Competing electronic states are found in the large majority of unconventional superconductors, including high-Tc cuprates, iron based superconductors and many heavy fermion systems. The complex interplay is reflected in phase diagrams as a function of doping or other tuning parameters involving besides superconducting other phases (often magnetic) and quantum critical points. Superconductivity is also found in the vicinity of charge density wave (CDW) order in phase diagrams reminiscent of superconductivity mediated by magnetic fluctuations. There is however less knowledge about the interplay of superconductivity and CDW compared to the magnetic analogon. Here we report about microscopic studies by muon spin rotation as a function of pressure of the Ca_3Ir_4Sn_13 and Sr_3Ir_4Sn_13 cubic compounds, which display superconductivity and a structural phase transition associated with the formation of a CDW. We find a strong enhancement of the superfluid density and of the coupling strength above a pressure of about 1.6 GPa giving direct evidence of the presence of a quantum critical point separating a superconducting phase coexisting with CDW from a pure superconducting phase. The superconducting order parameter in both phases are found to have the same s-wave symmetry. In spite of the conventional phonon-mediated BCS character of this compound, the dependence of the effective superfluid density on the critical temperature puts this system in the Uemura plot close to unconventional superconductors.
The recent discovery of pressure induced superconductivity in the binary helimagnet CrAs has attracted much attention. How superconductivity emerges from the magnetic state and what is the mechanism of the superconducting pairing are two important issues which need to be resolved. In the present work, the suppression of magnetism and the occurrence of superconductivity in CrAs as a function of pressure ($p$) were studied by means of muon spin rotation. The magnetism remains bulk up to $psimeq3.5$~kbar while its volume fraction gradually decreases with increasing pressure until it vanishes at $psimeq$7~kbar. At 3.5 kbar superconductivity abruptly appears with its maximum $T_c simeq 1.2$~K which decreases upon increasing the pressure. In the intermediate pressure region ($3.5lesssim plesssim 7$~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 ($rho_s$). A scaling of $rho_s$ with $T_c^{3.2}$ as well as the phase separation between magnetism and superconductivity point to a conventional mechanism of the Cooper-pairing in CrAs.
The magnetic penetration depth ($lambda$) as a function of applied magnetic field and temperature in SrPt$_3$P($T_csimeq8.4$ K) was studied by means of muon-spin rotation ($mu$SR). The dependence of $lambda^{-2}$ on temperature suggests the existence of a single $s-$wave energy gap with the zero-temperature value $Delta=1.58(2)$ meV. At the same time $lambda$ was found to be strongly field dependent which is the characteristic feature of the nodal gap and/or multi-gap systems. The multi-gap nature of the superconduicting state is further confirmed by observation of an upward curvature of the upper critical field. This apparent contradiction would be resolved with SrPt$_3$P being a two-band superconductor with equal gaps but different coherence lengths within the two Fermi surface sheets.
We investigated the Abrikosov vortex lattice (VL) of a pure Niobium single crystal with the muon spin rotation (mu SR) technique. Analysis of the mu SR data in the framework of the BCS-Gorkov theory allowed us to determine microscopic parameters and the limitations of the theory. With decreasing temperature the field variation around the vortex cores deviates substantially from the predictions of the Ginzburg-Landau theory and adopts a pronounced conical shape. This is evidence of partial diffraction of Cooper pairs on the VL predicted by Delrieu for clean superconductors.
Muon spin rotation (muSR) experiments were performed on the intercalated graphite CaC6 in the normal and superconducting state down to 20 mK. In addition, AC magnetization measurements were carried out resulting in an anisotropic upper critical field Hc2, from which the coherence lengths xi_ab(0)=36.3(1.5) nm and xi_c(0)=4.3(7) nm were estimated. The anisotropy parameter gamma_H= H_c2_ab/H_c2_c increases monotonically with decreasing temperature. A single isotropic s-wave description of superconductivity cannot account for this behaviour. From magnetic field dependent muSR experiments the absolute value of the in-plane magnetic penetretion depth lambda_ab=78(3) nm was determined. The temperature dependence of the superfluid density rho_s(T) is slightly better described by a two-gap than a single-gap model.
Zero and longitudinal field muon spin rotation (muSR) experiments were performed on the superconductors PrPt4Ge12 and LaPt4Ge12. In PrPt4Ge12 below Tc a spontaneous magnetization with a temperature variation resembling that of the superfluid density appears. This observation implies time-reversal symmetry (TRS) breaking in PrPt4Ge12 below Tc = 7.9 K. This remarkably high Tc for an anomalous superconductor and the weak and gradual change of Tc and of the related specific heat anomaly upon La substitution in La_(1-x)Pr_xPt_4Ge_(12) suggests that the TRS breaking is due to orbital degrees of freedom of the Cooper pairs.
In a recent article Tran et al. [Phys. Rev.B 78, 172505 (2008)] report on the result of the muon-spin rotation (muSR) measurements of Mo_3Sb_7 superconductor. Based on the analysis of the temperature and the magnetic field dependence of the Gaussian relaxation rate sigma_{sc} they suggest that Mo_3Sb_7 is the superconductor with two isotropic s-wave like gaps. An additional confirmation was obtained from the specific heat data published earlier by partly the same group of authors in [Acta Mater. 56, 5694 (2008)]. The purpose of this Comment is to point out that from the analysis made by Tran et al. the presence of two superconducting energy gaps in Mo_3Sb_7 can not be justified. The analysis of muSR data does not account for the reduction of sigma_{sc} with increasing temperature, and, hence, yields inaccurate information on the magnetic penetration depth. The specific heat data can be satisfactory described within the framework of the one-gap model with the small residual specific heat component. The experimental data of Tran et al., as well as our earlier published muSR data [Phys. Rev. B 78, 014502 (2008)] all seem to be consistent with is the presence of single isotropic superconducting energy gap in Mo_3Sb_7.
Using muon-spin rotation, we studied the in-plane (lambda_ab) and the out of plane (lambda_c) magnetic field penetration depth in SrFe_1.75Co_0.25As_2 (T_c=13.3 K). Both lambda_ab(T) and lambda_c(T) are consistent with the presence of two superconducting gaps with the gap to T_c ratios 2Delta/k_BT_c=7.2 and 2.7. The penetration depth anisotropy gamma_lambda=lambda_c/lambda_ab increases from gamma_lambda=2.1 at T_c to 2.7 at 1.6 K. The mean internal field in the superconducting state increases with decreasing temperature, just opposite to the diamagnetic response seen in magnetization experiments. This unusual behavior suggests that the external field induces a magnetic order which is maintained throughout the whole sample volume.
A detailed analysis of muon-spin rotation ($mu$SR) 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 to extract parameters such as the magnetic penetration depth $lambda$ and the coherence length $xi$ from the experimental $mu$SR spectra were investigated. The analysis of the simulated $mu$SR spectra showed that at high magnetic fields there is a strong correlation between obtained $lambda$ and $xi$ for any value of the Ginzburg-Landau parameter $kappa = lambda/xi$. The smaller the applied magnetic field is, the smaller is the possibility to find the correct value of $xi$. A simultaneous determination of $lambda$ and $xi$ without any restrictions is very problematic, independent 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 $lambda$ is practically independent of $xi$. The second-moment method frequently used to analyze $mu$SR spectra by means of a multi-component Gaussian fit, generally yields reliable values of $lambda$ in the whole range of applied fields $ H_{c1} ll H lesssim H_{c2}$ ($H_{c1}$ and $H_{c2}$ are the first and second critical fields, respectively). These results are also relevant for the interpretation of small-angle neutron scattering (SANS) experiments of the vortex state in type-II superconductors.
We investigate the magnetic penetration depth lambda in superconducting Ba_1-xK_xFe_2As_2 (T_csimeq32K) with muon-spin rotation (muSR) and angle-resolved photoemission (ARPES). Using muSR, we find the penetration-depth anisotropy gamma_lambda=lambda_c/lambda_{ab} and the second-critical-field anisotropy gamma_{H_c2} to show an opposite T-evolution below T_c. This dichotomy resembles the situation in the two-gap superconductor MgB_2. A two-gap scenario is also suggested by an inflection point in the in-plane penetration depth lambda_ab around 7K. The complementarity of muSR and ARPES allows us to pinpoint the values of the two gaps and to arrive to a remarkable agreement between the two techniques concerning the full T-evolution of lambda_ab. This provides further support for the described scenario and establishes ARPES as a tool to assess macroscopic properties of the superconducting condensate.
