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Measurements of intrinsic vortex lattice (VL) dynamics in superconductors as for instance VL melting or Bragg glass transitions are typically performed by e.g. macroscopic transport or surface sensitive measurement techniques. Therefore, usually thin superconducting films are used for microscopic measurements of VL dynamics. A direct consequence of using thin films is the strong influence of surface effects and defects, sample quality and geometry. We succeeded to combine time resolved stroboscopic small angle neutron scattering (SANS) with an advanced, time varying magnetic field setup allowing to extend the time window for slow dynamical processes to the range of 10 ms up to several minutes. The new results demonstrate that it is possible to observe directly the intrinsic dynamics of the VL in a bulk niobium single crystal on a microscopic scale without limitations due to surface effects. Field and temperature dependent relaxation times of the VL from 100 to 500 ms could be observed for the first time, allowing to directly measure the VL of the tilt modulus. This new experimental technique provides the possibility to study also the dynamical magnetic properties of various strongly correlated electron systems.

We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux lines in low Tc type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbour FLL direction. This tends to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo technique to observe the energy change of neutrons diffracted by moving flux lines. The μSR technique gives the distribution of values of magnetic field within the FLL. We have recently shown that one can perform μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors.

The asymmetry signal of a transverse field μSR time histogram is primarily the Fourier transform of the local field distribution P(b) for samples with static local fields b. The maximum entropy technique is used to produce a μSR lineshape which automatically deconvolutes the pulse structure of the beam (for pulsed facilities) and the time window. In this paper, we describe how to combine several component kernels to construct the transformation matrix for converting the lineshape into a time signal. We discuss the implications for improving the μSR maximum entropy (ME) algorithm under certain circumstances, and how dipolar broadening might be deconvoluted safely. This transformation may also be used to create accurate theoretical time signals for conventional fitting.

The maximum entropy (ME) analysis of μSR time spectra is used to produce the local field distribution P(b). The ME technique has user-defined constants in addition to the usual data manipulation parameters (such as the time range and binning) used in traditional fitting or Fourier transforms. The ME constants are the default level (used to suppress signals below the noise level) and a looseness factor (used to smooth the line shape). In this paper, we discuss how to automatically select values for these constants to ensure that the resulting P(b) is minimally distorted from the ideal and that the calculated errors are sensible.

Questions involving thin films, multilayered samples, surfaces and interfaces are generally not accessible by the conventional sources delivering muons with kinetic energy ∼4 MeV. The muon as a sensitive local magnetic and spin probe with complementary observational time window to other probes and techniques is able to offer unique new insights into these objects of investigations. Low energy muons (LE-μ + ) with tunable energy between ∼0.5 and 30 keV penetrate only to a depth between a few and few hundreds of nm depending on their energy. Hence they provide the desired non-destructive, non-invasive and microscopic probe for local investigations of properties near surfaces and in thin samples. The intensity of the LE-μ + source at PSI and the capability of the sample environment have been steadily evolving over the past years and the flux at the sample has now reached intensities of more than 700 μ + /s. After a summary of the most recent developments we give a brief overview of the experimental program together with some anticipated applications. The measurement of the value of local magnetic fields as a function of position below a surface on a scale of a few nm, which has provided the first direct confirmation of the London formula and has the potential to yield information crucial to understanding the details of the superconducting state, has been used to map films of non-conventional and conventional superconductors. Investigations of magnetic systems range from the first studies of magnetic properties of buried thin films to investigations of dimensional effects in a single spin glass layer and interlayer coupling in magnetic-nonmagnetic systems. The future prospects of this technique are outlined. To optimize the flux of LE-μ + at PSI a new, dedicated surface muon beam line has been designed. It is presently under construction and will be installed in 2003/2004. The predicted intensity increase by a factor of about ten will contribute to the realization of the full potential of polarized muons used as nanoprobes.

In muon spin rotation (μSR) measurements, the details of the local field distribution P ( b ) are of interest, so either a fast Fourier transform (FFT) or the maximum entropy method (MEM) is applied to extract P ( b ) from the μSR time spectra. Ideally, one would like to analyze the resulting P ( b ) as if it were a data set in its own right: fitting P ( b ) to appropriate theoretical functions and calculating its mean, second moment and third moment. This is only possible if there are rigorous errors associated with P ( b ). In this paper, we show that the maximum entropy method finds its maximum in a way analogous to χ 2 fitting. Calculation of a covariance matrix naturally follows. The covariance matrix demonstrates that the maximum entropy (ME) result P ( b ) has intrinsically correlated , not independent, errors. With proper care, P ( b ) can be fit and have its moments calculated. This method is not limited to μSR applications, it can be applied to other cases involving Fourier transforms of data, such as NMR.

We report on low energy muon spin rotation (LE-μSR) measurements of the magnetic penetration depth λ ab of a 700 nm thick YBa 2 Cu 3 O 7− δ film. The temperature dependence of the penetration depth is in good agreement with the results from conventional μSR measurements on single crystals. This demonstrates the potential of the new technique for thin film studies.

μSR and small-angle neutron scattering (SANS) have been used to probe the vortex arrangement in single crystals of the high-Tc superconductor Bi2.15Sr1.85CaCu2O8+δ which have been irradiated with heavy ions to produce columnar defects. The influence of these pinning sites on the spatial arrangement of the vortices is discussed, and the results are compared with numerical simulations.

The range of low-energy μ + in a thin Al film deposited on a quartz glass substrate has been investigated as a function of the μ + implantation energy by measuring the amplitude of the diamagnetic signal in a transverse field experiment. The μ + implantation energy was varied between 3.4 and 29.4 keV. The μ + asymmetry, which reflects the fraction of μ + stopped in Al, is found to decrease with increasing energy. The results are compared and found in good agreement with predictions of a Monte Carlo program, which simulates the implantation profiles of muons in matter.

We present the "rst lSR study of the dynamic magnetic behaviour of iron clusters supported in a non-magnetic thin "lm matrix. Thin "lm samples a!ord the possibility of very tight control over the cluster size, but are too thin for study with conventional lSR owing to the relatively long (of order 0.5 mm) stopping range of 4 MeV muons. In this study, the thin "lm samples were a 500 nm thick, silver matrix containing iron clusters with an equivalent iron concentration of 0.1% by volume. SQUID magnetometry showed a mean cluster diameter of 2.8 nm. Transverse low-energy lSR measurements in a "eld of 25 mT, applied normal to the plane of the "lm, were made in the temperature range 4.7}300 K. At low temperatures, a relaxation rate of 0.4 ls~1 was observed and interpreted as due to a static Lorentzian distribution of dipolar "elds with half-width 0.5 mT. At high temperatures, a motional narrowing of the "eld distribution, due to #uctuations in the orientation of the cluster moments, was observed. The #uctuations were found to follow an Arrhenius activation law, from which an activation energy of 51$9 K and an intrinsic cluster relaxation time of 12$4 ns were deduced. ( 2000 Elsevier Science B.V. All rights reserved.

Low-energy muon spin rotation (LE-μ+SR) measurements were performed on 3.4 and 9.1 nm epitaxial Cr(0 0 1) films buried by non-magnetic boundary layers to study the collapse of the spin-density wave (SDW) of bulk Cr, which is expected when decreasing the thickness of the film below the modulation period of the SDW ( ≈6 nm ). Magnetic phases of Cr are identified by the fast relaxation of the muon spin polarization. While a reduced Neel temperature of 285 K with respect to the bulk value is found for the 9.1 nm Cr layer, the 3.4 nm film remains in a magnetic phase over the investigated temperature range of 20–320 K.

The asymmetry signal of a μSR time histogram is theoretically the Fourier transform of the local field distribution P ( b ), for samples with static local fields. Commonly, P ( b ) is extracted from the time histograms by either a fast Fourier transform (FFT) or maximum entropy (ME). In this paper, we discuss how ME suppresses noise, and directly compare ME line shapes with FFTs.

We review how novel μSR measurements of the magnetic field distribution near the surface of a superconducting film of YBa2Cu3O7−δ in both the mixed state and the Meissner state are now possible using low-energy muons.

An overview of recent developments and of the present status concerning low-energy μSR (LE-μSR) at the Paul Scherrer Institute is given. We also discuss some schemes of possible future developments, which are able to improve the potential of the LE-μSR method.

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.

The bilayered ruthenate Sr 3 Ru 2 O 7 has a metamagnetic quantum critical point. This is the first example of a material with a quantum-critical end-point. This work addresses the problem of the metamagnetic criticality in this system through the measurement of spin fluctuations by inelastic neutron scattering. Our results show that incommensurate antiferromagnetic fluctuations are present in a wide range of applied fields. We have also observed how ferromagnetic fluctuations develop at the metamagnetic field. Finally, the intensity of the two types of fluctuations is followed as a function of the energy transfer between the neutron and the spins.

Using the technique of small angle neutron scattering (SANS) the vortex lattice of ultra-pure niobium has been investigated on an extremely fine temperature scale. As the temperature is increased towards T c 2 the longitudinal correlations of the vortices along their length improve, up to the resolution limited value of 100 μ m .

This article reviews the use of neutron small-angle scattering to determine the spatial distribution of the magnetic field within the bulk of a high-temperature superconductor. Results will be presented for experiments using single crystals of YBa 2 Cu 3 O 7 . The influence of pinning and anisotropy on the experimental data will be discussed together with the anomalous temperature dependence of the integrated intensity. Future directions for such work will be suggested.

We review the use of small-angle neutron diffraction to determine the spatial distribution of the magnetic field within the bulk of a superconductor in the mixed state. In high-Tc materials, which have long penetration depths, this technique presents some difficulties. However, the high κ, large anisotropy and the effects of temperature and pinning on the flux distribution provide many effects to be explored. Recent neutron observations of the flux-line distributions in high-Tc materials are described.

Small-angle neutron diffraction measurements from the flux lattice in a single crystal of the cubic Laves' phase superconductor, CeRu2, are reported. The mixed state is described in terms of aligned rigid bundles of vortices. The bundle diameters decrease above 1 2 H c 2 (consistent with collective weak pinning theory) and become comparable with the penetration length at a field at which a ‘peak effect’ is seen in magnetisation measurements. A clear memory of field histories that pass through the ‘peak effect’ region is also found; however, some of the induced disorder can be removed by subsequently cycling the field.

Neutron small-angle diffraction has been used to investigate the flux-line lattice structure within single crystals of the high-temperature superconductor Bi 2.15 Sr 1.95 CaCu 2 O 8 + x . The diffracted intensity goes rapidly to zero as the magnetic field or the temperature is increased. Melting at low fields as a function of temperature coincides with the appearence of finite resistance within the superconducting state. At low temperatures the diffracted intensity disappears in fields greater than ∼ 70 mT, probably due to the decomposition of the flux-line lattice into randomly pinned 2d “pancake” vortices.

The degree of perfection of flux lattices in superconductors in the mixed state, that may be obtained from small-angle neutron diffraction data, is discussed.

Neutron elastic scattering has been used to investigate the magnetic structure of neodymium in the 4- q state below 6K. The magnitudes and directions of the moments associated with each of the four wavevectors present in this phase have been determined, and the results compared to those obtained for the 3- q phase between 6 and 8K.

The low temperature magnetic phases of Nd 1- x Pr x (with x =0.05, 0.10 and 0.15) and Nd 94 Y 06 have been determined by neutron diffraction. The component modulation wave vectors of the 4- q phase are very sensitive to alloying. In Nd 90 Pr 10 , 48 magnetic satellites are observed around a reciprocal lattice point. The number of subharmonic reflections characterising the “archipelago” phase is reduced by alloying.

An investigation of the magnetic phase diagram of the dhcp cerium-neodymium alloy system has been performed through a series of neutron scattering, heat capacity and ac magnetic susceptibility measurements. A change from the incommensurate antiferromagnetic structure of neodymium to a ferromagnetic structure is reported.

The structural effects of simultaneous substitution of Li and Fe on Cu sites in YBa 2 Cu 3 O 7 have been investigated using powder neutron diffraction. The results are compared with data from samples containing only Li or Fe, and related to changes in T c .

Inelastic neutron scattering measurements have been performed on the system Ce0.75Y0.25 to determine the crystal field level scheme of the cerium ions in the double hexagonal close packed structure. The level scheme obtained is discussed in relation to the magnetic ordering observed below 7 K.