Search

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.

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.

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.

Pulsed NMR measurements of the nuclear magnetic susceptibility of liquid3He-4He solutions at saturated vapor pressure are presented. They extend over the whole temperature range between 50 mK and 825 mK, for both concentrations of the coexisting dilute and3He-rich phases. The results have been compared to those obtained with pure3He, and the temperature dependence of the ratio of molar susceptibilities of coexisting phases is derived. The consequences on the efficiency of fractional distillation as a method to enhance nuclear polarization 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

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.

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.

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.

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).

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.

Positive-muon spin-rotation and -relaxation measurements of the oxygen-deficient perovskite YBa2Cu3O(x) have revealed local antiferromagnetic order for x = 6.0-6.4 with a Neel temperature TN that decreases rapidly with increasing oxygen content x. For slowly annealed samples with x = 6.35-6.5 the superconducting transition temperature Tc increases smoothly with x from 25 K at x = 6.348 to 60 K at x = 6.507. Two such samples with x = 6.348 and x = 6.400 appear to 'switch' from superconductivity to antiferromagnetic order at lower temperatures.

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 .