Muon-spin-rotation studies of the temperature dependence of the magnetic penetration depth in the YBa2Cu3Ox family and related compounds

From SrTiO3 to Cuprates and Back to SrTiO3: A Way Along Alex Müller’s Scientific Career

K.A. Müller took a long route in science leaving many traces and imprints, which have been and are still today initiations for further research activities. We “walk” along this outstanding path but are certainly not able to provide a complete picture of it, since the way was not always straight, often marked by unintended detours, which had novel impact on the international research society.

EMuS Muon Facility and Its Application in the Study of Magnetism

A muon facility—EMuS (Experimental Muon Source)—at China Spallation Neutron Source (CSNS) has been studied since 2007. CSNS, which is designed to deliver a proton beam power of 100 kW at Phase-I, and will serve multidisciplinary research based on neutron scattering techniques, has just completed construction, and is ready to open to general users from September 2018. As an additional platform to CSNS, EMuS aims to provide different muon beams for multiple applications, among which, magnetism study by μSR techniques is a core part. By using innovative designs, such as a long target in conical shape situating in superconducting capture solenoids and forward collection method, EMuS can provide very intense muon beams with a proton beam of 5 kW and 1.6 GeV, from surface muons, decay muons, and high momentum muons to slow muons. In this article, the design aspects of EMuS, including general design, target station, muon beamlines, and μSR spectrometer, as well as prospects for applications on magnetism studies, will be reviewed.

Pressure-induced electronic phase separation of magnetism and superconductivity in CrAs

The recent discovery of pressure (p) induced superconductivity in the binary helimagnet CrAs has raised questions on how superconductivity emerges from the magnetic state and on the mechanism of the superconducting pairing. In the present work the suppression of magnetism and the occurrence of superconductivity in CrAs were studied by means of muon spin rotation. The magnetism remains bulk up to p  3.5 kbar while its volume fraction gradually decreases with increasing pressure until it vanishes at p  7 kbar. At 3.5 kbar superconductivity abruptly appears with its maximum T_c  1.2 K which decreases upon increasing the pressure. In the intermediate pressure region (3.5  p  7 kbar) the superconducting and the magnetic volume fractions are spatially phase separated and compete for phase volume. Our results indicate that the less conductive magnetic phase provides additional carriers (doping) to the superconducting parts of the CrAs sample thus leading to an increase of the transition temperature (T_c) and of the superfluid density (ρ_s). A scaling of ρ_s with as well as the phase separation between magnetism and superconductivity point to a conventional mechanism of the Cooper-pairing in CrAs.

Evidence for nonlocal electrodynamics in planar Josephson junctions

We study the temperature dependence of the critical current modulation I(c)(H) for two types of planar Josephson junctions: a low-Tc Nb/CuNi/Nb and a high-Tc YBa2Cu3O(7-δ) bicrystal grain-boundary junction. At low T both junctions exhibit a conventional behavior, described by the local sine-Gordon equation. However, at elevated T the behavior becomes qualitatively different: the I(c)(H) modulation field ΔH becomes almost T independent and neither ΔH nor the critical field for the penetration of Josephson vortices vanish at Tc. Such an unusual behavior is in good agreement with theoretical predictions for junctions with nonlocal electrodynamics. We extract absolute values of the London penetration depth λ from our data and show that a crossover from local to nonlocal electrodynamics occurs with increasing T when λ(T) becomes larger than the electrode thickness.

Concerning the superconducting gap symmetry in YBa₂Cu₃O₇- δ, YBa₂Cu₄O, and La₂ - xSrxCuO₄ determined from muon spin rotation in mixed states of crystals and powders

Muon spin rotation (μ(+)SR) measurements of square-root second moments of local magnetic fields σ in superconducting mixed states, as published for oriented crystals and powder samples of YBa(2)Cu(3)O(7 - δ) (δ≈0.05), YBa(2)Cu(4)O(8) and La(2 - x)Sr(x)CuO(4) (x ∼ 0.15-0.17), are subjected to comparative analysis for superconducting gap symmetry. For oriented crystals it is shown that anomalous dependences of σ on temperature T and applied field H, as-measured and extracted a- and b-axial components, are attributable to fluxon depinning and disorder that obscure the intrinsic character of the superconducting penetration depth. Random averages derived from oriented crystal data differ markedly from corresponding non-oriented powders, owing to the weaker influence of pinning in high-quality crystals. Related indicators for pinning perturbations, such as non-monotonic H dependence of σ, irreproducible data and strong H dependence of apparent transition temperatures, are also evident. Strong intrinsic pinning suppresses thermal anomalies in c-axis components of σ, which reflect nodeless gap symmetries in YBa(2)Cu(3)O(7 - δ) and YBa(2)Cu(4)O(8). For YBa(2)Cu(3)O(7 - δ), the crystal (a-b components, corrected for depinning) and powder data all reflect a nodeless gap (however, a-b symmetries remain unresolved for crystalline YBa(2)Cu(4)O(8) and La(1.83)Sr(0.17)CuO(4)). Inconsistencies contained in multiple and noded gap interpretations of crystal data, and observed differences between bulk μ(+)SR and surface-sensitive measurements are discussed.

Tuning the interlayer spacing of high-T_{c} Bi-based superconductors by intercalation: measuring the penetration depth and the two-dimensional superfluid density

Substantial control of the interlayer spacing in Bi-based high temperature superconductors has been achieved through the intercalation of guest molecules between the superconducting layers. Measurements using implanted muons reveal that the penetration depth increases with increasing layer separation while T_{c} does not vary appreciably, demonstrating that the bulk superfluid density is not the determining factor controlling T_{c}. Our results strongly suggest that for Bi-based high temperature superconductors the superfluid density appearing in the Uemura scaling relation rho_{s} proportional, variantT_{c} should be interpreted as the two-dimensional density within the superconducting layers, which we find to be constant for each class of system investigated.

Comparison of different methods for analyzing μSR line shapes in the vortex state of type-II superconductors

A detailed analysis of muon-spin rotation (μSR) spectra in the vortex state of type-II superconductors using different theoretical models is presented. Analytical approximations of the London and Ginzburg-Landau (GL) models, as well as an exact solution of the GL model were used. The limits of the validity of these models and the reliability for extracting parameters such as the magnetic penetration depth λ and the coherence length ξ from the experimental μSR spectra were investigated. The analysis of the simulated μSR spectra showed that at high magnetic fields there is a strong correlation between λ and ξ obtained for any value of the Ginzburg-Landau parameter κ = λ/ξ. The smaller the applied magnetic field, the smaller the possibility of finding the correct value of ξ. A simultaneous determination of λ and ξ without any restrictions is very problematic, regardless of the model used to describe the vortex state. It was found that for extreme type-II superconductors and low magnetic fields, the fitted value of λ is practically independent of ξ. The second-moment method frequently used to analyze μSR spectra by means of a multi-component Gaussian fit generally yields reliable values of λ over the whole range of applied fields [Formula: see text] (H(c1) and H(c2) are the first and second critical fields, respectively). These results are also relevant for the interpretation of small-angle neutron scattering experiments on the vortex state in type-II superconductors.

Pressure effects on the transition temperature and the magnetic field penetration depth in the pyrochlore superconductor RbOs2O6

Magnetization measurements under hydrostatic pressure up to 8 kbar in the pyrochlore superconductor RbOs2O6 (T(c) approximately or equal 6.3 K at p=0) were carried out. A positive pressure effect on T(c) with dT(c)/dp=0.090(3) K/kbar was observed, whereas no pressure effect on the magnetic penetration depth lambda was detected. The pressure independent ratio 2 Delta(0)/k(B)T(c)=3.72(2) (Delta(0) is the superconducting gap at zero temperature) was found to be close to the BCS value 3.52. Magnetization and muon-spin rotation measurements of lambda(T) indicate that RbOs2O6 is an adiabatic s-wave BCS-type superconductor. The value of lambda extrapolated to zero temperature and ambient pressure was estimated to be 230(30) nm.