low temperature, reminiscent of Pauli limiting. Indirect evidence for Pauli paramagnetic effects on the unpaired quasiparticles in the vortex cores are observed, but a direct detection lies below the measurement sensitivity. The superconducting anisotropy is found to be independent of temperature but increases for fields $\ensuremath{\gtrsim}1$ T, indicating multiband superconductvity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. Finally, the temperature dependence of the scattered intensity provides further support for gap nodes or deep minima in the superconducting gap.

In single-crystal superconductors in the mixed state, flux-line structures may have a lower symmetry than the host crystal. In this case, multiple degenerate flux lattice domains may be present simultaneously and give rise to complicated small-angle diffraction patterns. The interpretation of these patterns in terms of the flux lattice structure in a single domain is discussed, with particular reference to recently reported spontaneous symmetry-breaking flux-line lattice phases in niobium.

We report on small angle neutron scattering measurements of the vortex lattice in twin-free YBa2Cu3O7, extending the previously investigated maximum field of 11~T up to 16.7~T with the field applied parallel to the c axis. This is the first microscopic study of vortex matter in this region of the superconducting phase. We find the high field VL displays a rhombic structure, with a field-dependent coordination that passes through a square configuration, and which does not lock-in to a field-independent structure. The VL pinning reduces with increasing temperature, but is seen to affect the VL correlation length even above the irreversibility temperature of the lattice structure. At high field and temperature we observe a melting transition, which appears to be first order, with no detectable signal from a vortex liquid above the transition.

We report a detailed neutron diffraction study of both pinned and moving magnetic Flux Line Lattice (FLL) in NbTa and PbIn samples. In NbTa, the FLL presents a hexagonal lattice even in the absence of current, meanwhile PbIn presents a strongly dislocated phase. In PbIn, dislocations are eliminated by the application of transport current in agreement with theoretical predictions. On the other hand, the absence of curvature of the flux lines for subcritical currents confirm the presence of surface pinning of the FLL.

We have measured the diffracted neutron scattering intensities from the square magnetic flux lattice in the perovskite superconductor ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, which is thought to exhibit $p$-wave pairing with a two-component order parameter. The relative intensities of different flux lattice Bragg reflections over a wide range of field and temperature have been shown to be inconsistent with a single component Ginzburg-Landau theory but qualitatively agree with a two-component $p$-wave Ginzburg-Landau theory.

There are several ways of investigating#ux lines with polarised neutrons. We shall describe our recent work on IN15 at ILL, investigating spatially varying "elds perpendicular to the #uxoid axes, which are present with tilted "elds in anisotropic superconductors. These "eld components may be detected by polarisation analysis of neutrons di!racted by the #ux line lattice, and allow a detailed investigation of #ux structure in such materials as YBCO and NbSe 2 . A further application of polarised neutrons is the use of neutron spin-echo techniques to measure the speed of moving #ux lines. We have recently demonstrated this in an Nb}Ta alloy on instruments IN11 and IN15, by measuring the energy change of neutrons di!racted by #ux lines, which are moving under the in#uence of a transport current. We shall also comment on others’ work on the search for interference terms between #ux lattice and nuclear di!raction signals, and the use of neutron depolarisation for investigation of #ux distributions in superconductors. ( 1999 Elsevier Science B.V. All rights reserved.

A small angle neutron scattering study of the flux-line lattice in a large untwinned single crystal of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ is presented. In fields parallel to the $c$ axis, diffraction spots are observed corresponding to four orientations of a hexagonal lattice, distorted by the $a\ensuremath{-}b$ anisotropy. A value for the anisotropy, the penetration depth ratio, of ${\ensuremath{\lambda}}_{a}/{\ensuremath{\lambda}}_{b}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.18\left(2\right)$ was obtained. The high quality of the data is such that second-order diffraction is observed, indicating a well ordered FLL. With the field at 33\ifmmode^\circ\else\textdegree\fi{} to $c$, a field dependent reorientation of the lattice is observed around 3 T.

Using the technique of small angle neutron scattering (SANS) the vortex lattice of ultra-pure niobium has been investigated on an extremely fine temperature scale. As the temperature is increased towards T c 2 the longitudinal correlations of the vortices along their length improve, up to the resolution limited value of 100 μ m .

We review the evidence for unconventional superconductivity in Sr 2 RuO 4 ; the pairing in this material is certainly non-s-wave, and most of the current observations can be accounted for by a particular p-wave state, which is doubly degenerate and breaks time-reversal symmetry. Our observations of the flux lattice by small-angle neutron scattering contribute to this picture. The square flux lattice and the intensity of the diffracted signal indicate that superconductivity resides primarily on the γ sheet of the Fermi surface, which is derived from the Ru - d xy orbitals. This is in agreement with the “orbital-dependent” p-wave scenario. Furthermore, the shape of the flux lines derived from these measurements is strongly indicative of a two-component order parameter.

A muon-spin-rotation study of the flux-line lattice in is presented. For the field parallel to the crystallographic c-direction, the observed field distribution strongly indicates a square symmetry of the vortex lattice. We determine the value of the coherence length from the upper critical field and the Ginzburg-Landau parameter which is found to be from the field distribution. This gives a value for the penetration depth of . The temperature dependence of the penetration depth is measured.

High resolution, neutron small angle scattering studies have been performed to investigate the low field $(Bl250\mathrm{mT})$ region of the phase diagram for the vortex lattice in the superconducting state of ${\mathrm{YNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$. The data present clear evidence for a vortex lattice reorientation transition from a state with the diagonal of the rhombic unit cell along a $[110]$ direction to a $[100]$ direction. Above this transition the lattice distorts under the influence of the applied field until the apex angle becomes constant at some higher field. For $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$ a square lattice configuration is formed. These experiments confirm qualitatively many of the predictions of a general model based on nonlocal corrections to the London model as applied to this and similar materials.

Using the techniques of muon spin rotation and torque magnetometry, we investigate the crossover field B{sub cr} in Bi{sub 2.15}Sr{sub 1.85}Ca{sub 1}Cu{sub 2}O{sub 8+{delta}} at which the vortex lattice becomes disordered along the field direction. It is found that B{sub cr} scales as the projection of the applied field along the perpendicular to the superconducting planes. This has the implication that a field large enough to give a disordered lattice when applied perpendicular to the planes, can give a well-ordered vortex-line lattice for angles of the field to the c axis greater than a critical value. {copyright} {ital 1998} {ital The American Physical Society}

We report a study of the basal-plane anisotropy of the superfluid density in underdoped YBa2Cu4O8 (Y124), showing the effects of both the CuO2 planes and the fully occupied CuO chains. From small-angle neutron scattering measurements of the vortex lattice, we can infer the superconducting (SC) properties for a temperature (T) range T = 1.5 K to T-c and magnetic induction B from 0.1 to 6 T. We find that the superfluid density along a has a simple d-wave T dependence. However, along b (the chain direction) the superfluid density falls much more rapidly with T and also with increasing field. This strongly suggests the suppression of proximity-effect-induced superconductivity in the CuO chains. In addition, our results do not support a common framework for the low-field in-plane SC response in Y124 and related YBa2Cu3O7, and also indicate that any magnetic field induced charge-density-wave order in Y124 exists only for fields above 6 T.

Muon spin rotation ({mu}SR) measurements have been performed on the organic superconductor {kappa}-(BEDT-TTF){sub 2}Cu(SCN){sub 2} in order to investigate its exotic vortex behavior. Previously unobserved features of the {mu}SR line shapes have been measured at low fields and temperatures. In the mixed state the existence of a lattice composed of linear vortices is demonstrated at low fields. The breakup of this well-ordered lattice has furthermore been observed as a function of both field and temperature. {copyright} {ital 1997} {ital The American Physical Society}

We observe a flux lattice with square symmetry in the superconductor YNi{sub 2}B{sub 2}C when the applied field is parallel to the {ital c} axis of the crystal. A square lattice observed previously by Yaron {ital et al.} in the isostructural magnetic analog ErNi{sub 2}B{sub 2}C was attributed to the interaction between magnetism in that system and the flux lattice. Since the Y-based compound does not order magnetically, it is clear that the structure of the flux lattice is unrelated to magnetic order. We do not observe any change in the mosaic or direction of the flux lines with applied field; these phenomena may be related to magnetism. In YNi{sub 2}B{sub 2}C, the strength of the flux lattice signal was seen to fall off rapidly with applied field; the results imply considerable disorder in the arrangement of the flux lines at 2.5T, but are not consistent with melting. We see a markedly anisotropic flux lattice when the applied field is at 60{degree} to the {ital c} axis. In this case, the flux lattice is observed to be a distorted hexagon. {copyright} {ital 1997} {ital The American Physical Society}

A detailed study has been made of a transition in the flux lattice of the superconductor ${\mathrm{Bi}}_{2.15}$${\mathrm{Sr}}_{1.85}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ using the technique of muon-spin rotation. The results are in excellent agreement with a recent theoretical analysis on the low-field phase diagram of highly anisotropic superconductors. In particular, the important role of electromagnetic interactions between vortex segments is demonstrated. The form of the phase boundary suggests that the transition may be identified with a simultaneous melting and decoupling of the vortices in adjacent layers.

We review some of the assumptions made in the use of muon spin rotation in superconductors: i.e. that the muons are implanted at random positions in the flux lattice, remain static after implantation and do not appreciably affect the properties of the surrounding superconductor; also that the flux lines are straight and static, and that the observed muon rotation frequency spectrum reflects the microscopic distribution of field values. We shall show how evidence for and against the truth of these assumptions in particular cases may be obtained from the μSR results themselves or by comparison with other measurements, and how this in turn may lead to deeper understanding of flux line structure and motion in superconductors.

We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn₅ with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H II 100], a single VL orientation is observed, while a 90° reorientation transition is found for H II [110]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Γ=2.0±0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H II [001]. At high fields, above which the upper critical field (Hc2) becomes a first-order transition, an increased disordering of the VL is observed.

We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux lines in low T c type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbor FLL direction. This tends to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo technique to observe the energy change of neutrons diffracted by moving flux lines. The muon spin rotation (μSR) technique gives the distribution of values of magnetic field within the FLL. We have recently succeeded in performing μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors.

The vortex lattice (VL) in the high-κ superconductor YBa2Cu3O7, at 2 K and with the magnetic field parallel to the crystal c axis, undergoes a sequence of transitions between different structures as a function of applied magnetic field. However, from structural studies alone, it is not possible to determine precisely the system anisotropy that governs the transitions between different structures. To address this question, here we report new small-angle neutron scattering measurements of both the VL structure at higher temperatures and the field and temperature dependence of the VL form factor. Our measurements demonstrate how the influence of anisotropy on the VL, which in theory can be parameterized as nonlocal corrections, becomes progressively important with increasing magnetic field, and suppressed by increasing the temperature toward Tc. The data indicate that nonlocality due to different anisotropies plays an important role in determining the VL properties.

By neutron scattering, we have observed a well-ordered magnetic vortex lattice (VL) in KFe${}_{2}$As${}_{2}$ single crystals. With the field along the $c$ axis, a nearly isotropic hexagonal VL is formed, with no symmetry transitions up to high fields, indicating a small anisotropy of the superconducting state around this axis. This rules out line nodes parallel to the $c$ axis, and thus $d$-wave or anisotropic $s$-wave pairing. However, the strong temperature dependence of the signal at $T\ensuremath{\ll}{T}_{c}$ shows that extremely small gap values exist; these may arise from nodal lines perpendicular to the $c$ axis.

Superconducting vortex lattices, glasses and liquids attract great interest as model systems of crystallization and as a source of microscopic information of the nature of superconductivity. We report for the first time direct microscopic measurements of the vortex lattice tilt modulus c44 in ultra-pure niobium using time-resolved small angle neutron scattering. Besides a general trend to faster vortex lattice dynamics for increasing temperatures we observe a dramatic changeover of the relaxation process associated with the non-trivial vortex lattice morphology in the intermediate mixed state. This changeover is attributed to a Landau-branching of the Shubnikov domains at the surface of the sample. Our study represents a showcase for how to access directly vortex lattice melting and the formation of vortex matter states for other systems., 14 pages, 14 figures

The microscopic magnetic field distribution in the mixed state of single-crystal ${\mathrm{Bi}}_{2.15}$${\mathrm{Sr}}_{1.85}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ has been measured using the muon spin rotation technique. A study of the line shapes as a function of temperature and magnetic field gives evidence for an abrupt change of flux-lattice structure which is attributed to the presence of a flux-lattice melting line in the B-T phase diagram. In addition, the data suggest the existence of a crossover field above which the flux structure is more 2D in nature.

We report on small angle neutron scattering observations of the flux line lattice (FLL) in a single crystal of YBa[sub 2]Cu[sub 3]O[sub 7]. To probe the mass anisotropy ratio, [ital m][sub 3]/[ital m][sub 1], measurements were made as a function of angle, [Theta], between the 8 kOe applied field and the crystallographic (001) axis for 0[degree][le][Theta][le]80[degree]. With the rotation about an [ital a]/[ital b] (or [ital y]) axis, two symmetry-related distorted hexagonal FLL domains formed. Contrary to theoretical prediction, the lattices formed are consistent with a rotation of the short basis vector, [bold a][sub 1], from the [ital x] axis by 15[degree], after the effects of anisotropy are removed. The mass ratio is 20[plus minus]2, which is slightly lower than published values. The temperature dependence of the intensity is not conventional.

X-ray diffraction studies have been made of the antiferromagnetic ordering in the rare earth metal samarium, at the Synchrotron Radiation Source, Daresbury Laboratory. We have observed diffraction peaks which reflect the magnetic order on the hexagonal sites in the lattice and which are in agreement with previous neutron measurements. We have also observed the energy dependence of the resonant enhancement at both the LIII and LII absorption edges of Sm.

The state of the vortex lattice extremely close to the superconducting to normal transition in an applied magnetic field is investigated in high-purity niobium. We observe that thermal fluctuations of the order parameter broaden the superconducting to normal transition into a crossover but no sign of a first-order vortex lattice melting transition is detected in measurements of the heat capacity or the small-angle neutron scattering (SANS) intensity. Direct observation of the vortices via SANS always finds a well-ordered vortex lattice. The fluctuation broadening is considered in terms of the lowest Landau-level theory of critical fluctuations and scaling is found to occur over a large ${H}_{c2}(T)$ range.

We report superconducting (SC) properties of stoichiometric LiFeAs (Tc = 17 K) studied by small-angle neutron scattering (SANS) and angle-resolved photoemission (ARPES). Although the vortex lattice exhibits no long-range order, well-defined SANS rocking curves indicate better ordering than in chemically doped 122-compounds. The London penetration depth of 210 nm, determined from the magnetic field dependence of the form factor, is compared to that calculated from the ARPES band structure with no adjustable parameters. Its temperature dependence is best described by a single isotropic SC gap of 3.0 meV, which agrees with the ARPES value of 3.1 meV and corresponds to the ratio 2Delta/kTc = 4.1, approaching the weak-coupling limit predicted by the BCS theory. This classifies LiFeAs as a weakly coupled single-gap superconductor, similar to conventional metals., Comment: 4 pages, 4 figures

The disordered flux line lattice in single crystals of the slightly overdoped ${\text{BaFe}}_{2\ensuremath{-}x}{\text{Co}}_{x}{\text{As}}_{2}$ ($x=0.19$, ${T}_{\text{c}}=23\text{ }\text{K}$) superconductor is studied by magnetization measurements, small-angle neutron scattering, and magnetic force microscopy (MFM). In the whole range of magnetic fields up to 9 T, vortex pinning precludes the formation of an ordered Abrikosov lattice. Instead, a vitreous vortex phase (vortex glass) with a short-range hexagonal order is observed. Statistical processing of MFM data sets lets us directly measure its radial and angular distribution functions and extract the radial correlation length $\ensuremath{\zeta}$. In contrast to predictions of the collective pinning model, no increase in the correlated volume with the applied field is observed. Instead, we find that $\ensuremath{\zeta}$ decreases as $(1.3\ifmmode\pm\else\textpm\fi{}0.1){R}_{1}\ensuremath{\propto}{H}^{\ensuremath{-}1/2}$ over four decades of the applied magnetic field, where ${R}_{1}$ is the radius of the first coordination shell of the vortex lattice. Such universal scaling of $\ensuremath{\zeta}$ implies that the vortex pinning in iron arsenides remains strong even in the absence of static magnetism. This result is consistent with all the real and reciprocal-space vortex-lattice measurements in overdoped as-grown ${\text{BaFe}}_{2\ensuremath{-}x}{\text{Co}}_{x}{\text{As}}_{2}$ published to date and is thus sample independent. The failure of the collective pinning model suggests that the vortices remain in the single-vortex pinning limit even in high-magnetic fields up to 9 T.

The non-centrosymmetric heavy fermion compound CePt3Si orders antiferromag-netically at TN = 2.2K, followed by a superconducting transition, where Ts = 0.45 K for high quality samples and Ts = 0.75K for lower quality samples. We have used neutron Larmor diffraction to measure the temperature dependence and distribution of the lattice constants in a single crystal of CePt3Si with Ts = 0.75K. In our study we observe an unusually wide range of lattice parameters for the a-axis and c-axis with Δa/a ≈ Δc/c ≈ 10−3. Small angle neutron scattering suggests an abundance of defects along the lattice planes. When taking into account the pressure dependence of Ts our study attributes the increased value of Ts in low quality samples to an effective negative pressure.

We report on small-angle neutron scattering studies of the intrinsic vortex lattice (VL) structure in detwinned YBa2Cu3O7 at 2 K, and in fields up to 10.8 T. Because of the suppressed pinning to twin-domain boundaries, a new distorted hexagonal VL structure phase is stabilized at intermediate fields. It is separated from a low-field hexagonal phase of different orientation and distortion by a first-order transition at 2.0(2) T that is probably driven by Fermi surface effects. We argue that another first-order transition at 6.7(2) T, into a rhombic structure with a distortion of opposite sign, marks a crossover from a regime where Fermi surface anisotropy is dominant, to one where the VL structure and distortion is controlled by the order-parameter anisotropy.

We have mapped out the high-field phase diagram of the vortex lattice in lightly twinned ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7}$ by employing small-angle neutron scattering. This extends previous measurements [S. P. Brown et al., Phys. Rev. Lett. 92, 067004 (2004)] in which we reported a transition in local flux-line coordination from distorted triangular to square as a function of field applied parallel to the crystal $c$ axis. At high fields, we observe a transition back to triangular coordination with increasing angle between the applied field and $c$ axis or with increasing temperature. At lower fields, our results may be interpreted in terms of a field-induced reduction of the basal-plane $a\text{\ensuremath{-}}b$ anisotropy. Tilting the flux lines away from the $c$ axis reduces the pinning by twin planes, changes the orientation of the vortex lattice nearest-neighbor directions, and the transition between square and hexagonal vortex lattices becomes first order.

Small-angle neutron diffraction measurements from the flux lattice in a single crystal of the cubic Laves' phase superconductor, CeRu2, are reported. The mixed state is described in terms of aligned rigid bundles of vortices. The bundle diameters decrease above 1 2 H c 2 (consistent with collective weak pinning theory) and become comparable with the penetration length at a field at which a ‘peak effect’ is seen in magnetisation measurements. A clear memory of field histories that pass through the ‘peak effect’ region is also found; however, some of the induced disorder can be removed by subsequently cycling the field.

We have used the technique of small-angle neutron scattering to observe magnetic flux lines directly in a ${\mathrm{Y}\mathrm{B}\mathrm{a}}_{2}{\mathrm{C}\mathrm{u}}_{3}{\mathrm{O}}_{7}$ single crystal at fields higher than previously reported. For field directions close to perpendicular to the ${\mathrm{C}\mathrm{u}\mathrm{O}}_{2}$ planes, we find that the flux lattice structure changes smoothly from a distorted triangular coordination to nearly perfectly square as the magnetic induction approaches 11 T. The orientation of the square flux lattice is as expected from recent $d$-wave theories but is $45\ifmmode^\circ\else\textdegree\fi{}$ from that recently observed in ${\mathrm{L}\mathrm{a}}_{1.83}{\mathrm{S}\mathrm{r}}_{0.17}{\mathrm{C}\mathrm{u}\mathrm{O}}_{4+\ensuremath{\delta}}$.

Neutron small-angle diffraction has been used to investigate the flux-line lattice structure within single crystals of the high-temperature superconductor Bi 2.15 Sr 1.95 CaCu 2 O 8 + x . The diffracted intensity goes rapidly to zero as the magnetic field or the temperature is increased. Melting at low fields as a function of temperature coincides with the appearence of finite resistance within the superconducting state. At low temperatures the diffracted intensity disappears in fields greater than ∼ 70 mT, probably due to the decomposition of the flux-line lattice into randomly pinned 2d “pancake” vortices.

The magnetic phase diagram of slightly overdoped La{2-x}Sr{x}CuO{4} (x=0.17) is characterised by a field-induced hexagonal to square transition of the vortex lattice at low fields (~0.4 Tesla) [R. Gilardi et al., Phys. Rev. Lett. 88, 217003 (2002)]. Here we report on a small angle neutron scattering study of the vortex lattice at higher fields, that reveals no further change of the coordination of the square vortex lattice up to 10.5 Tesla applied perpendicular to the CuO2 planes. Moreover, it is found that the diffraction signal disappears at temperatures well below Tc, due to the melting of the vortex lattice., 3 pages, 2 figures. Presented at the New3SC-4 meeting, San Diego, Jan. 16-21 2003; to be published in Int. J. Mod. Phys. B

We report muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ measurements on the moving vortex lattice (VL) in the type-II superconductor Pb-In, backed up by small-angle neutron scattering (SANS) observations on the same sample. We observe a motional narrowing of the $\ensuremath{\mu}\mathrm{SR}$ lineshape $p(B)$ and by SANS, alignment of the VL to the direction of vortex motion. We have calculated the $\ensuremath{\mu}\mathrm{SR}$ lineshape expected with a range of orientations of the moving VL. We demonstrate how the new $\ensuremath{\mu}\mathrm{SR}$ results give information on the moving VL which is complementary and consistent with the SANS data.

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.

We report on detailed small-angle neutron scattering measurements with polarization analysis from the flux-line lattice in the anisotropic superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ When the field was applied at an angle to the principal axes we have observed spin-flip neutron diffraction consistent with local transverse field components. From a detailed study of the angle dependence of the magnitude of the spin-flip neutron-scattered intensity we have found that the transverse-field components are larger than predicted by an anisotropic London model for reasonable mass anisotropy values. The transverse-field components are consistent with a reduced c-axis coherence length at low temperature.

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.

mu SR has been used to probe the structure and stability of the flux vortex array in the organic superconductor kappa-(BEDT-TTF)(2)Cu(SCN)(2), At temperatures below 5 K and fields below 5 mT the internal field distribution is found to closely match that expected for a three dimensional (3D) Abrikosov flux line lattice (FLL). Careful studies in this 3D-FLL regime have enabled an improved measurement of the temperature dependence of the superconducting penetration depth to be made. A linear term is found in the temperature dependence of the penetration depth, suggesting the presence of line nodes in the gap parameter and d-wave pairing.

High resolution, neutron small angle scattering experiments have been performed on the flux-line lattice within the mixed state of the type-II superconductors YNi2B2C and TmNi2B2C. In the Y compound clear evidence is found for a transition at low fields from a distorted hexagonal lattice with its diagonal along a [110] direction to a [100] direction as the field is increased. At higher fields the lattice is found to be square. These results are in

The degree of perfection of flux lattices in superconductors in the mixed state, that may be obtained from small-angle neutron diffraction data, is discussed.

We have used the neutron spin-echo technique to measure the small energy change of neutrons which are diffracted by a moving vortex lattice in a low-pinning Nb-Ta superconducting sample. A transport current was passed in the mixed state to cause flux line movement. In the case of uniform motion, the flux velocity ${\mathbf{v}}_{L}$ was given as expected by the values of electric and magnetic fields, via $\mathbf{E}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}{\mathbf{v}}_{L}\ensuremath{\wedge}\mathbf{B}$. We show that with a nonuniformly moving vortex lattice, one can measure the dispersion of the velocities, opening up new possibilities for investigating moving vortex lines.

Muon-spin rotation (μSR) measurements have been used to study the vortex lattice and its instabilities in the organic superconductors κ-ET 2 Cu(SCN) 2 and β-ET 2 IBr 2 . We ascribe the field- and temperature-dependent destruction of the vortex lattice to the large anisotropy found in these materials.

We report further on an investigation of magnetic vortex lattice (VL) structures in a single crystal of pure niobium with the magnetic field applied along a fourfold symmetry axis. New VL structures are observed, all of which spontaneously break some crystal symmetry. This symmetry-breaking causes multiple degenerate VL domains to exist within the sample. Through small rotations of the sample away from the fourfold axis, we can lift the degeneracy and associate diffraction spots with VL domains.

Muon spin rotation ( μ SR) studies of the vortex lattice in the superconductor κ-(BEDT-TTF) 2 Cu(SCN) 2 have revealed a crossover from a quasi-2 d to a vortex-line lattice structure for fields below a characteristic field B cr The μ SR-lineshapes measured from the vortex-line lattice have allowed a re-evaluation of the in-plane penetration depth.

We describe small-angle neutron scattering (SANS) studies of vortex structures in the high T c superconductor YBa 2 Cu 3 O 7 in the mixed state. The SANS technique is a unique tool for probing the crystallography of a flux line arrangement in the bulk sample that can measure the values of the characteristic lengths and the effect of defects on lattice arrangement and orientation extremely accurately. The effects of crystal anisotropy on the field distribution in a vortex line is the topic of this paper

From small-angle neutron scattering studies of the flux line lattice (FLL) in CeCoIn5, with magnetic field applied parallel to the crystal c-axis, we obtain the field and temperature dependence of the FLL form factor (FF), which is a measure of the spatial variation of the field in the mixed state. We extend our earlier work (Bianchi et al 2008 Science 319 177) to temperatures up to 1250 mK. Over the entire temperature range, paramagnetism in the flux line cores results in an increase of the FF with field. Near Hc2 the FF decreases again, and our results indicate that this fall-off extends outside the proposed Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) region. Instead, we attribute the decrease to a paramagnetic suppression of Cooper pairing. At higher temperatures, a gradual crossover toward more conventional mixed state behavior is observed., New Journal of Physics, 12, ISSN:1367-2630