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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.

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.

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

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.

We investigated the dynamics of 18-arm polyisoprene star polymer solutions well above their overlap concentration c*. Combining neutron spin echo spectroscopy (NSE) and selective H/D labelling, we were able to separate inter- (collective) and intra-star (self ) dynamics. Only at low Q-vectors do self and collective dynamics become discernible. Here, collective dynamics are found to be consistent with a colloidal approach resulting from star–star interactions. The collective short time diffusion coefficient Deff is well described by the term D0/S(Q), with D0 the diffusion coefficient at infinite dilution. At Qm, the peak position in the structure factor S(Q), no difference is observable between collective and self dynamics. For covering the slowed-down dynamics at Qm the time range of NSE was extended for the first time up to 350 ns using long wavelengths, λ=19 A, at IN15 (ILL, Grenoble). We found that S(Q,t)/S(Q,0) relaxes into a concentration-dependent plateau. The plateau height gives the mean-square displacement 1/2 of star cores, which is related to the blob size ξ of the surrounding star polymer solution obtained by dynamic light scattering.

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

We have searched for anomalous internal magnetic fields in highTc materials which are predicted to occur in anyon and flux phase models of superconductivity. The magnitude, anisotropy and temperature dependence of the observed fields inc-axis oriented samples of sintered YBa2CuO3O7 and of thick-film Bi2Sr2CaCu2O8 are consistent with a conventional nuclear dipolar origin. An upper limit of ≲0.08 mT is set for any anomalous magnetic fields along thec-axis atμ+ sites in bulk CuO2 superconductors.

A combination of μSR and17O nuclear quadrupolar μLCR has been used to obtain detailed information on the muon site in YBa2Cu3O7. The rms magnitude of the nuclear dipolar fields in YBa2Cu3O7 enriched with 38%17O is about twice that in the natural16O sample. In addition the17O μLCR spectrum shows that the electric field gradient tensor at the oxygen closest to the muon is almost equal to that measured by NMR for the CuO2 plane sites O(2,3). These results suggest that the muon in fully oxygenated YBa2Cu3O7 is located at a single site 1.0 A from an oxygen ion, probably O(2,3).

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.

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.

We describe how the ferromagnetic spin echo technique may be used to make a direct and microscopic measurement of the motion of flux lines in a superconductor under the influence of an applied current. Our experimental results agree well with theory and indicate that both the value and distribution of velocities of flux lines may be measured.

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 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.

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.

Internal magnetic fields in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{x}}$ and ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_{4}$ have been investigated below 90 mK using muon spin rotation. In ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{x}}$ the static internal magnetic field at the muon site due to magnetic ordering remains constant with increasing x up until x=6.30 and then rapidly approaches zero just above x=6.44. In heavily doped samples of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{x}}$ (x\ensuremath{\ge}6.54, ${T}_{c}$\ensuremath{\ge}52 K) and ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathrm{y}}$${\mathrm{Sr}}_{\mathrm{y}}$${\mathrm{CuO}}_{4}$ (y=0.15, ${T}_{c}$=37 K) we find little evidence for static or slowly fluctuating electronic moments. These results clearly establish that static magnetic order is destroyed in regions of high carrier concentration.

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 .