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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. ( 2000 Elsevier Science B.V. All rights reserved.

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 new ultra-high-resolution neutron spin-echo spectrometer at the ILL, Grenoble, extends the time range for measurements of the intermediate scattering function S(q, t) far beyond what has previously been possible. This new dynamic range approaching the microsecond opens up the possibility for exploring dynamic phenomena which have been previously unobservable. The various design ideas for the three operational modes (standard, neutron optical focusing, and time of flight) will be presented. The standard and focusing configurations are currently operational. In the normal mode, Fourier times between 0.03 and 360 ns and momentum transfers q between 0.01 and 0.6 A−1 are accessible. Under focusing conditions, the smallest attainable q is about 0.002 A−1, and closes the gap to light scattering. Two examples of experiments will be presented: the reptation dynamics in an entangled linear polymer melt, and the superparamagnetic fluctuations of magnetic monodomain nano-particles.

The crystal structure of high-quality single crystals of YBa 2 Cu 3 O 6 + x grown in zirconia curcibles was studied systematically versus oxygen concentration by four-circle neutron diffraction at room temperature. The oxygen contents ranged from x = 0.18 (insulating, tetragonal phase) to x = 0.96 (superconducting, orthorhombic phase). In the orthorhombic phase, both twinned and detwinned samples were measured. A detailed discussion is presented of the systematic changes taking place in the atomic positions and Debye-Waller factors as the oxygen content is varied. Some qualitative highlights are that one can identify two distinct regions within the unit cell: the characteristics of the atoms near the CuO x basal plane are essentially driven by the effect of oxygen addition, whereas near the CuO 2 bilayer, the trends are more subtle and presumably dominated by charge transfer and bond-distance effects. Also, there is neither an abrupt change of the apical-oxygen position at the orthorhombic to tetragonal transition, nor is there any indication of depletion of the atomic sites except for the chain-site oxygen. The superconducting critical temperatures or Neel temperatures, as well as the existence of oxygen-ordered superstructures are reported.

We present measurements or Ortho-III phase correlations in an untwinned single crystal of YBa2Cu3O6.77 by neutron scattering and the novel method of hard (95 keV) X-ray scattering. The Ortho-III ordering is essentially two-dimensional, exhibiting Lorentzian peak shapes in the a-b plane. At room temperature, the correlation lengths deduced from the Lorentzian peak widths are about 5 unit cells (⋍20 A) along h and 19 unit cells (⋍74 A) along k, and are comparable to some correlation lengths measured for the Ortho-II phase. Upon heating, the superstructure intensity was found to decrease rapidly at temperatures above 50°C with about 10% of the original intensity remaining at 100°C and completely vanishing above 150°C. Such a low transition temperature explains why this phase is more difficult to observe than other superstructures, such as the Ortho-II.

The thermal impedance of thin Mylar and Kapton foils separating two liquid helium baths has been measured below 100 mK. It can be analysed in terms of a boundary Kapitza resistance which is substantially smaller than that of most materials.

We have measured the vapour pressure of oxygen in Y1Ba2Cu3Ox as a function of x at constant temperature between 450°C and650°C for pressures between 10 m Torr and 1000 Torr. From these vapour pressure curves we have determined ( ∂x ∂μ ) T (μ is the chemical potential), a thermodynamic response function analogous to the compressibility and specific heat. ( ∂x ∂μ ) T is a quantity which is sensitive to the oxygen configuration and which can be calculated by any candidate theory on the thermodynamics of oxygen. So, the measured ( ∂x ∂μ ) T curves should help in the search to determine the correct model for oxygen thermodynamics in Y1Ba2Cu3Ox. In this paper we use a simple quasi-chemical approximation with an empirical x and T dependent on-site energy to accurately fit the vapour pressure curves. This fit provides a fairly simple method to empirically reproduce the vapour pressure as a function of x and T, which should prove useful in materials preparation.

Neutron spin-echo spectroscopy was used to resolve for the first time the slow relaxation component associated with the fluctuations of the whole spin particle in monodomain Fe particles in an alumina matrix. These fluctuations are progressively freezing with decreasing temperature. A distribution of relaxation times was observed most likely due to a finite particle size distribution. As a result, one will have to measure at significantly longer Fourier times in order to quantify the freezing behaviour.

The copper complex C18H28O2N2Cu(NO)2 carries three spins S = 1 2 . It crystallizes with two molecules in the asymmetric unit. Its susceptibility reveals positive intramolecular magnetic interactions, but negative intermolecular interactions. We have investigated its spin density with polarized neutrons at T = 40 K and T = 4.10 K. At the higher temperature, the spin density is well localized on the Cu atom and the two NO groups of each molecule. At the lower temperature, the spin density exists, for each molecule, on the Cu atom and on one of the two NO groups only. There is a practical dimerization on two NO groups, belonging to the different molecules, facing each other, and distant only by 3.40 A.

It is known since a decade that polyethylene shows a characteristic deviation from the Rouse dynamics, i.e. pronounced entanglement effects, now observable in neutron spin-echo (NSE) spectroscopy as a plateau at high Fourier times t . Earlier spin-echo data were limited to t =20–40 ns and could only determine entanglement distances but not decide between competing models. The now available time range up to 200 ns and more at the IN15 (ILL) NSE spectrometer allowed to distinguish the various models and to decide in favour of de Gennes’ Reptation model. In this model the restriction of motion originates from a trapping of the chains in a virtual tube. We present a series of new NSE-data from PE-melts at 509 K with different molecular weights between M w =12 000 g / mol and M w =190 000 g / mol extending to 170 ns that allow for the first time a systematic investigation of the reptation dynamics of PE-melts over a wide range of molecular weights.

A new ultra-high resolution neutron spin-echo spectrometer at the ILL (Grenoble) extends the time range for measurements of the intermediate scattering function S(Q,t) far beyond what has previously been possible. The spectrometer design is traditional, utilizing long neutron wavelengths (8–25 A) and large, homogeneous precession coils to reach Fourier times approaching the microsecond. The standard operational mode is currently functional, providing a Fourier time range of 0.03–180 ns, and a momentum transfer between 0.01 and 0.2 A−1. The other two operational modes (neutron optical focusing and time of flight) are also discussed.

The magnetic ordering of the bilayered Heisenberg antiferromagnet YBa2Cu3O6+x with weak XY-anisotropy was investigated for temperatures close to the magnetic transition temperature TN. We find that the magnitude of the sublattice magnetization is well described by a power law ∼ eβ [e = (TN − T)/TN] with critical exponent β2D = 0.26(1) in the region 5 × 10−2 > e > 5 × 10 −3 and with β3D = 0.35(5) in the region 5 × 10−3 > e > 5 × 10−4, reflecting a dimensional crossover at T ≈ 0.995 TN. We present results which suggest the magnetic reflections ( 1 2 h, 1 2 h,0) , indicative of a small component of the electron moments perpendicular to the ab-plane.

Neutron spin echo studies on an amorphous strong random magnetic anisotropy system reveal nonexponential spin relaxation to temperatures greater than 10Tg.

Magnetic ordering has been investigated by neutron scattering on an YBa 2 Cu 3 O 6+ x single crystal with x =0.1 and x =0.18, and an Al doped YBa 2 (Cu 2.86 Al 0.14 )O 6.25 crystal. For the undoped crystal an antiferromagnetic ordering transition (AFI) was observed at T N =410 K and 368 K (respectively for x=0.1 and x=0.18), but no second antiferromagnetic transition was found down to 2 K. In contrast, an antiferromagnetic reordering (AFII) was observed for the aluminum doped sample below T 2 =8 K. This shows the high sensitivity of this second phase to impurities and indicates that this reordering is not necessarily an intrinsic property of YBa 2 Cu 3 O 6+ x .

In YBa 2 Cu 3−x Al x O 6+δ single crystals antiferromagnetic AFII ordering has been observed below 18 K by neutron diffraction. The transition temperature T 2 to the AFI ordering increases with x and δ.

We have studied the magnetic ordering of the Cu and Pr ions in PrBa 2 Cu 3 O 6+x by neutron diffraction on single crystals with different oxygen contents. Two types of Cu ordering were observed, qualitatively similar to the anti-ferromagnetic phases reported in some studies of YBa 2 Cu 3 O 6+x . A third magnetic structure was observed below 15K, which we believe corresponds to the magnetic ordering of the Pr sub-lattice.

Neutron and synchrotron x-ray measurements of the Ortho-II superstructure reflections on a high quality single crystal of YBa 2 Cu 3 O 6.5 revealed that the intrinsic line shape is a Lorentzian to the power 5 2 . It is argued that such a line shape implies late-stage domain coarsening of a quenched system ordering in three dimensions (d=3) with a two component order parameter (n=2).

Muon Spin Rotation (μ + SR) studies of flux vortex structure in single crystal, crushed crystal, thick film, and sintered specimens of Bi 2 Sr 2 CaCu 2 O 8 are reported. Field-Cooled & Zero-Field-Cooled measurements indicate that the flux vortices in the mixed state of each material are highly mobile at temperatures above a pinning/freezing temperature T p c . Measurements on the thick film sample with H ext =10, 4.1, 2 and 1kG show that T p decreases with increasing field strength.

YBa2Cu3Ox is known to be antiferromagnetic (AFM) for x ≲ 6.45 but the details of its sublattice magnetization(s) are still controversial. A zero-field μ+SR investigation of the x- and T-dependence of the local fields at several muon sites reveals sharp changes at 10K and 80K for an oriented powder sample with x ≈ 6.0, but other x ≈ 6.0 samples do not show the same features. The direction of the local field at one μ+ site is shown to be along the ĉ-axis. For x < 6.0 the samples still show local spin freezing up to 300K, but coherent AFM order is lost even at 3K.

Resistivity, susceptibility and μ + SR measurements have been used to investigate the ( x , T ) phase diagram of YBa 2 Cu 3 O x . Carefully annealed samples are antiferromagnetic (AFM) insulators for 6.0 ≲ x ≲ 6.35 and nonmagnetic superconductors (SC) for 6.5 ≲ x ≲ 7.0; SC coexists with AFM or spin glass (SG) static magnetic order at low temperatures for 6.38 ≲ x ≲ 6.48. A sample with x = 6.462 is SC below 25 K and simultaneously magnetic below 10 K; the internal diamagnetism of the SC state is progressively reduced as local spin freezing sets in at low temperatures.

The internal magnetic fields in La 1.85 Sr 0.15 CuO 4 and YBa 2 Cu 3 O x have been investigated below 90 mK using muon spin rotation. In YBa 2 Cu 3 O x the magnetic order parameter remains constant with increasing x up until x =6.30 and then rapidly approaches zero just above x =6.44. We find little evidence for static or slowly fluctuating electronic moments in superconducting La 1.85 Sr 0.15 CuO 4 .