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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.

Using the technique of neutron spin-echo spectroscopy, we have conducted a direct measurement of the superparamagnetic relaxation of nanoscale, magnetic monodomain iron particles in the time range between 0.01 and 160 nsec and for momentum transfers $q$ between 0.035 and $0.15{\AA{}}^{\ensuremath{-}1}$. Using a phenomenological model which includes the effect of a particle size distribution, we are able to determine the temperature $T$ and $q$ dependence of the longitudinal superspin relaxation time spanning 4 orders of magnitude. We find that for $T\ensuremath{\lesssim}40\mathrm{K}$, interparticle correlations affect the longitudinal superspin fluctuations.

In this paper we show that the concentration dependence of the plateau shear elastic modulus and of the viscosity can be understood if two lengths, the correlation length of concentration fluctuations and the tube diameter, are considered. To interpret the temperature variation of the viscosity and of the self-diffusion coefficient with the solvent quality, one has to take into account the local viscosity to which monomers are sensitive. This concentration dependent local viscosity, deduced from neutron spin-echo measurements, is independent of the polymer molecular weights, solvent viscosities and Θ temperatures. The local viscosity decreases to reach the solvent viscosity value at high temperature, that is, under good solvent conditions. The role of the macroscopic concentration on a local scale, seems to indicate that, in semidilute Θ solutions, the polymers are transparent to each other, as far as dynamic properties are concerned.

The dynamic structure factor $S(q,t)$ of polyethylene (PEB-2) was measured by neutron spin echo in the Fourier time range of $t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.3--175$ nsec and for momentum transfers $q$ between 0.05 and $0.145{\AA{}}^{\ensuremath{-}1}$ to test the validity of competing phenomenological theories of relaxation in polymer melts. Previous spin-echo experiments limited to $tl25$ nsec were equally well described by a variety of models. This ambiguity has now been lifted, and the experiment clearly favors the reptation model, showing that the dominant relaxation mechanism in entangled linear polymers is via reptation.

A general method for the model-free reconstruction of magnetization densities is presented. The technique is based upon the maximum-entropy principle and is valid for systems with any space-group symmetry, any physically reasonable ordered moment and allows for the incorporation of relevant corrections such as extinction. Thus, it is possible, for the first time, to reconstruct the real-space magnetization densities in essentially any physical system exhibiting a ferromagnetic spin alignment (either natural or induced) from polarized neutron diffraction experiments. The technique is illustrated for the purely organic ferromagnet, β-4,4,5,5-tetramethyl-2-p-(nitrophenyl)-3-oxido-4,5-dihydroimidazolium 1-oxyl.

The structural behavior of mm{sup 3}-sized single crystals of YBa{sub 2}Cu{sub 3}O{sub 6+{ital x}} with oxygen concentrations close to the metal-insulator transition is studied as a function of temperature, using 95-keV synchrotron x-ray diffraction. At {ital x}=0.36, no evidence is found of a room-temperature phase separation into tetragonal and orthorhombic phases, nor of a phase boundary between Ortho-II and tetragonal. Instead, we observe two distinct phase transitions: tetragonal to Ortho-I with a critical temperature {ital T}{sub {ital O}I}=246(2){degree}C and Ortho-I to Ortho-II with {ital T}{sub {ital O}II}=85(10){degree}C. Measurements of the spontaneous strain show the {ital O}/{ital T} transition to be nearly continuous with a critical exponent {beta}=0.34(2), consistent with a 3D Ising model driven weakly first order, presumably by the strain. A memory effect is observed, where relics of the twin domains{emdash}possibly related to tweed formations{emdash}continue to exist in the tetragonal phase when the temperature is increased above {ital T}{sub {ital O}I}. Corresponding measurements for {ital x}=0.35 gave similar results{emdash}with {ital T}{sub {ital O}I}=181(2){degree}C, {ital T}{sub {ital O}II}=95(10){degree}C, and {beta}=0.35(2){emdash}but with the appearance of a small tetragonal component at room temperature. This component is interpreted as a nonequilibrium feature. In both cases the Ortho-I to Ortho-II transformations are very broadmore » with a characteristic temperature dependence of the widths of the superstructure peaks that are similar to results obtained in a previous study for {ital x}=0.50. By comparison of the Ortho-II correlation lengths along {ital a}, {ital b}, and {ital c} with the corresponding data for {ital x}=0.50 we find evidence for a strong {ital x} dependency of {ital ASYNNNI}-type effective interaction parameters. (Abstract Truncated)« less

The magnetic ordering in single crystals of PrBa{sub 2}Cu{sub 3}O{sub 6+{ital x}} has been investigated by elastic neutron scattering over the full range of temperatures for reduced and oxygenated crystals. The crystals were grown in alumina crucibles and therefore contained dissolved aluminum on the Cu(1) site. Both aluminum and oxygen contents were analyzed in detail in order to establish their effects on the magnetic ordering. Our crystals exhibited Pr ordering and the two types of antiferromagnetic Cu ordering frequently reported in related compounds, but our results differ in several respects from previous studies. We observed three-dimensional (3D) collinear ordering of the Pr moments in the oxygenated crystal, with a finite correlation length of (34{plus_minus}3) A parallel to the {ital c} axis, but in contrast to earlier neutron scattering results, which tentatively placed the Pr moment as being parallel to the {ital c} axis, we find the moment to be aligned well away from the {ital c} axis, in agreement with recent {sup 170}Yb{sup 3+} M{umlt o}ssbauer spectroscopy results. Ridges of scattering indicative of 2D magnetic ordering were seen in both oxygenated and reduced crystals, though we believe different magnetic moments are responsible in each case. The Pr N{acute e}el temperaturesmore » were suppressed compared with those reported for nominally pure samples. We have observed a very small 3D-ordered moment on the Cu(1) site in the second type of Cu antiferromagnetic ordering (in the reduced crystal), but an ordered Cu(1) moment may not necessarily be a characteristic of this structure. Our results are discussed with reference to previous works, and in the light of the Al substitution. {copyright} {ital 1996 The American Physical Society.}« less

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.

Aluminum-doped, oxygen-deficient YBa{sub 2}Cu{sub 3{minus}{ital x}}Al{sub {ital x}}O{sub 6+{delta}} single crystals with different Al contents {ital x} (0{le}{ital x}{le}0.19) and O contents (0.18{le}{delta}{le}0.36) were studied by magnetic neutron diffraction. All of the Al-doped single crystals show two magnetic transitions, the first between the paramagnetic state and the AFI phase, and a second transition at low temperatures between the AFI and the AFII phase. The Neel temperature {ital T}{sub {ital N}} of the antiferromagnetic AFI phase is found to be insensitive to the Al content {ital x} as well as the O content 6+{delta} in the {ital x}-{delta} region investigated so far. In a limited temperature interval the order parameter shows the components of both the AFI and AFII phases indicating competing interactions. For some crystals a complete reordering to the AFII phase at 4.2 K can be observed. Although the antiferromagnetic ordering pattern is different for the AFI and AFII phase, the ordered moments on the Cu sites are within the experimental error ({l_angle}{ital S}{r_angle}{sub Cu(2)}{approx}0.56{mu}{sub {ital B}}, {l_angle}{ital S}{r_angle}{sub Cu(1)}{approx}0{mu}{sub {ital B}}) identical in the two phases. Comparison of Al-doped crystals with pure crystals of the same oxygen content shows that the presence of excess oxygen only ({delta}{gt}0) ismore » not sufficient to obtain the AFII ordering at low temperatures. Instead, the AFII ordering is triggered by the creation of the local magnetic moments in Cu-O-Al chain fragments.« less

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.

Magnetic ordering has been investigated by means of neutron scattering in an YBa2Cu3O6+x single crystal prepared with two different oxygen concentrations, x=0.1 and x=0.18, and in an aluminum-doped YBa2(Cu3-yAly)O6+x crystal with x=0.25 and y=0.14. For the undoped crystal, a magnetic ordering transition was observed at TN=410 (respectively for x=0.1 and x=0.18), but no second magnetic transition was found down to 2 K. In contrast, an antiferromagnetic reordering was observed for the aluminum-doped sample with a transition temperature T2=8 K. This implies a high sensitivity of this second phase to impurities and indicates that the transition is not necessarily an intrinsic property of YBa2Cu3O6+x.

A lattice-gas model for the high-temperature oxygen-ordering thermodynamics in YBa[sub 2]Cu[sub 3]O[sub 6+[ital x]] is presented, which assumes constant effective pair interactions between oxygen atoms and includes in a simple fashion the effect of the electron spin and charge degrees of freedom. This is done using a commonly utilized picture relating the creation of mobile electron holes and unpaired spins to the insertion of oxygen into the basal plane. The model is solved using the nearest-neighbor square approximation of the cluster-variation method. In addition, preliminary Monte Carlo results using next-nearest-neighbor interactions are presented. The model is compared to experimental results for the thermodynamic response function, [ital kT]([partial derivative][ital x]/[partial derivative][mu])[sub [ital T]] ([mu] is the chemical potential), the number of monovalent copper atoms, and the fractional site occupancies. The model drastically improves the agreement with measured values of [ital kT]([partial derivative][ital x]/[partial derivative][mu])[sub [ital T]] as compared to bare lattice-gas models. Additionally, the monovalent copper count, in contrast to the standard lattice-gas models, is determined self-consistently and agrees qualitatively with experiment.

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.

A closed-cycle distillation column was operated on a helium-3--helium-4 mixture in an attempt to ``separate'' the two nuclear spin states of helium-3. For the atoms in the dilute phase, a steady-state polarization 3.5 times larger than that of the equilibrium was obtained; possible ways to improve this result are discussed.

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.

Analyse des courbes d'aimantation a champs eleves de ce polycristal. Ajustement au modele anisotrope linearise de Ginzburg-Landau pour des grains orientes presque aleatoirement. On obtient la distribution d'orientation approximative. On en deduit ce parametre κ 2 (T) pres de T c

Several recent models of high-${\mathit{T}}_{\mathit{c}}$ superconductivity predict static internal magnetic fields along the c axis due to spontaneously broken parity and time-reversal symmetries. Muon spin relaxation has been used to study the internal fields in c-axis-oriented samples of sintered ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and of thick-film ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$. The magnitude, anisotropy, and temperature dependence of the observed fields favor a nuclear dipolar origin. Any anomalous fields at ${\mathrm{\ensuremath{\mu}}}^{+}$ sites in bulk ${\mathrm{CuO}}_{2}$ superconductors must be \ensuremath{\lesssim}0.08 mT.

In dense solution high functionality star polymers show ordering phenomena which give rise to a well-pronounced peak in the static structure factor, S exp(Q), observed by small-angle neutron scattering. The concentration dependence of S exp (Q) gives evidence for unusual phase behaviour as predicted by theory. In addition, the dynamics of the star polymer solutions is dominated by an increasing amount of structural arrest with increasing concentration. The mean square displacement obtained from neutron spin-echo spectroscopy is compared to the blob size obtained from dynamic light scattering. Thermal energy enables each star core to perform restricted motion over a spatial extent equal to the blob size of the surrounding dense star polymer solution.

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.