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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.

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.

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.