We present a study of the vortex lattice in untwinned YBa2Cu3O7−x crystals, using a combination of muon spin rotation and neutron small angle scattering measurements. Both methods show a very sharp melting temperature consistent with a first order transition. The dependence of the melting temperature on the angle of the field with respect to the crystallographic c-axis is studied. The results are compared to thermal measurements.

We present a study of the vortex lattice in untwinned YBa2Cu3O7−x crystals, using a combination of muon spin rotation and neutron small angle scattering measurements. Both methods show a very sharp melting temperature consistent with a first order transition. The dependence of the melting temperature on the angle of the field with respect to the crystallographic c-axis is studied. The results are compared to thermal measurements.

We investigate the superconducting behaviour of Bi doped Pb. Pure lead shows type-I behaviour entering an intermediate state in a magnetic field. High dopings of Bi (>3%) lead to type-II behaviour showing a mixed state, where the magnetic field penetrates the superconductor in the form of a flux lattice. At intermediate doping, the sample shows both type-I and type-II behaviour depending on the temperature. This arises because the Ginzburg-Landau parameter κ passes through its critical value of 1/ √

We present a study of the vortex lattice in untwinned YBa$_2$Cu$_3$O$_{7-x}$ crystals, using a combination of muon spin rotation and neutron small angle scattering measurements. Both methods show a very sharp melting temperature consistent with a first order transition. The dependence of the melting temperature on the angle of the field with respect to the crystallographic c-axis is studied. The results are compared to thermal measurements.

We investigate the superconducting behaviour of Bi doped Pb. Pure lead shows type-I behaviour entering an intermediate state in a magnetic field. High dopings of Bi (>3 the magnetic field penetrates the superconductor in the form of a flux lattice. At intermediate doping, the sample shows both type-I and type-II behaviour depending on the temperature. This arises because the Ginzburg-Landau parameter κ passes through its critical value of 1/√(2) with temperature.

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.

The phenomenon of superconductivity continues to be of considerable scientific and practical interest. Underlying this phenomenon is the formation of electron pairs, which in conventional superconductors do not rotate about their centre of mass (‘ s -wave’ pairing; refs 1 , 2 ). This contrasts with the situation in high-temperature superconductors, where the electrons in a pair are believed to have two units of relative angular momentum (‘ d -wave’ pairing; ref. 3 and references therein). Here we report small-angle neutron-scattering measurements of magnetic flux lines in the perovskite superconductor Sr 2 RuO 4 ( ref. 4 ), which is a candidate for another unconventional paired electron state—‘ p -wave’ pairing, which has one unit of angular momentum 5 , 6 , 7 . We find that the magnetic flux lines form a square lattice over a wide range of fields and temperatures, which is the result predicted by a recent theory 8 , 9 of p -wave superconductivity in Sr 2 RuO 4 . This theory also indicates that only a fraction of the electrons are strongly paired and that the orientation of the square flux lattice relative to the crystal lattice will determine which parts of the three-sheet Fermi surface of this material are responsible for superconductivity. Our results suggest that superconductivity resides mainly on the ‘γ’ sheet 9 .

The phenomenon of superconductivity continues to be of considerable scientific and practical interest. Underlying this phenomenon is the formation of electron pairs, which in conventional superconductors do not rotate about their centre of mass ('s-wave' pairing; refs 1, 2). This contrasts with the situation in high-temperature superconductors, where the electrons in a pair are believed to have two units of relative angular momentum ('d-wave' pairing; ref. 3 and references therein). Here we report small-angle neutron-scattering measurements of magnetic flux lines in the perovskite superconductor Sr2RuO4 (ref. 4), which is a candidate for another unconventional paired electron state-'p-wave' pairing, which has one unit of angular momentum(5-7). We find that the magnetic flux lines form a square lattice over a wide range of fields and temperatures, which is the result predicted by a recent theory(8,9) of p-wave superconductivity in Sr2RuO4. This theory also indicates that only a fraction of the electrons are strongly paired and that the orientation of the square flux lattice relative to the crystal lattice will determine which parts of the three-sheet Fermi surface of this material are responsible for superconductivity. Our results suggest that superconductivity resides mainly on the 'gamma' sheet(9).

Small-angle neutron scattering (SANS) is an extremely powerful probe of the vortex state in type II superconductors. The technique may be further enhanced by the use of polarised neutrons and the application of the neutron spin-echo method. We discuss some recent applications of these techniques to the study of both conventional and unconventional superconducting materials, and describe the unique information which SANS can provide on the vortex state.

μSR and small-angle neutron scattering (SANS) have been used to probe the vortex arrangement in single crystals of the high-Tc superconductor Bi2.15Sr1.85CaCu2O8+δ which have been irradiated with heavy ions to produce columnar defects. The influence of these pinning sites on the spatial arrangement of the vortices is discussed, and the results are compared with numerical simulations.

Muon-spin rotation (μSR) measurements have been used to study the superconducting vortex properties of the organic superconductors κ-(BEDT-TTF)2Cu(SCN)2, α-(BEDT-TTF)2NH4Hg(SCN)4 and β-(BEDT-TTF)2IBr2. These materials all have highly anisotropic structures consisting of metallic layers of BEDT-TTF molecules alternating with less well conducting anion layers. Varying the anion gives rise to a change in the anisotropy of the superconductivity and also to changes in the superconducting transition temperature. We have used both transverse and longitudinal magnetic fields to study the three-dimensional flux line lattice that is present at low temperatures and fields and to study also the loss of flux lattice order that occurs on increasing the temperature and field.

Muon-spin rotation (mu SR) and torque magnetometry have been used to probe the anisotropy of an untwinned single crystal of YBa2Cu3O7-delta. The absence of twin planes allows the ratios of all three principal components of the superconducting effective mass tensor to be determined. The values for the in-plane anisotropy are in good agreement with values obtained by other techniques. The out-of-plane anisotropies as measured by mu SR are also found to be in good agreement with other microscopic measurements, but somewhat lower than those resulting from torque measurements on this and other crystals.

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.

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.

1School of Physics and Astronomy, University of St. Andrews, St. Andrews, Fife KY169SS, United Kingdom 2Physik-Institut der Universität Zürich, Zürich, Switzerland 3School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom 4Institut Laue-Langevin, Grenoble, France 5Gesellschaft für Schwerionenforschung, D-64291 Darmstadt, Germany 6National Research Institute of Metals, Tsukuba University, Ibaraki 305, Japan 7SRL-ISTEC, Koto-ku, Toykyo 135, Japan (Received 25 November 1997 )

Using the techniques of muon spin rotation and torque magnetometry, we investigate the crossover field B-cr in Bi2.15Sr1.85Ca1Cu2O8+delta at which the vortex lattice becomes disordered along the field direction. It is found that B-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.

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.

We present muon-spin rotation measurements on the cuprate superconductor Bi2Sr2CaCu2O8+δ, in the presence of columnar defects. The results are compared to measurements on the pristine material, and indicate a strong suppression of thermal fluctuations of the vortex positions in the irradiated material.

Using the techniques of muon spin rotation and torque magnetometry, we investigate the crossover field ${B}_{\mathrm{cr}}$ in ${\mathrm{Bi}}_{2.15}{\mathrm{Sr}}_{1.85}{\mathrm{Ca}}_{1}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ at which the vortex lattice becomes disordered along the field direction. It is found that ${B}_{\mathrm{cr}}$ 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.

We have performed muon-spin rotation (μSR) measurements on the organic superconductor K-(BEDT-TTF)2CU(SCN)2 as a function of the angle between the applied field and the superconducting planes. The measurements are found to have much in common with those on the anisotropic cuprate superconductor Bi2Sr2CaCu2O8 + δ.