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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.

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.

This paper describes a study of superparamagnetism in iron nanoclusters using low energy μSR, including for the first time zero field measurements, which yield an intrinsic nanocluster superparamagnetic relaxation rate of ν0=67±15 MHz and an energy barrier of ΔE=37±4 K. TEM micrographs of the embedded clusters show there to be a range of shapes and also sizes, which is bourne out by SQUID magnetometry measurements.

The recent development at the Paul Scherrer Institute of a beam of low energy muons allows depth dependent muon spin rotation and relaxation investigations in thin samples, multilayers and near surface regions (low energy μSR, LE-μSR). After a brief overview of the LE-μSR method, some representative experiments performed with this technique will be presented. The first direct determination of the field profile just below the surface of a high-temperature superconductor in the Meissner phase illustrates the power and sensitivity of low energy muons as near-surface probe and is an example of general application to depth profiling of magnetic fields. The evolution of the flux line lattice distribution across the surface of a YBa2Cu3O7 film in the vortex phase has been investigated by implanting muons on both sides of a normal-superconducting boundary. A determination of the relaxation time and energy barrier to thermal activation in iron nanoclusters, embedded in a silver thin film matrix (500nm), demonstrates the use of slow muons to measure the properties of samples that cannot be made thick enough for the use of conventional μSR. Other experiments investigated the magnetic properties of thin Cr(001) layers at thicknesses above and below the collapse of the spin density wave.

Recent experimental results indicate that superconductivity in Sr2RuO4 is described by the p-wave E_u representation of the D_{4h} point group. Results on the vortex lattice structures for this representation are presented. The theoretical results are compared with experiment., Comment: 4 pages, 3 figures, M2S-HTSC-VI proceedings

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.

Muon-spin rotation $(\ensuremath{\mu}\mathrm{SR})$ and torque magnetometry have been used to probe the anisotropy of an untwinned single crystal of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ The absence of twin planes allows the ratios of all three principal components of the superconducting effective mass tensor to be determined. The values for the in-plane anisotropy are in good agreement with values obtained by other techniques. The out-of-plane anisotropies as measured by $\ensuremath{\mu}\mathrm{SR}$ are also found to be in good agreement with other microscopic measurements, but somewhat lower than those resulting from torque measurements on this and other crystals.

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.

We have measured the diffracted neutron scattering intensities from the square magnetic flux lattice in the perovskite superconductor ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, which is thought to exhibit $p$-wave pairing with a two-component order parameter. The relative intensities of different flux lattice Bragg reflections over a wide range of field and temperature have been shown to be inconsistent with a single component Ginzburg-Landau theory but qualitatively agree with a two-component $p$-wave Ginzburg-Landau theory.

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.

Low energy (16 keV) muons were used to probe the dynamic magnetic behaviour of iron nanoclusters embedded in a silver thin film matrix. The silver film was 500 nm thick and contained a volume fraction of 0.1% iron. Measurements were made in a field of 25 mT, applied normal to the plane of the film, in the temperature range 4.7 K to 300 K. At temperatures above 20 K thermal activation of the cluster moments was seen as a narrowing of the field distribution sensed by the implanted muons. An intrinsic cluster relaxation time of τ0 = 12 ± 4 ns and an activation energy of 51 ± 9 K were deduced from fits to the data. SQUID magnetometry of thicker (1.5 µm) but otherwise identical films on graphite substrates showed the clusters to have a volume of the order of 10-26 m3, from which a cubic anisotropy constant of K = 2.3 ± 0.4 × 105 J m-3 was calculated. Remanence measurements showed no evidence of a preferred orientation for the magnetization of the cluster assembly.

Muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ measurements of the magnetic-field distribution $n(B)$ in the vortex state of the oxygen deficient high-${T}_{c}$ superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.60}$ reveal a vortex-lattice melting transition at much lower temperature than that in the fully oxygenated material. The transition is best described by a model in which adjacent layers of ``pancake'' vortices decouple in the liquid phase. In some samples we also observe changes in $n(B)$ which are consistent with a vortex lattice which becomes disordered along the field direction above a crossover field ${B}_{\mathrm{cr}}.$ A transition of this nature has previously been reported in the highly anisotropic superconductor ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+y}.$

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.

At the Paul Scherrer Institute slow positive muons (μ+) with nearly 100% polarization and an energy of about 10 eV are generated by moderation of an intense secondary beam of surface muons in an appropriate condensed gas layer. These epithermal muons are used as a source of a tertiary beam of tunable energy between 10 eV and 20 keV. The range of these muons in solids is up to 100 nm which allows the extension of the μ+SR techniques (muon spin rotation, relaxation, resonance) to the study of thin films. A basic requirement for the proper interpretation of μ+SR results on thin films and multi-layers is the knowledge of the depth distribution of muons in matter. To date, no data are available concerning this topic. Therefore, we investigated the penetration depth of μ+ with energies between 8 keV and 16 keV in Cu/SiO2 samples. The experimental data are in agreement with simulated predictions. Additionally, we present two examples of first applications of low energy μ+ in μ+SR investigations. We measured the magnetic field distribution inside a 500-nm thin High-TC superconductor (YBa2Cu3O7-δ), as well as the depth dependence of the field distribution near the surface. In another experiment a 500-nm thin sample of Fe-nanoclusters (diameter 2.4(4) nm), embedded in an Ag matrix with a volume concentration of 0.1%, was investigated with transverse field μ+SR.

The phenomenon of superconductivity continues to be of considerable scientific and practical interest. Underlying this phenomenon is the formation of electron pairs, which in conventional superconductors do not rotate about their centre of mass (‘s -wave’ pairing; refs 1, 2). This contrasts with the situation in high-temperature superconductors, where the electrons in a pair are believed to have two units of relative angular momentum (‘d -wave’ pairing; ref. 3 and references therein). Here we report small-angle neutron-scattering measurements of magnetic flux lines in the perovskite superconductor Sr2RuO4 (ref. 4), which is a candidate for another unconventional paired electron state—‘p -wave’ pairing, which has one unit of angular momentum5,6,7. We find that the magnetic flux lines form a square lattice over a wide range of fields and temperatures, which is the result predicted by a recent theory8,9 of p -wave superconductivity in Sr2RuO4. This theory also indicates that only a fraction of the electrons are strongly paired and that the orientation of the square flux lattice relative to the crystal lattice will determine which parts of the three-sheet Fermi surface of this material are responsible for superconductivity. Our results suggest that superconductivity resides mainly on the ‘γ’ sheet9.

Positive muon spin rotation/relaxation (μ+SR) was used to study the effects of substitution of small amounts of transition metals (Co, Ni and Zn) for Cu in superconducting Nd1.85Ce0.15CuO4. As expected, Zn doping has only a small effect upon T2c, presumably due to randomness and/or a change in the charge carrier density; however, the same quantity (1%) of Co or Ni suppresses T2c dramatically. In the case of Co, this may be due to the observed onset of disordered but near-static magnetism below 50 K; in the case of Ni there is no evidence of static paramagnetic moments down to 4 K, so rapidly fluctuating momentts (τ2c < 10 ns, too fast to affect the muon spin) must be present, if pair-breaking is the predominant mechanism for suppression of T2c.

We report muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ measurements on the moving vortex lattice (VL) in the type-II superconductor Pb-In, backed up by small-angle neutron scattering (SANS) observations on the same sample. We observe a motional narrowing of the $\ensuremath{\mu}\mathrm{SR}$ lineshape $p(B)$ and by SANS, alignment of the VL to the direction of vortex motion. We have calculated the $\ensuremath{\mu}\mathrm{SR}$ lineshape expected with a range of orientations of the moving VL. We demonstrate how the new $\ensuremath{\mu}\mathrm{SR}$ results give information on the moving VL which is complementary and consistent with the SANS data.

Measurements of the spin rotation and depolarization of implanted positive muons have revealed that La2SrCu2O6+δ and La2CaCu2O6+δ display magnetic ordering similar to that of La2−xSrxCuO4−y and YBa2Cu3Ox. A superconducting phase was detected in La2CaCu2O6+δ (δ ≥ 0.05), with onset at ∼ 45K and accompanied by a change in the muon spin precession signals from the majority antiferromagnetic phase, phenomena absent in La2SrCu2O6+δ. This behaviour was attributed to mobility and local clustering of intercalated oxygen excess in the layer between the CuO2 planes., Work suported by the NRC and NSERC of Canada, CICYT and the MIDAS project, Spain; and the USA-DOE.

In this paper, we report the long range oscillatory spin polarization effects of Ni and Zn doping in YBa 2 Cu 3 O 7 by 89 Y NMR. From comparison of the magnetic moments of the Ni and Zn impurities measured by susceptibility ( p Ni =1.6 μ B and p zn =0.36 μ B ) with the impurity-induced NMR linewidths, we find that the Ni moments couple much more weakly to the conduction band than the Zn moments, by a factor which might be a large as 21.

This round table discussion considered coordinating improvements in the portability and quality of μSR analysis software. Panel members were Tanya Riseman, Ivan D. Reid (PSI), Steve P. Cottrell (ISIS), Jess H. Brewer (TRIUMF), and Mark Koennecke (PSI); Mark is a developer of the new neutron and X-ray scattering data format NeXus.

Recent muon spin rotation experiments measuring the magnetic penetration depth in high-T c superconductors are critically discussed. The field distribution in the mixed state is obtained using a simple model which takes into account the significant electronic anisotropy of these materials. From the obtained lineshape, new estimates for the London penetration depth along the hard direction in La 1.85 Sr 0.15 CuO 4 and YBa 2 Cu 3 O 7−δ are given.