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The magnetic properties of iron-based superconductors $A$Fe$_2$As$_2$ ($A=$K, Cs, and Rb), which are characterized by the V-shaped dependence of the critical temperature ($T_{\rm c}$) on pressure ($P$) were studied by means of the muon spin rotation/relaxation technique. In all three systems studied the magnetism was found to appear for pressures slightly below the critical one ($P_{\rm c}$), i.e. at pressure where $T_{\rm c}(P)$ changes the slope. Rather than competing, magnetism and superconductivity in $A$Fe$_2$As$_2$ are coexisting at $P\gtrsim P_{\rm c}$ pressure region. Our results support the scenario of a transition from one pairing state to another, with different symmetries on either side of $P_{\rm c}$., Comment: 7 pages, 3 figures

The temperature dependent measurements of the thermodynamic critical field and the specific heat for the pressure stabilized Ga-II phase of elemental Gallium are presented. The discussion of these and other Ga phases data in the context of elemental and binary phonon-mediated type-I superconductors allowed to establish simple scaling relations between BCS quantities such as $B_{\rm c}(0)/T_{\rm c}\sqrt{\gamma_{\rm e}}$ and the specific heat jump at $T_{\rm c}$ versus the coupling strength $2\Delta/k_{\rm B} T_{\rm c}$ [$\Delta$ and $B_{\rm c}(0)$ are the zero-temperature values of the superconducting energy gap and the thermodynamic critical field, respectively, $T_{\rm c}$ is the transition temperature, and $\gamma_{\rm e}$ is the electronic specific heat]. The scaling relations can be analytically expressed by taking into account strong-coupling corrections to BCS theory. Such correlations can naturally explain the linear relation between $B_{\rm c}(0)$ and $T_{\rm c}$, which holds for type-I superconducting materials., Comment: 6 pages, 3 figures

The application of the muon-spin rotation/relaxation ($\mu$SR) technique for studying type-I superconductivity is discussed. In the intermediate state, i.e. when a type-I superconducting sample with non-zero demagnetization factor $N$ is separated into normal state and Meissner state (superconducting) domains, the $\mu$SR technique allows to determine with very high precision the value of the thermodynamic critical field $B_{\rm c}$, as well as the volume of the sample in the normal and the superconducting state. Due to the microscopic nature of $\mu$SR technique, the $B_{\rm c}$ values are determined directly via measurements of the internal field inside the normal state domains. No assumptions or introduction of any type of measurement criteria are needed. Experiments performed on a 'classical' type-I superconductor, a cylindrically shaped $\beta-$Sn sample, allowed to reconstruct the full $B-T$ phase diagram. The zero-temperature value of the thermodynamic critical field $B_{\rm c}(0)=30.578(6)$ mT and the transition temperature $T_{\rm c}=3.717(3)$ K were determined and found to be in a good agreement with the literature data. An experimentally obtained demagnetization factor is in very good agreement with theoretical calculations of the demagnetization factor of a finite cylinder. The analysis of $B_{\rm c}(T)$ dependence within the framework of the phenomenological $\alpha-$model allow to obtain the value of the superconducting energy gap $\Delta=0.59(1)$ meV, of the electronic specific heat $\gamma_e=1.781(3)$ ${\rm mJ}/{\rm mol}\; {\rm K}^2$ and of the jump in the heat capacity ${\Delta C(T_c)}/{\gamma T_{\rm c}}=1.55(2)$., Comment: 14 pages, 15 pictures

The superconductivity in the Bi-II phase of elemental Bismuth (transition temperature $T_{\rm c}\simeq3.92$ K at pressure $p\simeq 2.80$ GPa) was studied experimentally by means of the muon-spin rotation as well as theoretically by using the Eliashberg theory in combination with Density Functional Theory calculations. Experiments reveal that Bi-II is a type-I superconductor with a zero temperature value of the thermodynamic critical field $B_{\rm c}(0)\simeq31.97$~mT. The Eliashberg theory approach provides a good agreement with the experimental $T_{\rm c}$ and the temperature evolution of $B_{\rm c}$. The estimated value for the retardation (coupling) parameter $k_{\rm B}T_{\rm c}/\omega_{\rm ln} \approx 0.07$ ($\omega_{\rm ln}$ is the logarithmically averaged phonon frequency) suggests that Bi-II is an intermediately-coupled superconductor., Comment: 6 pages, 2 figures

Identifying the symmetry of the wave function describing the Cooper pairs is pivotal in understanding the origin of high-temperature superconductivity in iron-based superconductors. Despite nearly a decade of intense investigation, the answer to this question remains elusive. Here we use the muon spin rotation/relaxation (muSR) technique to investigate the underlying symmetry of the pairing state of the FeSe superconductor, the basic building block of all iron-chalcogenide superconductors. Contrary to earlier muSR studies on powders and crystals, we show that while the superconducting gap is most probably anisotropic but nodeless along the crystallographic c-axis, it is nodal in the ab-plane, as indicated by the linear increase of the superfluid density at low temperature. We further show that the superconducting properties of FeSe display a less pronounced anisotropy than expected., Comment: 13 Pages, 8 figures (Accepted in PRB Rapid)

Magnetism induced by external pressure ($p$) was studied in a FeSe crystal sample by means of muon-spin rotation. The magnetic transition changes from second-order to first-order for pressures exceeding the critical value $p_{{\rm c}}\simeq2.4-2.5$ GPa. The magnetic ordering temperature ($T_{{\rm N}}$) and the value of the magnetic moment per Fe site ($m_{{\rm Fe}}$) increase continuously with increasing pressure, reaching $T_{{\rm N}}\simeq50$~K and $m_{{\rm Fe}}\simeq0.25$ $\mu_{{\rm B}}$ at $p\simeq2.6$ GPa, respectively. No pronounced features at both $T_{{\rm N}}(p)$ and $m_{{\rm Fe}}(p)$ are detected at $p\simeq p_{{\rm c}}$, thus suggesting that the stripe-type magnetic order in FeSe remains unchanged above and below the critical pressure $p_{{\rm c}}$. A phenomenological model for the $(p,T)$ phase diagram of FeSe reveals that these observations are consistent with a scenario where the nematic transitions of FeSe at low and high pressures are driven by different mechanisms., Comment: 10 pages, 7 figyres

We report muon spin relaxation rate measurements on films composed of aluminum grains having a size of a few nm, with a large energy level splitting of the order of 100 K. The films range from weakly metallic to insulating. In the insulating case the low temperature relaxation rate is consistent with the presence of single electron spins in grains having an odd number of electrons. The relaxation rate temperature dependence follows an activation law having an energy scale in agreement with the average level splitting. In weakly metallic films the relaxation rate is smaller and decreases faster with temperature. Overall our observations are in line with the presence of a Kubo spin in Al nano-size grains due to quantum size effects., Comment: 14 pages, 5 figures, including supplementary material

Using muon-spin rotation the pressure-induced superconductivity in the Bi-III phase of elemental Bismuth (transition temperature $T_{\rm c}\simeq7.05$ K) was investigated. The Ginzburg-Landau parameter $\kappa=\lambda/\xi=30(6)$ ($\lambda$ is the magnetic penetration depth, $\xi$ is the coherence length) was estimated which is the highest among single element superconductors. The temperature dependence of the superconducting energy gap [$\Delta(T)$] reconstructed from $\lambda^{-2}(T)$ deviates from the weak-coupled BCS prediction. The coupling strength $2\Delta/k_{\rm B}T_{\rm c}\simeq 4.34$ was estimated thus implying that Bi-III stays within the strong coupling regime. The Density Functional Theory calculations suggest that superconductivity in Bi-III could be described within the Eliashberg approach with the characteristic phonon frequency $\omega_{\rm ln}\simeq 5.5$ meV. An alternative pairing mechanism to the electron-phonon coupling involves the possibility of Cooper pairing induced by the Fermi surface nesting., Comment: 5 pages, 4 figures

We present muon spin rotation measurements on superconducting Cu intercalated Bi$_2$Se$_3$, which was suggested as a realization of a topological superconductor. We observe a clear evidence of the superconducting transition below 4 K, where the width of magnetic field distribution increases as the temperature is decreased. The measured broadening at mK temperatures suggests a large London penetration depth in the $ab$ plane ($\lambda_{\mathrm{eff}}\sim 1.6$ $\mathrm{\mu}$m). We show that the temperature dependence of this broadening follows the BCS prediction, but could be consistent with several gap symmetries.

The magnetic order induced by the pressure was studied in single crystalline FeSe by means of muon-spin rotation ($\mu$SR) technique. By following the evolution of the oscillatory part of the $\mu$SR signal as a function of angle between the initial muon-spin polarization and 101 axis of studied crystal it was found that the pressure induced magnetic order in FeSe corresponds either to the collinear (single-stripe) antiferromagnetic order as observed in parent compounds of various FeAs-based superconductors or to the Bi-Collinear order as obtained in FeTe system, but with the Fe spins turned by 45$^{\rm o}$. The value of the magnetic moment per Fe atom was estimated to be $\simeq 0.13-0.14$~$\mu_{\rm B}$ at $p\simeq 1.9$~GPa., Comment: 4 pages, 4 figures. The Supplemental Information is available upon request

In 1933, Meissner and Ochsenfeld reported the expulsion of magnetic flux, the diamagnetic Meissner effect, from the interior of superconducting lead. This discovery was crucial in formulating the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. In exotic superconducting systems BCS theory does not strictly apply. A classical example is a superconductor-magnet hybrid system where magnetic ordering breaks time-reversal symmetry of the superconducting condensate and results in the stabilisation of an odd-frequency superconducting state. It has been predicted that under appropriate conditions, odd-frequency superconductivity should manifest in the Meissner state as fluctuations in the sign of the magnetic susceptibility meaning that the superconductivity can either repel (diamagnetic) or attract (paramagnetic) external magnetic flux. Here we report local probe measurements of faint magnetic fields in a Au/Ho/Nb trilayer system using low energy muons, where antiferromagnetic Ho (4.5 nm) breaks time-reversal symmetry of the proximity induced pair correlations in Au. From depth-resolved measurements below the superconducting transition of Nb we observe a local enhancement of the magnetic field in Au that exceeds the externally applied field, thus proving the existence of an intrinsic paramagnetic Meissner effect arising from an odd-frequency superconducting state.

Metal-to-insulator transitions (MITs) are a dramatic manifestation of strong electron correlations in solids1. The insulating phase can often be suppressed by quantum tuning, i.e. varying a nonthermal parameter such as chemical composi- tion or pressure, resulting in a zero-temperature quantum phase transition (QPT) to a metallic state driven by quantum fluctuations, in contrast to conventional phase transitions driven by thermal fluctuations. Theories of exotic phenomena known to occur near the Mott QPT such as quantum criticality and high-temperature superconductivity often assume a second-order QPT, but direct experimental evidence for either first- or second-order behavior at the magnetic QPT associated with the Mott transition has been scarce and further masked by the superconducting phase in unconventional superconductors. Most measurements of QPTs have been performed by volume-integrated probes, such as neutron scattering, magnetization, and transport, in which discontinuous behavior, phase separation, and spatially inhomogeneous responses are averaged and smeared out, leading at times to misidentification as continuous second-order transitions. Here, we demonstrate through muon spin relaxation/rotation (MuSR) experiments on two archetypal Mott insulating systems, composition-tuned RENiO3 (RE=rare earth element) and pressured-tuned V2O3, that the QPT from antiferromagnetic insulator to paramagnetic metal is first-order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value across the phase diagram until it is suddenly destroyed at the QPT. These findings call for further investigation into the role of inelastic soft modes and the nature of dynamic spin and charge fluctuations underlying the transition., Comment: Main text: 9 pages, 3 figures; Supplementary Information: 2 pages, 2 figures

The role played by the insulating intermediate (Li$_{0.84}$Fe$_{0.16}$)OH layer on magnetic and superconducting properties of (Li$_{0.84}$Fe$_{0.16}$)OHFe$_{0.98}$Se was studied by means of muon-spin rotation. It was found that it is not only enhances the coupling between the FeSe layers for temperatures below $\simeq 10$ K, but becomes superconducting by itself due to the proximity to the FeSe ones. Superconductivity in (Li$_{0.84}$Fe$_{0.16}$)OH layers is most probably filamentary-like and the energy gap value, depending on the order parameter symmetry, does not exceed 1-1.5 meV., Comment: 5 pages, 3 figures. The Supplementary Information file is available upon request

The low-energy muon facility at PSI provides nearly fully polarized positive muons with tunable energies in the keV range to carry out muon spin rotation (LE-muSR) experiments with nanometer depth resolution on thin films, heterostructures, and near-surface regions. The low-energy muon beam is focused and transported to the sample by electrostatic lenses. In order to achieve a minimum beam spot size at the sample position and to enable the steering of the beam in the horizontal and vertical direction, a special electrostatic device has been implemented close to the sample position. It consists of a cylinder at ground potential followed by four conically shaped electrodes, which can be operated at different electric potential. In LE-muSR experiments, an electric field at the sample along the beam direction can be applied to accelerate/decelerate muons to different energies (0.5-30 keV). Additionally, a horizontal or vertical magnetic field can be superimposed for transverse or longitudinal field muSR experiments. The focusing properties of the conical lens in the presence of these additional electric and magnetic fields have been investigated and optimized by Geant4 simulations. Some experimental tests were also performed and show that the simulation well describes the experimental setup., Comment: 22 pages,11figures

The PSI low-energy $\mu$SR spectrometer is an instrument dedicated to muon spin rotation and relaxation measurements. Knowledge of the muon beam parameters such as spatial, kinetic energy and arrival-time distributions at the sample position are important ingredients to analyze the $\mu$SR spectra. We present here the measured energy losses in the thin carbon foil of the muon start detector deduced from time-of-flight measurements. Muonium formation in the thin carbon foil (10 nm thickness) of the muon start detector also affect the measurable decay asymmetry and therefore need to be accounted for. Muonium formation and energy losses in the start detector, whose relevance increase with decreasing muon implantation energy ($<10$ keV), have been implemented in Geant4 Monte Carlo simulation to reproduce the measured time-of-flight spectra. Simulated and measured time-of-flight and beam spot agrees only if a small fraction of so called "unmoderated" muons which contaminate the mono-energetic muon beam of the $\mu$SR spectrometer is introduced. Moreover the sensitivity of the beam size and related upstream-downstream asymmetry for a specially shaped "nose" sample plate has been studied for various beam line settings, which is of relevance for the study of thermal muonium emission into vacuum from mesoporous silica at cryogenic temperatures., Comment: Paper submitted to JINST for review on 15th Jun 2015

Identifying the superconducting (SC) gap structure of the iron-based high-temperature superconductors (Fe-HTS's) remains a key issue for the understanding of superconductivity in these materials. In contrast to other unconventional superconductors, in the Fe-HTS's both $d$-wave and extended s-wave pairing symmetries are close in energy, with the latter believed to be generally favored over the former. Probing the proximity between these very different SC states and identifying experimental parameters that can tune them, are of central interest. Here we report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth (lambda) in the optimally doped Fe-HTS Ba_0.65Rb_0.35Fe_2As_2. At ambient pressure this material is known to be a nodeless s-wave superconductor. Upon pressure a strong decrease of (lambda) is observed, while the SC transition temperature remains nearly constant. More importantly, the low-temperature behavior of (1/lambda^{2}) changes from exponential saturation at zero pressure to a power-law with increasing pressure, providing unambiguous evidence that hydrostatic pressure promotes nodal SC gaps. Comparison to microscopic models favors a d-wave over a nodal s^{+-}-wave pairing as the origin of the nodes. Our results provide a new route of understanding the complex topology of the SC gap in Fe-HTS's., Comment: 33 pages and 12 figures (including supplementary information)

The Meissner effect and the associated perfect "bulk" diamagnetism together with zero resistance and gap opening are characteristic features of the superconducting state. In the pseudogap state of cuprates unusual diamagnetic signals as well as anomalous proximity effects have been detected but a Meissner effect has never been observed. Here we have probed the local diamagnetic response in the normal state of an underdoped La1.94Sr0.06CuO4 layer (up to 46 nm thick, critical temperature Tc' < 5 K) which was brought into close contact with two nearly optimally doped La1.84Sr0.16CuO4 layers (Tc \approx 32 K). We show that the entire 'barrier' layer of thickness much larger than the typical c axis coherence lengths of cuprates exhibits a Meissner effect at temperatures well above Tc' but below Tc. The temperature dependence of the effective penetration depth and superfluid density in different layers indicates that superfluidity with long-range phase coherence is induced in the underdoped layer by the proximity to optimally doped layers; however, this induced order is very sensitive to thermal excitation., Comment: 7 pages, 7 figures + Erratum

We investigate the coupling between the magnetic and superconducting order parameters in an 8 m long meander line ("wire") made of a La1.94Sr0.06CuO4 film with a cross section of 0.5 x 100 um^2. The magnetic order parameter is determined using the Low-Energy muon spin relaxation technique. The superconducting order parameter is characterized by transport measurements and modified by high current density. We find that, when the superconducting order parameter is suppressed by the current, the magnetic transition temperature, Tm, increases. The extracted sign and magnitude of the Ginzburg-Landau coupling constant indicate that the two orders are repulsive, and that our system is located close to the border between first and second order phase transition., Comment: 5 pages, 4 figures