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We present small angle neutron scattering studies of the magnetic vortex lattice (VL) in Ca$_{0.04}$Y$_{0.96}$Ba$_{2}$Cu$_{3}$O$_{7}$ up to a field of 16.7 T, and Ca$_{0.15}$Y$_{0.85}$Ba$_{2}$Cu$_{3}$O$_{7}$ up to 25 T. We find that the series of vortex lattice structure transitions have shifted down in field relative to those reported for the undoped compound. We attribute this mainly to the weakening of the 1-D superconductivity in the Cu-O chains by the disorder introduced by doping. The hole doping by calcium is also expected to alter the Fermi velocity and it reduces the upper critical field of the system. The high-field structure of the vortex lattice is similar to recent measurements on the parent compound in fields of 25~T, which indicates that the fundamental \textit{d}-wave nature of the superconducting gap is unchanged by calcium doping. This is corroborated by the temperature dependence of the VL form factor which also shows the same \textit{d}-wave behaviour as observed in other cuprates. We also find evidence of Pauli paramagnetic effects in the field dependence of the VL form factor., Comment: 9 pages, 6 figures

We report on the evolution with magnetic field and temperature of the vortex lattice (VL) in fully-oxygenated YBa2Cu3O7 as studied by time-of-flight small angle neutron scattering. Using the HFM/EXED beamline, we have obtained data up to 25.9 T - much higher than that available previously. Our VL structure results indicate the progressive suppression by field of the superconductivity along the crystallographic b (CuO chain) direction. The intensity of the diffracted signal reveals the spatial variation of magnetization caused by the VL (the "form factor"). Instead of a rapid fall-off with field, as seen in superconductors with smaller upper critical fields, we find that the form factor is almost constant with field above about 12 T. We speculate that this is due to Pauli paramagnetic moments, which increase at high fields due to alignment of the spins of quasiparticles in the vortex cores., Comment: 8 pages, 6 figures

The charge density wave in the high-temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) is now known to have two different ordering tendencies differentiated by their $c$-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDW in neighbouring CuO$_2$ bilayers. This discovery has prompted a number of fundamental questions. For example, how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use high-energy x-ray diffraction to study YBa$_2$Cu$_3$O$_{6.67}$ as a function of magnetic field and temperature. We show that regions of the sample with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a weak or fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is furthermore concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations have an important impact on superconducting and normal state properties of underdoped YBCO., Comment: 9 pages, 5 figures, and supplementary information

The application of large magnetic fields ($B \sim B_{c2}$) to layered cuprates suppresses their high temperature superconducting behaviour and reveals competing ground states. In the widely-studied material YBa$_2$Cu$_3$O$_{6+x}$ (YBCO), underdoped ($p \sim 1/8$) samples show signatures of field-induced electronic and structural changes at low temperatures. However, the microscopic nature of the field-induced reconstruction and the high-field state are unclear. Here we report an x-ray study of the high-field charge density wave (CDW) in YBCO, for doping, $0.1 \lesssim p \lesssim 0.13$. For $p \sim 0.123$, we find that a field ($B \sim 10$~T) induces new CDW correlations along the CuO chain ($b$) direction only, leading to a 3-D ordered state along this direction at $B \sim 15$~T. The CDW signal along the $a$-direction is also enhanced by field, but does not develop a new pattern of correlations. We find that field modifies the coupling between the CuO$_2$ bilayers in the YBCO structure, and causes the sudden appearance of 3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW at low and high fields, allowing recently suggested Fermi surface reconstruction., Comment: 4 pages 5 figures

All underdoped high-temperature cuprate superconductors appear to exhibit charge density wave (CDW) order, but both the underlying symmetry breaking and the origin of the CDW remain unclear. We use X-ray diffraction to determine the microscopic structure of the CDW in an archetypical cuprate YBa$_2$Cu$_3$O$_{6.54}$ at its superconducting transition temperature Tc ~ 60 K. We find that the CDWs present in this material break the mirror symmetry of the CuO2 bilayers. The ionic displacements in a CDW have two components: one perpendicular to the CuO$_2$ planes, and another parallel to these planes, which is out of phase with the first. The largest displacements are those of the planar oxygen atoms and are perpendicular to the CuO$_2$ planes. Our results allow many electronic properties of the underdoped cuprates to be understood. For instance, the CDW will lead to local variations in the doping (or electronic structure) giving an explicit explanation of the appearance of density-wave states with broken symmetry in scanning tunnelling microscopy (STM) and soft X-ray measurements.

We report small-angle neutron scattering measurements of the vortex lattice (VL) structure in single crystals of the lightly underdoped cuprate superconductor YBa2Cu3O6.85. At 2 K, and for fields of up to 16 T applied parallel to the crystal c-axis, we observe a sequence of field-driven and first-order transitions between different VL structures. By rotating the field away from the c-axis, we observe each structure transition to shift to either higher or lower field dependent on whether the field is rotated towards the [100] or [010] direction. We use this latter observation to argue that the Fermi surface morphology must play a key role in the mechanisms that drive the VL structure transitions. Furthermore, we show this interpretation is compatible with analogous results obtained previously on lightly overdoped YBa2Cu3O7. In that material, it has long-been suggested that the high field VL structure transition is driven by the nodal gap anisotropy. In contrast, the results and discussion presented here bring into question the role, if any, of a nodal gap anisotropy on the VL structure transitions in both YBa2Cu3O6.85 and YBa2Cu3O7.

We have observed a magnetic vortex lattice (VL) in BaFe2(As_{0.67}P_{0.33})2 (BFAP) single crystals by small-angle neutron scattering (SANS). With the field along the c-axis, a nearly isotropic hexagonal VL was formed in the field range from 1 to 16 T, which is a record for this technique in the pnictides, and no symmetry changes in the VL were observed. The temperature-dependence of the VL signal was measured and confirms the presence of (non d-wave) nodes in the superconducting gap structure for measurements at 5 T and below. The nodal effects were suppressed at high fields. At low fields, a VL reorientation transition was observed between 1 T and 3 T, with the VL orientation changing by 45{\deg}. Below 1 T, the VL structure was strongly affected by pinning and the diffraction pattern had a fourfold symmetry. We suggest that this (and possibly also the VL reorientation) is due to pinning to defects aligned with the crystal structure, rather than being intrinsic., Comment: 9 pages, 9 figures

To explore the doping dependence of the recently discovered charge density wave (CDW) order in YBa2Cu3Oy, we present a bulk-sensitive high-energy x-ray study for several oxygen concentrations, including strongly underdoped YBa2Cu3O6.44. Combined with previous data around the so-called 1/8 doping, we show that bulk CDW order exists at least for hole concentrations (p) in the CuO2 planes of 0.078 <~ p <~ 0.132. This implies that CDW order exists in close vicinity to the quantum critical point for spin density wave (SDW) order. In contrast to the pseudogap temperature T*, the onset temperature of CDW order decreases with underdoping to T_CDW ~ 90K in YBa2Cu3O6.44. Together with a weakened order parameter this suggests a competition between CDW and SDW orders. In addition, the CDW order in YBa2Cu3O6.44 shows the same type of competition with superconductivity as a function of temperature and magnetic field as samples closer to p = 1/8. At low p the CDW incommensurability continues the previously reported linear increasing trend with underdoping. In the entire doping range the in-plane correlation length of the CDW order in b-axis direction depends only very weakly on the hole concentration, and appears independent of the type and correlation length of the oxygen-chain order. The onset temperature of the CDW order is remarkably close to a temperature T^\dagger that marks the maximum of 1/(T_1T) in planar 63^Cu NQR/NMR experiments, potentially indicating a response of the spin dynamics to the formation of the CDW. Our discussion of these findings includes a detailed comparison to the charge stripe order in La2-xBaxCuO4., Comment: 11 pages, 5 figures

We present a volume-sensitive high-energy x-ray diffraction study of the underdoped cuprate high temperature superconductor La2-xSrxCuO4 (x = 0.12, Tc=27 K) in applied magnetic field. Bulk short-range charge stripe order with propagation vector q_ch = (0.231, 0, 0.5) is demonstrated to exist below T_ch = 85(10) K and shown to compete with superconductivity. We argue that bulk charge ordering arises from fluctuating stripes that become pinned near boundaries between orthorhombic twin domains., Comment: 5 pages, 4 figures. To be submitted to Phys. Rev. Lett

A new method is presented for the analysis of small angle neutron scattering data from quasi-2D systems such as flux lattices, Skyrmion lattices, and aligned liquid crystals. A significant increase in signal to noise ratio, and a natural application of the Lorentz factor can be achieved by taking advantage of the knowledge that all relevant scattering is centered on a plane in reciprocal space. The Bayesian form ensures that missing information is treated in a controlled way and can be subsequently included in the analysis. A simple algorithm based on Gaussian probability assumptions is provided which provides very satisfactory results. Finally, it is argued that a generalised model-independent Bayesian data analysis method would be highly advantageous for the processing of neutron and x-ray scattering data.

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.