An overview of recent developments and of the present status concerning low-energy mu SR (LE-mu SR) 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-mu SR method. (C) 2000 Elsevier Science B.V. All rights reserved.

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.

Muon-spin rotation (mu SR) and torque magnetometry have been used to probe the anisotropy of an untwinned single crystal of YBa2Cu3O7-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 mu 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.

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 magnetic penetration depth in the vortex state of YBa{sub 2}Cu{sub 3}O{sub 6.95} has been measured as a function of temperature T and magnetic field H applied along the {cflx c} axis. The internal field distribution in single crystals was fit assuming a triangular vortex lattice with an average in-plane penetration depth {lambda}{sub ab}=({lambda}{sub a}{lambda}{sub b}){sup 1/2}=1155(3) {Angstrom}, extrapolated to T=0 and H=0; {lambda}(H,T) increases with both T and H. The large T-independent increase in {lambda}{sub ab} with H is attributed to a strong nonlinear response as a result of the unconventional pairing in the superconducting state. {copyright} {ital 1997} {ital The American Physical Society}

The vortex state of a type-II superconductor produces a distinctive mu(+)SR line shape with features determined by the average internal held B-0, the magnetic penetration depth lambda, the superconducting coherence length xi, and the degree of disorder in the vortex lattice. Only in the high field regime (lambda much greater than L>xi, where L is the intervortex spacing) do the vortex cores (of radius approximate to xi) occupy a large enough area that they are observable in the line shape as a high field cutoff. Our mu(+)SR measurements of the held distributions in a mosaic of single crystals of YBa2Cu3O6.95 in fields of 1.9, 4.1, 4.7, and 6.5 T(B-0 parallel to ($) over cap c) show all the features of the line shape. We find lambda = 0.15+/-0.01 mu m at 10 K and the Ginzburg-Landau parameter kappa=lambda/xi=69.6+/-1.4 constant between 30 and 75 K; this is the only measurement to date of kappa in YBa2Cu3O6.95 below the irreversibility temperature. Due to disorder in the vortex lattice, either-from pinning or from vortex fluctuations that are quasistatic on the time scale of mu(+)SR, the observed line shape is "smeared" relative to that predicted for a perfect lattice. From the degree of smearing, we estimate an upper limit of 5.5% for the rms deviation of individual vortices from their ideal positions.

We have studied flux-depinning phenomena in the Bi2Sr2CaCu2O8 (Bi 2:2:1:2) and Pb-doped Pb0.7Bi1.3Sr2CaCu2O8 (Pb-Bi 2:2:1:2) systems using the transverse-field muon-spin-relaxation (muSR) technique. Comparison of field-cooled (FC) and zero-field-cooled (ZFC) results with external fields applied along the c axis of single-crystal specimens defines an irreversibility temperature (depinning temperature) T(irr): the FC and ZFC relaxation rates are essentially identical above T(irr), while the relaxation rate in the ZFC measurements is larger than that in the FC measurements below T(irr), reflecting the increased inhomogeneity of the local fields in the ZFC measurements due to flux pinning. The irreversibility line T(irr)(H) in the H-T phase diagram for Bi 2:2:1:2, obtained by muSR measurements for several fields, is compared with previous results from ac-susceptibility and mechanical-oscillator measurements. Using a superconducting-quantum-interference-device (SQUID) magnetometer, the time-dependent diamagnetic magnetization has been measured in the same Bi 2:2:1:2 crystals. We show that the results from muSR and these other techniques can be explained consistently within a framework of the flux-creep model. The irreversibility temperature in Pb-Bi 2:2:1:2, determined by muSR measurements, is significantly higher than that in the pure Bi 2:2:1:2 system. This result, together with the larger critical current and the higher activation energy U0 in the Pb-Bi 2:2:1:2 crystals as found by the SQUID magnetization measurements, suggests an enhancement of flux pinning by the Pb doping. We also compare the muSR results in sintered ceramic, oriented film, and single-crystal specimens in the pure Bi 2:2:1:2 system, and discuss possible effects of sample morphology on muSR measurements.

We have measured the magnetic penetration depth of the high-${\mathit{T}}_{\mathit{c}}$ superconducting system ${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.97}$ for 0.05\ensuremath{\le}x\ensuremath{\le}0.4 using the technique of transverse-field muon-spin relaxation. The temperature dependence is similar to that of the related compounds ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ with varying oxygen content. The zero-temperature relaxation rate and ${\mathit{T}}_{\mathit{c}}$ both decrease monotonically with x, in a manner similar to those of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ with increasing \ensuremath{\delta}. This observation is consistent with the interpretation that Pr is nearly tetravalent in this system so that ${\mathit{T}}_{\mathit{c}}$ is largely suppressed by means of the filling of holes in the conducting ${\mathrm{CuO}}_{2}$ planes. The influence of pair breaking, finite mean free path, and correlation with results for other high-${\mathit{T}}_{\mathit{c}}$ superconductors are discussed.

The muon-spin relaxation rate $\ensuremath{\sigma}$ has been measured in the high-${T}_{c}$ superconductors $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ for $x=6.66, 6.95, 7.0$, and ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_{4}$ in transverse external magnetic fields \ensuremath{\sim}1-4 kG. We find a simple relation which connects the transition temperature ${T}_{c}$, the magnetic-field penetration depth ${\ensuremath{\lambda}}_{L}$, the carrier concentration ${n}_{s}$, and the effective mass ${m}^{*}$ as ${T}_{c}\ensuremath{\propto}\ensuremath{\sigma}\ensuremath{\propto}\frac{1}{{\ensuremath{\lambda}}_{L}^{2}}\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}}$. The linear dependence ${T}_{c}\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}}$ suggests a high-energy scale for the coupling between superconducting carriers.

The recent discovery1,2 of superconductivity in the three-dimensional perovskite system (Ba, K)BiO3 has added a new group of compounds to the family of high-transition-temperature (high-Tc) superconductors. (Ba, K)BiO3 contains a three-dimensional BiO network rather than the CuO planes found in two-dimensional high-Tc systems such as YBa2Cu3O7, (La1.85Sr0.15)CuO4, Bi–Ca–Sr–Cu–O and Tl–Ba–Ca–Cu–O. There are, however, a few key features shared by (Ba, K)BiO3 and the two-dimensional systems; for example the parent compounds BaBiO3 and La2CuO4 both have one valence electron per Bi (or Cu) and doping by K (or Sr) introduces holes into the system as charge carriers. To explore the possible effects of magnetism in the (Ba, K)BiO3 system and its related compounds, we have performed muon spin rotation (μSR) experiments on BaBiO3, (Ba, K)BiO3 and Ba(Bi0.9Pb0.1)O3, the latter being a member of another oxide superconductor system, Ba(Pb, Bi)O3 (ref. 3), to search for static magnetic order. In the present study, no signature of magnetic order was found in any of the above systems above T = 10 K. This is in sharp contrast to the two-dimensional systems, where static magnetic order appears in the vicinity of superconductivity.

Recent progress of our pSR measurements on high-Tc and related systems is presented.Static magnetic order has been found and studied in LazCuO4, (L%-,Sr,)Cu04, YBa2Cu30,, YBa2 (Cu3-,Cox) 0 7 , as well as in B ~~S T ~Y C U ~O ~.NO magnetic order was found in the 3-dimensional systems BaBi03, Ba(Pbo.lBio.g)0 3 , and (BaK) Bi03 above T = 10 K.The anisotropy of the magnetic field penetration depht X has been observed by using a c-axis alligned sintered pellet specimen of YBa2Cu307.The temperature dependence of All (for c 11 HQxt) indicates isotropic superconducting energy gap without any anomalies.Based on the muon spin relaxation rate a observed in (random) pellet specimens of various high-Tc superconductors, we found a linear relation between TC and a o: 1 1 ~~ o: ns/m', which suggests a high energy scale of superconducting coupling.Deviations from this linear relation are seen for samples with large carrier concentrations n..

Muon spin rotation and neutron scattering studies on powder and single-crystal specimens of La2CuO4-y are compared. The apparent difference between the muon and neutron results for the ordered moment in the antiferromagnetic state is interpreted as the signature of increasingly short-ranged spatial spin correlations with increasing oxygen content.