The magnetic and superconducting properties of a series of underdoped $Ba_{1-x}Na_{x}Fe_{2}As_{2}$ (BNFA) single crystals with $0.19 \leq x\leq 0.34$ has been investigated with the complementary muon-spin-rotation ($μ$SR) and infrared spectroscopy techniques. The focus has been on the different antiferromagnetic states in the underdoped regime and their competition with superconductivity, especially for the ones with a tetragonal crystal structure and a so-called double-$Q$ magnetic order. Besides the collinear state with a spatially inhomogeneous spin-charge-density wave (i-SCDW) order at $x=0.24$ and $0.26$, that was previously identified in BNFA, we obtained evidence for an orthomagnetic state with a "hedgehog"-type spin vortex crystal (SVC) structure at $x=0.32$ and $0.34$. Whereas in the former i-SCDW state the infrared spectra show no sign of a superconducting response down to the lowest measured temperature of about 10K, in the SVC state there is a strong superconducting response similar to the one at optimum doping. The magnetic order is strongly suppressed here in the superconducting state and at $x=0.34$ there is even a partial re-entrance into a paramagnetic state at $T<<T_c$.
The superconducting properties of CaTSi3 (where T = Pt and Ir) have been investigated using muon spectroscopy. Our muon-spin relaxation results suggest that in both these superconductors time-reversal symmetry is preserved, while muon-spin rotation data show that the temperature dependence of the superfluid density is consistent with an isotropic s-wave gap. The magnetic penetration depths and upper critical fields determined from our transverse-field muon-spin rotation spectra are found to be 448(6) and 170(6) nm, and 3800(500) and 1700(300) G, for CaPtSi3 and CaIrSi3 respectively. The superc…
Using muon spin rotation (\muSR) and infrared spectroscopy we investigated the recently discovered superconductor K0.73Fe1.67Se2 with Tc = 32 K. We show that the combined data can be consistently described in terms of a macroscopically phase segregated state with a matrix of ~88% volume fraction that is insulating and strongly magnetic and inclusions with a ~12% volume fraction which are metallic, superconducting and non-magnetic. The electronic properties of the latter, in terms of the normal state plasma frequency and the superconducting condensate density, appear to be similar as in other i…
The formalism for analysing the magnetic field distribution in Pauli limited superconductors developed earlier is applied to the field dependence of the vortex lattice static linewidth measured in Muon Spin Rotation ($μ$SR) experiments. In addition to writing analytical formulae for the static linewidth for the vortex structure in the limit of independent vortices (i.e. moderate magnetic fields), we use Abrikosov's analysis to describe the field variations of the static linewidth at the approach of the superconductor to metal transition in the limit where the critical field is determined by Pa…
The superconducting properties of Lu2Fe3Si5 with Tc = 6.1 K have been investigated using low-temperature transverse-field muon spin rotation ($μ$SR) and specific heat measurements. The magnetic penetration depth at zero temperature is 353(1) nm. However, the temperature dependence of the magnetic penetration depth is consistent with a two gap s+s-wave model. Low-temperature specific heat measurements on the same sample also show evidence of two distinct superconducting gaps.
Noncentrosymmetric materials are promising paradigm to explore unconventional superconductivity. In particular, several Re containing noncentrosymmetric materials have attracted considerable attention due to a superconducting state with a broken time reversal symmetry. A comprehensive study on the superconducting ground state of NbReSi was investigated using magnetization, resistivity, and muon spin rotation/relaxation measurements. Zero field muon spectroscopy results showed the absence of any spontaneous magnetic field below the superconducting transition temperature, T$ _{c} $ = 6.29 K, ind…
The magnetic field probability P(B) is calculated from the Ginzburg-Landau theory for various lattices of vortex lines in type-II superconductors: Ideal triangular lattices, lattices with various shear strains and with a super lattice of vacancies, and lattices of short vortices in films whose magnetic field ''mushrooms'' near the surface.
The superfluid density ρ_s in underdoped (T_c\simeq23K), optimally doped (T_c\simeq35K) and overdoped (T_c\simeq29K) single crystalline (BiPb)_2(SrLa)_2CuO_{6+δ} samples was studied by means of muon-spin rotation (\muSR). By combining the \muSR data with the results of ARPES measurements on similar samples [Nature 457, 296 (2009)] good self-consistent agreement is obtained between two techniques concerning the temperature and the doping evolution of ρ_s.
We report muon spin rotation and magnetization measurements on the magnetic superconductor RbEuFe$_{4}$As$_{4}$ under hydrostatic pressures up to 3.8 GPa. At ambient pressure, RbEuFe$_{4}$As$_{4}$ exhibits a superconducting transition at $T_{c} \approx$ 36.5 K and a magnetic transition at $T_{m} \approx$ 15 K below which the magnetic and the superconducting order coexist. With increasing pressure, $T_{c}$ decreases while $T_{m}$ and the ordered Eu magnetic moment increase. In contrast to iron-based superconductors with ordering Fe moments, the size of the ordered Eu moment is not proportional …
We report on measurements of the in-plane magnetic penetration λ_{ab} in the optimally doped cuprate superconductor (BiPb)_2(SrLa)_2CuO_6+δ(OP Bi2201) by means of muon-spin rotation (\muSR). We show that in unconventional $d-$wave superconductors (like OP Bi2201), \muSR experiments conducted in various magnetic fields allow to evaluate the zero-field magnetic penetration depth λ_0, which relates to the zero-field superfluid density in terms of ρ_s\proptoλ_0^-2.
Recently, high entropy alloys (HEAs) have emerged as a new platform for discovering superconducting materials and offer avenues to explore exotic superconductivity. The highly disordered nature of HEA suggests regular phonon required for BCS superconductivity may be unlikely to occur. Therefore understanding the microscopic properties of these superconducting HEA is important. We report the first detailed characterization of the superconducting properties of the noncentrosymmetric ($α$-Mn structure) HEA {(HfNb)}$_{0.10}${(MoReRu)}$_{0.90}$, and {(ZrNb)}$_{0.10}${(MoReRu)}$_{0.90}$ by using mag…
Point contact tunneling (PCT) and low energy muon spin rotation (LE-muSR) are used to probe, on the same samples, the surface superconducting properties of micrometer thick niobium films deposited onto copper substrates using different sputtereing techniques: diode, dc magnetron (dcMS) and HIPIMS. The combined results are compared to radio-frequency tests performances of RF cavities made with the same processes. Degraded surface superconducting properties are found to yield lower quality factors and stronger Q slope. In addition, both techniques find evidence for surface paramagnetism on all s…
With muon spin rotation ($ μ$SR) we studied the transition between the orthorhombic antiferromagnetic (o-AF) and the tetragonal antiferromagnetic (t-AF) states of a weakly underdoped Ba$ _{1-x} $K$ _{x} $Fe$ _{2} $As$ _{2} $ single crystal. We observed some characteristic changes of the magnitude and the orientation of the magnetic field at the muon site which, due to the fairly high point symmetry of the latter, allow us to identify the magnetic structure of the t-AF state. It is the so-called, inhomogeneous double-$\mathbf{Q}$ magnetic structure with $ c $-axis oriented moments which has a v…
From muon spin rotation measurements on under- to overdoped Bi-2212 crystals we obtain evidence for a two-stage transition of the vortex matter as a function of temperature. The first transition is well known and related to the irreversibility line (IL). The second one is located below the IL and has not been previously observed. It occurs for all three sets of crystals and is unrelated to the vortex mobility. Our data are consistent with a two-stage melting scenario where the intra-planar melting of the vortex lattice and the inter-planar decoupling of the vortex lines occur independently.
Systems with strong spin-orbit coupling have been a topic of fundamental interest in condensed matter physics due to the exotic topological phases and the unconventional phenomenon they exhibit. In this particular study, we have investigated the superconductivity in the transition-metal ternary noncentrosymmetric compounds LaMSi (M = Ni, Pt) with different spin-orbit coupling strength, using muon-spin rotation and relaxation measurements. Transverse-field measurements made in the vortex state indicate that the superconductivity in both materials is fully gapped, with a conventional s-wave pair…
The anisotropy and temperature dependence of the magnetic field penetration depth in the iron-based superconductor KFe$_2$As$_2$ have been measured down to 20 mK by means of muon spin rotation. We have observed that the flux-line lattice forms triangular symmetry when we applied the field parallel to c-axis, suggesting the interaction between vortices should be isotropic. The temperature dependence of the penetration depth observd with an applied field parallel and perpendicular to c-axis are different. These results can be accounted for by a superconducting gap function with a horizontal line…
The in-plane magnetic penetration depth λ_{ab} of the iron selenide superconductor with the nominal composition FeSe_0.85 was studied by means of muon-spin rotation. The measurements of λ_{ab}^{-2}(T) are inconsistent with the presence of nodes in the gap as well as with a simple isotropic s-wave type of the order parameter, but can be equally well described within a two-gap (s+s) and an anisotropic s-wave gap picture. This implies that the superconducting energy gap in FeSe_0.85 contains no nodes.
We report transverse-field (TF) muon spin rotation experiments on single crystals of the topological superconductor Sr$_x$Bi$_2$Se$_3$ with nominal concentrations $x=0.15$ and $0.18$ ($T_c \sim 3$ K). The TF spectra ($B= 10$ mT), measured after cooling to below $T_c$ in field, did not show any additional damping of the muon precession signal due to the flux line lattice within the experimental uncertainty. This puts a lower bound on the magnetic penetration depth $λ\geq 2.3 ~μ$m. However, when we induce disorder in the vortex lattice by changing the magnetic field below $T_c$ a sizeable dampin…
Noncentrosymmetric superconductors with $α$-manganese structure has attracted much attention recently, after the discovery of time-reversal symmetry breaking in all the members of Re$_{6}$X (X = Ti, Hf, Zr) family. Similar to Re$_{6}$X, NbOs$_{2}$ also adopts $α$-$Mn$ structure and found to be superconducting with critical temperature $T_{c}$ $\approx$ 2.7 K. The results of the resistivity, magnetization, specific heat and muon-spin relaxation/rotation measurements show that NbOs$_{2}$ is a weakly coupled type-II superconductor. Interestingly, the zero-field muon experiments indicate that the …
Superconducting high entropy alloy (HEA) are emerging as a new class of superconducting materials. It provides a unique opportunity to understand the complex interplay of disorder and superconductivity. We report the synthesis and detail bulk and microscopic characterization of Nb$_{60}$Re$_{10}$Zr$_{10}$Hf$_{10}$Ti$_{10}$ HEA alloy using transport, magnetization, specific heat, and muon spin rotation/relaxation ($μ$SR) measurements. Bulk superconductivity with transition temperature $T_{C}$ = 5.7 K confirmed by magnetization, resistivity, and heat capacity measurements. Zero-field $μ$SR measu…
The magnetic phase diagram of EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ was investigated by means of magnetization and muon-spin rotation studies as a function of chemical (isovalent substitution of As by P) and hydrostatic pressure. The magnetic phase diagrams of the magnetic ordering of the Eu and Fe spins with respect to P content and hydrostatic pressure are determined and discussed. The present investigations reveal that the magnetic coupling between the Eu and the Fe sublattices strongly depends on chemical and hydrostatic pressure. It is found that chemical and hydrostatic pressure have a sim…
Using muon spin rotation and infrared spectroscopy we study the relation between magnetism and superconductivity in Ba$ _{1-x} $K$ _{x} $Fe$ _{2} $As$ _{2} $ single crystals from the underdoped to the slightly overdoped regime. We find that the Fe magnetic moment is only moderately suppressed in most of the underdoped region where it decreases more slowly than the Néel-temperature, $ T^{\mathrm{N}} $. This applies for both the total Fe moment obtained from muon spin rotation and for the itinerant component that is deduced from the spectral weight of the spin-density-wave pair breaking peak in …
Measurements of the in-plane magnetic field penetration depth λ_{ab} in Fe-based superconductors with the nominal composition SmFeAsO_0.85 (T_c\simeq52K) and NdFeAsO_0.85 (T_c\simeq51K) were carried out by means of muon-spin-rotation. The absolute values of λ_{ab} at T=0 were found to be 189(5)nm and 195(5)nm for Sm and Nd substituted samples, respectively. The analysis of the magnetic penetration depth data within the Uemura classification scheme, which considers the correlation between the superconducting transition temperature T_c and the effective Fermi temperature T_F, reveal that both fa…
The oxygen-isotope (^16O/^18O) effect (OIE) on the in-plane penetration depth $λ_{ab} (0)$ in underdoped Y_{1-x}Pr_xBa_2Cu_3O_{7-delta} was studied by muon-spin rotation. A pronounced OIE on $λ_{ab}^{-2}(0)$ was observed with a relative isotope shift of $Δλ^{-2}_{ab}/λ^{-2}_{ab}$=-5(2)% for x =0.3 and -9(2)% for x=0.4. It arises mainly from the oxygen-mass dependence of the in-plane effective mass $m_{ab}^{\ast}$. The OIE exponents of T_{c} and of $λ_{ab}^{-2}(0)$ exhibit a relation that appears to be generic for cuprate superconductors.
The effect of pressure on the copper and praseodymium magnetic order in the system Nd(1-x)$Pr(x)Ba2Cu3$O7 with x=0.3, 0.5, 0.7, and 1 was investigated by means of the muon spin rotation (muSR) technique. It was found that the effect of pressure on the Neel temperatures of both copper and praseodymium is positive for the whole range of Pr concentrations (0.3<x<1) studied. These findings are in contrast with a number of previous reports and clarify some of the puzzles related to the effect of pressure on superconductivity and magnetism in the praseodymium-substituted R}(1-x)$Pr(x)Ba2Cu3O7 system…
Muon spin rotation (muSR) experiments were performed on the intercalated graphite CaC6 in the normal and superconducting state down to 20 mK. In addition, AC magnetization measurements were carried out resulting in an anisotropic upper critical field Hc2, from which the coherence lengths xi_ab(0)=36.3(1.5) nm and xi_c(0)=4.3(7) nm were estimated. The anisotropy parameter gamma_H= H_c2_ab/H_c2_c increases monotonically with decreasing temperature. A single isotropic s-wave description of superconductivity cannot account for this behaviour. From magnetic field dependent muSR experiments the abso…
Muon spin rotation (mSR) measurements of the in-plane penetration depth lambda_ab have been performed in the electron-doped infinite layer high-Tc superconductor (HTS) Sr0.9La0.1CuO2. Absence of the magnetic rare-earth ions in this compound allowed to measure for the first time the absolute value of lambda_ab(0) in electron-doped HTS using mSR. We found lambda_ab(0)=116(2) nm. The zero-temperature depolarization rate sigma(0)?1/lambda_ab(0)^2=4.6(1) MHz is more than four times higher than expected from the Uemura line. Therefore this electron-doped HTS does not follow the Uemura relation found…
Muon-spin rotation experiments were performed on the pnictide high temperature superconductor SmFeAsO$_{1-x}$F$_{x}$ with x=0.18 and 0.3. We observed an unusual enhancement of slow spin fluctuations in the vicinity of the superconducting which suggests that the spin fluctuations contribute to the formation of an unconventional superconducting state. An estimate of the in-plane penetration depth $λ_{ab}(0)=190(5)$\thinspace nm was obtained, which confirms that the pnictide superconductors obey an Uemura-style relationship between $T_{\mathrm{c}}$ and $λ_{ab}(0)^{-2}$.
We report muon spin rotation measurements on a single crystal of the marginal type-II superconductor V. The measured internal magnetic field distributions are modeled assuming solutions of the Ginzburg-Landau (GL) equations for an ideal vortex lattice obtained using (i) an iterative procedure developed by E.H. Brandt, Phys. Rev. Lett. 78, 2208 (1997) and (ii) a variational method. Both models yield qualitatively similar results. The magnetic penetration depth (lambda) and the GL coherence length (xi) determined from the data analysis exhibit strong field dependences, which are attributed to ch…
Muon-spin rotation has been used to probe vortex state in Sr$_2$RuO$_4$. At moderate fields and temperatures a lattice of triangular symmetry is observed, crossing over to a lattice of square symmetry with increasing field and temperature. At lower fields it is found that there are large regions of the sample that are completely free from vortices which grow in volume as the temperature falls. Importantly this is accompanied by {\it increasing} vortex density and increasing disorder within the vortex-cluster containing regions. Both effects are expected to result from the strongly temperature-…
The Meissner effect has been directly demonstrated by depth-resolved muon spin rotation measurements in high-quality thin films of the T'-structured cuprate, T'-La$_{1.9}$Y$_{0.1}$CuO$_4$, to confirm bulk superconductivity ($T_c\simeq21$ K) in its {\sl undoped} state. The gradual expelling of an external magnetic field is observed over a depth range of $\sim$100 nm in films with a thickness of 275(15) nm, from which the penetration depth is deduced to be 466(22) nm. Based on this result, we argue that the true ground state of the "parent" compound of the $n$-type cuprates is not a Mott insulat…
The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli limited heavy electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to Muon Spin Rotation ($μ$SR) experiment. On the basis of the Ginzburg-Landau expansion for the superconductor free energy we study the evolution with respect to external field of the static linewidth both in the limit of independent vortices (low magnetic field) and in the near $H_\mathrm{c2}^\mathrm{p}(T)$ regime by using an extension of the Abrikosov analysis to Pauli limited superconduc…
We report muon spin relaxation/rotation (uSR) measurements of single crystal Ba(Fe1-xCox)2As2 with x=0.038 and 0.047. Zero field (ZF)-uSR and Transverse field (TF)-iSR measurements of these underdoped samples find the presence of magnetism and superconductivity. We find internal fields along the c-axis whose magnitude decreases with increasing doping. We find evidence for a low-temperature volume fraction that is only weakly magnetic, where that volume fraction increases with increasing Co doping of the sample. TF-uSR measurements show slight changes in the spectra that indicate magnetic inhom…
We argue that claims about magnetic field dependence of the magnetic field penetration depth lambda, which were made on the basis of moun-spin-rotation studies of some superconductors, originate from insufficient accuracy of theoretical models employed for the data analysis. We also reanalyze some of already published experimental data and demonstrate that numerical calculations of Brandt [E.H. Brandt, Phys. Rev. B 68, 54506 (2003)] may serve as a reliable and powerful tool for the analysis of the data collected in experiments with conventional superconductors. Furthermore, one can use this ap…
Muon-spin rotation spectroscopy has been used to measure the internal magnetic field distribution in NbSe2 for Hc1 << H < 0.25 Hc2. The deduced profiles of the supercurrent density indicate that the vortex-core radius in the bulk decreases sharply with increasing magnetic field. This effect, which is attributed to increased vortex-vortex interactions, does not agree with the dirty-limit microscopic theory. A simple phenomenological equation in which the core radius depends on the intervortex spacing is used to model this behaviour. In addition, we find for the first time that the in-plane magn…
The pressure dependence of the magnetic penetration depth in polycrystalline samples of YBa2Cu3Ox with different oxygen concentrations x = 6.45, 6.6, 6.8, and 6.98 was studied by muon spin rotation (muSR). The pressure dependence of the superfluid density (p_s) as a function of the superconducting transition temperature Tc is found to deviate from the usual Uemura line. The ratio (dTc/dP)/(dp_s/dP) is factor of 2 smaller than that of the Uemura relation. In underdoped samples, the zero temperature superconducting gap and the BCS ratio both increase with increasing external hydrostatic pressure…
Topological superconductivity is an exotic phenomenon due to the symmetry-protected topological surface state, in which a quantum system has an energy gap in the bulk but supports gapless excitations confined to its boundary. Symmetries including central and time-reversal (TRS), along with their relations with topology, are crucial for topological superconductivity. We report muon spin relaxation/rotation ($μ$SR) experiments on a topological noncentrosymmetric superconductor PbTaSe$_2$ to study its TRS and gap symmetry. Zero-field $μ$SR experiments indicate the absence of internal magnetic fie…
The performance of superconducting radiofrequency (SRF) cavities used for particle accelerators depends on two characteristic material parameters: field of first flux entry $H_{entry}$ and pinning strength. The former sets the limit for the maximum achievable accelerating gradient, while the latter determines how efficiently flux can be expelled related to the maximum achievable quality factor. In this paper, a method based on muon spin rotation ($μ$SR) is developed to probe these parameters on samples. It combines measurements from two different spectrometers, one being specifically built for…
Measurements of the magnetic field penetration depth λin superconductor Mo_3Sb_7 (T_c~2.1 K) were carried out by means of muon-spin-rotation. The absolute values of λ, the Ginzburg-Landau parameter κ, the first H_{c1} and the second H_{c2} critical fields at T=0 are λ(0)=720(100)nm, κ(0)=55(9), μ_0H_{c1}(0)=1.8(3)mT, and μ_0H_{c2}(0)=1.9(2)T. The zero temperature value of the superconducting energy gap Δ(0) was found to be 0.35(1)meV corresponding to the ratio 2Δ(0)/k_BT_c=3.83(10). At low temperatures λ^{-2}(T) saturates and becomes constant below T~0.3T_c, in agreement with what is expected …
Superfluid density ($n_s$) in the mixed state of an iron pnictide superconductor Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ is determined by muon spin rotation for a sample with optimal doping ($x=0.4$). The temperature dependence of $n_s$ is perfectly reproduced by the conventional BCS model for s-wave paring, where the order parameter can be either a single-gap with $Δ=8.35(6)$ meV [$2Δ/k_BT_c=5.09(4)$], or double-gap structure with $Δ_1=12$ meV (fixed) [$2Δ_1/k_BT_c=7.3$] and $Δ_2=6.8(3)$ meV [$2Δ_2/k_BT_c=4.1(2)$]. The latter is consistent with the recent result of angle-resolved photo-emssion spectr…
The in-plane magnetic penetration depth λ_{ab} in optimally doped (BiPb)_2(SrLa)_2CuO_{6+δ} (OP Bi2201) was studied by means of muon-spin rotation. The measurements of λ_{ab}^{-2}(T) are inconsistent with a simple model of a d-wave order parameter and a uniform quasiparticle weight around the Fermi surface. The data are well described assuming the angular gap symmetry obtained in ARPES experiments [Phys. Rev. Lett {\bf 98}, 267004 (2007)], where it was shown that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. We find that the remaining parts o…
Local magnetic field distribution B(r) in the mixed state of a boride superconductor, YB6, is studied by muon spin rotation (muSR). A comparative analysis using the modified London model and Ginzburg-Landau (GL) model indicates that the GL model exhibits better agreement with muSR data at higher fields, thereby demonstrating the importance of reproducing the field profile near the vortex cores when the intervortex distance becomes closer to the GL coherence length. The temperature and field dependence of magnetic penetration depth ($λ$) does not show any hint of nonlocal effect nor of low-lyin…
We present our results of a local probe study on EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals with $x$=0.13, 0.19 and 0.28 by means of muon spin rotation and ${}^{57}$Fe Mössbauer spectroscopy. We focus our discussion on the sample with $x$=0.19 viz. at the optimal substitution level, where bulk superconductivity ($T_{\text{SC}}=28$ K) sets in above static europium order ($T^{\text{Eu}}=20$K) but well below the onset of the iron antiferromagnetic (AFM) transition ($\sim$100 K). We find enhanced spin dynamics in the Fe sublattice closely above $T_{\text{SC}}$ and propose that these are r…
Muon spin rotation/relaxation measurements were performed to investigate magnetic properties of FeSe$_{1-x}$S$_x$ thin films on LaAlO$_3$. A drastic decrease of the initial asymmetry was observed together with the peak structure in the temperature dependence of the relaxation rate of muon spins almost at the same temperature where kink anomalies were observed in the temperature dependent resistivity. With increasing S content, the anomaly temperature increased and the magnetic fluctuations at the lowest temperature were suppressed. These results show that the S substitution induces magnetism a…
We present uSR investigations on SmFeAsO_1-xF_x showing coexistence of magnetic order and superconductivity only in a very narrow F-doping range. The sharp crossover between the two types of order is similar to that observed in LaFeAsO_1-xF_x, suggesting a common behavior for the 1111 pnictides. The analysis of the muon asymmetry demonstrates that the coexistence must be nanoscopic, i.e. the two phases must be finely interspersed over a typical length-scale of few nm. In this regime both the magnetic and the superconducting transition temperatures collapse to very low values. Our data suggest …
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 $κ=λ/ξ=30(6)$ ($λ$ is the magnetic penetration depth, $ξ$ is the coherence length) was estimated which is the highest among single element superconductors. The temperature dependence of the superconducting energy gap [$Δ(T)$] reconstructed from $λ^{-2}(T)$ deviates from the weak-coupled BCS prediction. The coupling strength $2Δ/k_{\rm B}T_{\rm c}\simeq 4.34$ was estimated thus implying that Bi-I…
The focus of this paper is on recent progress in muon spin rotation (muSR) studies of the vortex cores in type-II superconductors. By comparison of muSR measurements of the vortex core size in a variety of materials with results from techniques that directly probe electronic states, the effect of delocalized quasiparticles on the spatial variation of field in a lattice of interacting vortices has been determined for both single-band and multi-band superconductors. These studies demonstrate the remarkable accuracy of what some still consider an exotic technique. In recent years muSR has also be…
We report muon spin relaxation and rotation ($μ$SR) measurements on hydrothermally-grown single crystals of the tetragonal superconductor~FeS, which help to clarify the controversial magnetic state and superconducting gap symmetry of this compound. $μ$SR time spectra were obtained from 280~K down to 0.025~K in zero field (ZF) and applied fields up to 20 mT. In ZF the observed loss of initial asymmetry (signal amplitude) and increase of depolarization rate~$Λ_\mathrm{ZF}$ below 10~K indicate the onset of static magnetism, which coexists with superconductivity below $T_c$. Transverse-field $μ$SR…
Superconductors usually display either type-I or type-II superconductivity and the coexistence of these two types in the same material, for example at different temperatures is rare in nature. We the employed muon spin rotation (muSR) technique to unveil the superconducting phase diagram of the dodecaboride ZrB12 and obtained clear evidence of both type-I and type-II characteristics. Most importantly, we found a region showing unusual behavior where the usually mutually exclusive muSR signatures of type-I and type-II superconductivity coexist. We reproduced that behavior in theoretical modelin…
The quasiparticle excitations in the mixed state of Cd2Re2O7 have been studied by means of muon spin rotation/relaxation. The temperature dependence of the magnetic penetration depth (lambda) is consistent with a nearly isotropic superconducting order parameter, although a slight discrepancy which is dependent on the details in the analysis may be present. This is also supported by the relatively weak field dependence of lambda.
Measurements of the magnetic penetration depth (lambda) in the Fe-based superconductor Ba_(1-x)Rb_xFe_2As_2 (x=0.3, 0.35, 0.4) were carried out using the muon-spin rotation muSR technique. The temperature dependence of lambda is well described by a two-gap s+s-wave scenario with a small gap Delta_1 = 1 - 3 mev and a large gap Delta_2 = 7 - 9 mev. By combining the present data with those obtained for RbFe_2As_2 a decrease of the BCS ratio 2Delta_2/(k_B)(T_c) with increasing Rb content x is observed. On the other hand, the BCS ratio 2Delta_1/(k_B)(T_c) is almost independent of x. In addition, th…
We investigated the superconducting state of the noncentrosymmetric superconductors Li$_2$Pd$_x$Pt$_{3-x}$B with superconducting transition temperature $T_c$= 5.16(8) K ($x$=2.25), 3.56(8) K ($x=1.5$) and 2.60 K ($x=0$) by means of muon-spin rotation ($μ$SR) and specific heat experiments. The $μ$SR relaxation rate $σ_{sc}$ was found to be constant at low temperatures for all the compounds. Data taken at different magnetic fields show that the magnetic penetration depth $λ$ is field-independent for Li$_2$Pd$_{2.25}$Pt$_{0.75}$B and Li$_2$Pt$_{3}$B. The electronic contribution to the specific he…
Muon-spin rotation (muSR) experiments are often used to study the magnetic field distribution in type-II superconductors in the vortex state. Based on the determination of the magnetic penetration depth it is frequently speculated---also controversially---about the order-parameter symmetry of the studied superconductors. This article reports on a combined muSR and magnetization study of the mixed state in the cuprate high-temperature superconductor La_{1.83}Sr_{0.17}CuO_{4} in a low magnetic field of 20 mT applied along the c axis of a single crystal. The macroscopic magnetization measurements…
The internal field distribution in the vortex state of YBa2Cu3O6.60 is shown to be a sensitive measure of both the magnetic penetration depth and the vortex-core radius. The temperature dependence of the vortex core radius is found to be weaker than in the conventional superconductor NbSe2 and much weaker than theoretical predictions for an isolated vortex. The effective vortex-core radius decreases sharply with increasing H, whereas the penetration depth is found to be much stronger than in NbSe2.
Measurements of the magnetic field penetration depth $λ$ in the ternary boride superconductor Li$_2$Pd$_3$B ($T_c\simeq7.3$ K) have been carried out by means of muon-spin rotation ($μ$SR). The absolute values of $λ$, the Ginzburg-Landau parameter $κ$, and the first $H_{c1}$ and the second $H_{c2}$ critical fields at T=0 obtained from $μ$SR were found to be $λ(0)=252(2)$ nm, $κ(0)=27(1)$, $μ_0H_{c1}(0)=9.5(1)$ mT, and $μ_0H_{c2}(0)=3.66(8)$ T, respectively. The zero-temperature value of the superconducting gap $Δ_0=$1.31(3) meV was found, corresponding to the ratio $2Δ_0/k_BT_c=4.0(1)$. At low …
We present a low-energy muon-spin-rotation study of the magnetic and superconducting properties of YBa2Cu3O7/PrBa2Cu3O7 trilayer and bilayer heterostructures. By determining the magnetic-field profiles throughout these structures we show that a finite superfluid density can be induced in otherwise semiconducting PrBa2Cu3O7 layers when juxtaposed to YBa2Cu3O7 "electrodes" while the intrinsic antiferromagnetic order is unaffected.
We report zero-field muon spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon spin precession frequency below the Curie temperature $T_C = 3$ K. The $μ^+$ precession frequency persists below the bulk superconducting transition temperature $T_{sc} = 0.5$ K, where it measures a local magnetic field $B_{loc} = 0.015$ T. The amplitude of the $μ$SR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on th…
The recent observation of superconductivity with critical temperatures up to 55 K in the FeAs based pnictide compounds marks the first discovery of a non copper-oxide based layered high-Tc superconductor (HTSC) [1-3]. It has raised the suspicion that these new materials share a similar pairing mechanism to the cuprates, since both exhibit superconductivity following charge doping of a magnetic parent material. Here we present a muon spin rotation study on SmFeAsO1-xFx (x=0-0.30), which shows that static magnetism persists well into the superconducting regime. The analogy with the cuprates is q…
The magnetic penetration depth $λ$ in the mixed state of MgB$_2$ has been determined microscopically from the field distribution around magnetic vortices probed by muon spin rotation. Both the temperature and magnetic field dependence of $λ$ strongly suggest the presence of delocalized quasiparticles around the vortex cores. In particular, the effect of Doppler shift has been clearly observed as a finite gradient of the field dependence of $λ$, strongly suggesting an anisotropic order parameter with the region of a vanishingly small energy gap.
Appearance of strong spin-orbit coupling (SOC) is apparent in ternary equiatomic compounds with 5$d$-electrons due to the large atomic radii of transition metals. SOC plays a significant role in the emergence of unconventional superconductivity. Here we examined the superconducting state of HfIrSi using magnetization, specific heat, zero and transverse-field (ZF/TF) muon spin relaxation/rotation ($μ$SR) measurements. Superconductivity is observed at $T_\mathrm{C}$ = 3.6 K as revealed by specific heat and magnetization measurements. From the TF$-μ$SR analysis it is clear that superfluid density…
