Local magnetic behaviour of highly disordered undoped and Co-doped Bi2Se3 nanoplates: a muon spin relaxation study.

Magnetism induced by defects in nominally non-magnetic solids has attracted intense scientific interest in recent years. The local magnetism in highly disordered undoped and Co-doped topological insulator (TI) Bi2Se3nanoplates has been investigated by muon spin relaxation (µSR). UsingµSR spectroscopy, together with other macroscopic characterizations, we find that these nanoplates are composed of a core with both static fields and dynamically fluctuating moments, and a shell with purely dynamically fluctuating moments. The fluctuations in the core die out at low temperatures, while those in the shell continue till 2 K. When Bi2Se3is doped with Co, the static magnetic component increases, whilst keeping the dual (static-plus-dynamic) nature intact. The findings indicate that highly disordered TI's could constitute a new class of promising magnetic materials that can be engineered by magnetic impurity doping.

Antiferromagnetic Correlations in Strongly Valence Fluctuating CeIrSn.

CeIrSn with a quasikagome Ce lattice in the hexagonal basal plane is a strongly valence fluctuating compound, as we confirm by hard x-ray photoelectron spectroscopy and inelastic neutron scattering, with a high Kondo temperature of T_{K}∼480 K. We report a negative in-plane thermal expansion α/T below 2 K, which passes through a broad minimum near 0.75 K. Volume and a-axis magnetostriction for B∥a are markedly negative at low fields and change sign before a sharp metamagnetic anomaly at 6 T. These behaviors are unexpected for Ce-based intermediate valence systems, which should feature positive expansivity. Rather they point towards antiferromagnetic correlations at very low temperatures. This is supported by muon spin relaxation measurements down to 0.1 K, which provide microscopic evidence for a broad distribution of internal magnetic fields. Comparison with isostructural CeRhSn suggests that these antiferromagnetic correlations emerging at T≪T_{K} result from geometrical frustration.

Chiral singlet superconductivity in the weakly correlated metal LaPt3P.

Chiral superconductors are novel topological materials with finite angular momentum Cooper pairs circulating around a unique chiral axis, thereby spontaneously breaking time-reversal symmetry. They are rather scarce and usually feature triplet pairing: a canonical example is the chiral p-wave state realized in the A-phase of superfluid He3. Chiral triplet superconductors are, however, topologically fragile with the corresponding gapless boundary modes only weakly protected against symmetry-preserving perturbations in contrast to their singlet counterparts. Using muon spin relaxation measurements, here we report that the weakly correlated pnictide compound LaPt3P has the two key features of a chiral superconductor: spontaneous magnetic fields inside the superconducting state indicating broken time-reversal symmetry and low temperature linear behaviour in the superfluid density indicating line nodes in the order parameter. Using symmetry analysis, first principles band structure calculation and mean-field theory, we unambiguously establish that the superconducting ground state of LaPt3P is a chiral d-wave singlet.

Machine learning approach to muon spectroscopy analysis.

In recent years, artificial intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised machine learning (ML) algorithm called principal component analysis (PCA) as a tool to analyse the data from muon spectroscopy experiments. Specifically, we apply the ML technique to detect phase transitions in various materials. The measured quantity in muon spectroscopy is an asymmetry function, which may hold information about the distribution of the intrinsic magnetic field in combination with the dynamics of the sample. Sharp changes of shape of asymmetry functions-measured at different temperatures-might indicate a phase transition. Existing methods of processing the muon spectroscopy data are based on regression analysis, but choosing the right fitting function requires knowledge about the underlying physics of the probed material. Conversely, PCA focuses on small differences in the asymmetry curves and works without any prior assumptions about the studied samples. We discovered that the PCA method works well in detecting phase transitions in muon spectroscopy experiments and can serve as an alternative to current analysis, especially if the physics of the studied material are not entirely known. Additionally, we found out that our ML technique seems to work best with large numbers of measurements, regardless of whether the algorithm takes data only for a single material or whether the analysis is performed simultaneously for many materials with different physical properties.

Investigation of superconducting gap structure in HfIrSi using muon spin relaxation/rotation.

We have investigated the superconducting state of HfIrSi using magnetization, specific heat, muon spin rotation and relaxation ([Formula: see text]SR) measurements. Superconductivity was observed at [Formula: see text] K in both specific heat and magnetization measurements. From an analysis of the transverse-field [Formula: see text]SR data, it is clear that the temperature variation of superfluid density is well fitted by an isotropic Bardeen-Cooper-Schrieffer (BCS) type s-wave gap structure. The superconducting carrier density [Formula: see text] m-3, the magnetic penetration depth, [Formula: see text] nm, and the effective mass, [Formula: see text], were calculated from the TF-[Formula: see text]SR data. Zero-field [Formula: see text]SR data for HfIrSi reveal the absence of any spontaneous magnetic moments below [Formula: see text], indicating that time-reversal symmetry (TRS) is preserved in the superconducting state of HfIrSi. Theoretical investigations suggest that the Hf and Ir atoms hybridize strongly along the c-axis, and that this is responsible for the strong three-dimensionality of this system which screens the Coulomb interaction. As a result, despite the presence of d-electrons in HfIrSi, these correlation effects are weakened, making the electron-phonon coupling more important.

Ir 5d-band derived superconductivity in LaIr3.

The superconducting properties of rhombohedral LaIr3 were examined using susceptibility, resistivity, heat capacity, and zero-field (ZF) and transverse-field (TF) muon spin relaxation and rotation ([Formula: see text]SR) measurements. The susceptibility and resistivity measurements confirm a superconducting transition below [Formula: see text] K. Two successive transitions are observed in the heat capacity data, one at [Formula: see text] K and a second at 1.2 K below [Formula: see text]. The heat capacity jump is [Formula: see text], which is lower than 1.43 expected for Bardeen-Cooper-Schrieffer (BCS) weak-coupling limit. TF-[Formula: see text]SR measurements reveal a fully gapped s-wave superconductivity with [Formula: see text], which is small compared to the BCS value of 3.56, suggesting weak-coupling superconductivity. The magnetic penetration depth, [Formula: see text], estimated from TF-[Formula: see text]SR gives [Formula: see text] nm, a superconducting carrier density [Formula: see text] carriers m-3 and a carrier effective-mass enhancement factor [Formula: see text]. ZF-[Formula: see text]SR data show no evidence for any spontaneous magnetic fields below [Formula: see text], which demonstrates that time-reversal symmetry is preserved in the superconducting state of LaIr3.

Nodeless s-wave superconductivity in the [Formula: see text]-Mn structure type noncentrosymmetric superconductor TaOs: a [Formula: see text]SR study.

Noncentrosymmetric superconductors can lead to a variety of exotic properties in the superconducting state such as line nodes, multigap behavior, and time-reversal symmetry breaking. In this paper, we report the properties of a new noncentrosymmetric superconductor TaOs, using muon spin relaxation and rotation measurements. It is shown using the zero-field muon experiment that TaOs preserve the time-reversal symmetry in the superconducting state. From the transverse field muon measurements, we extract the temperature dependence of [Formula: see text], which is proportional to the superfluid density. This data can be fit with a fully gapped s-wave model for [Formula: see text] = 2.01 [Formula: see text] 0.02. Furthermore, the value of magnetic penetration depth is found to be 5919 [Formula: see text] 45 [Formula: see text], which is consistent with the value obtained from the bulk measurements.

Superconductivity and the upper critical field in the chiral noncentrosymmetric superconductor NbRh2B2.

NbRh2B2 crystallises in a chiral noncentrosymmetric structure and exhibits bulk type-II superconductivity below [Formula: see text] K. Here we show that the temperature dependence of the upper critical field deviates from the behaviour expected for both Werthamer-Helfand-Hohenberg and the Ginzburg-Landau models and that [Formula: see text] T exceeds the Pauli paramagnetic limit, [Formula: see text] T. We explore the reasons for this enhancement. Transverse-field muon spectroscopy measurements suggest that the superconducting gap is either s-wave or [Formula: see text]-wave, and the pressure dependence of [Formula: see text] reveals the superconducting gap is primarily s-wave in character. The magnetic penetration depth [Formula: see text] nm. Heat capacity measurements reveal the presence of a multigap [Formula: see text]-wave superconducting order parameter and moderate electron-phonon coupling.

Evidence of a Nodal Line in the Superconducting Gap Symmetry of Noncentrosymmetric ThCoC_{2}.

The newly discovered noncentrosymmetric superconductor ThCoC_{2} exhibits numerous types of unconventional behavior in the field dependent heat capacity data. Here we present the first measurement of the gap symmetry of ThCoC_{2} by muon spin rotation and relaxation (µSR) measurements. The temperature dependence of the magnetic penetration depth measured using the transverse field µSR experiment reveals the evidence of a nodal pairing symmetry. To understand this finding, we carry out calculations of the superconducting pairing eigenvalue and eigenfunction (pairing symmetry) due to the spin-fluctuation mechanism by directly implementing the ab initio band structures. We find that the system possesses a single Fermi surface with considerable three dimensionality and a strong nesting along the k_{z} direction. Such nesting promotes a superconducting state with a cosk_{z}-like pairing symmetry with a prominent nodal line on the k_{z}=±π/2 plane. The result agrees well with the experimental data.

Muons at ISIS.

For the last 30 years, muon experiments at ISIS pulsed neutron and muon facility at the Rutherford Appleton Laboratory, Oxfordshire have been making a significant contribution to a number of scientific fields. The muon facilities at ISIS consist of eight experimental areas. The European Commission Muon facility consists of three experimental areas with a fixed momentum (28 MeV c-1). The RIKEN-RAL facility has a variable momentum (17-90 MeV c-1) and a choice of negative or positive muons delivering muons to four experimental areas. There is also an area recently used for a muon ionization cooling experiment. In this paper, the ISIS pulsed muon facilities are reviewed, including the beam characteristics that could be useful for muography experiments.This article is part of the Theo Murphy meeting issue 'Cosmic-ray muography'.

Depth dependant element analysis of PbMg1/3Nb2/3O3 using muonic x-rays.

The relaxor PbMg1/3Nb2/3O3 (PMN) has received attention due to its potential applications as a piezoelectric when doped with PbTiO3 (PT). Previous results have found that there are two phases existing in the system, one linked to the near-surface regions of the sample, the other in the bulk. However, the exact origin of these two phases is unclear. In this paper, depth dependant analysis results from negative muon implantation experiments are presented. It is shown that the Pb content is constant throughout all depths probed in the sample, but the Mg and Nb content changes in the near-surface region below 100 µm. At an implantation depth of 60 µm, it is found that there is a 25% increase in Mg content, with a simultaneous 5% decrease in Nb content in order to maintain charge neutrality. These results show that the previously observed skin effects in PMN are due to a change in concentration and unit cell.

Superconducting properties and µSR study of the noncentrosymmetric superconductor Nb0.5Os0.5.

The properties of the noncentrosymmetric superconductor (α-[Formula: see text] structure) Nb0.5Os0.5 have been investigated using resistivity, magnetization, specific heat, and muon spin relaxation and rotation (µSR) measurements. These measurements suggest that Nb0.5Os0.5 is a weakly coupled ([Formula: see text]) type-II superconductor ([Formula: see text]), having a bulk superconducting transition temperature T c = 3.07 K. The specific heat data fits well with the single-gap BCS model indicating nodeless s-wave superconductivity in Nb0.5Os0.5. The µSR measurements also confirm [Formula: see text]-wave superconductivity with the preserved time-reversal symmetry.

Time-Reversal Symmetry Breaking in Re-Based Superconductors.

To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation and relaxation (µSR) studies of superconducting noncentrosymmetric Re_{0.82}Nb_{0.18} (T_{c}=8.8 K) and centrosymmetric Re (T_{c}=2.7 K). In Re_{0.82}Nb_{0.18}, the low-temperature superfluid density and the electronic specific heat evidence a fully gapped superconducting state, whose enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling. In both Re_{0.82}Nb_{0.18} and pure Re, the spontaneous magnetic fields revealed by zero-field µSR below T_{c} indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric ReT (T=transition metal), yet its preservation in the isostructural noncentrosymmetric superconductors Mg_{10}Ir_{19}B_{16} and Nb_{0.5}Os_{0.5}, strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and ReT. We discuss the superconducting order parameter symmetries that are compatible with the experimental observations.

Superconducting gap structure in the electron doped BiS2-based superconductor.

The influence of electron doping on semimetallic SrFBiS2 has been investigated by means of resistivity, zero and transverse - field (ZF/TF) muon spin relaxation/rotation (µSR) experiments. SrFBiS2 is semimetallic in its normal state and small amounts of La doping results in bulk superconductivity at 2.8 K, at ambient pressure. The temperature dependence of the superfluid density as determined by TF-µSR can be best modelled by an isotropic s - wave type superconducting gap. We have estimated the magnetic penetration depth [Formula: see text] nm, superconducting carrier density [Formula: see text] carriers m-3 and effective-mass enhancement m * = 1.558 m e. Additionally, there is no clear sign of the occurrence of spontaneous internal magnetic fields below [Formula: see text], which implies that the superconducting state in this material can not be categorized by the broken time-reversal symmetry which is in agreement with the previous theoretical prediction.

The new high field photoexcitation muon spectrometer at the ISIS pulsed neutron and muon source.

A high power pulsed laser system has been installed on the high magnetic field muon spectrometer (HiFi) at the International Science Information Service pulsed neutron and muon source, situated at the STFC Rutherford Appleton Laboratory in the UK. The upgrade enables one to perform light-pump muon-probe experiments under a high magnetic field, which opens new applications of muon spin spectroscopy. In this report we give an overview of the principle of the HiFi laser system and describe the newly developed techniques and devices that enable precisely controlled photoexcitation of samples in the muon instrument. A demonstration experiment illustrates the potential of this unique combination of the photoexcited system and avoided level crossing technique.

Muon spin relaxation study on itinerant ferromagnet CeCrGe3 and the effect of Ti substitution on magnetism of CeCrGe3.

A Muon spin relaxation (µSR) study has been performed on the Kondo lattice heavy fermion itinerant ferromagnet CeCrGe3. Recent investigations of bulk properties have revealed a long-range ordering of Cr moments at Tc = 70 K in this compound. Our µSR investigation between 1.2 K and 125 K confirm the bulk magnetic order which is marked by a loss in initial asymmetry below 70 K accompanied with a sharp increase in the muon depolarization rate. Field dependent µSR spectra show that the internal field at the muon site is higher than 0.25 T apparently due to the ferromagnetic nature of ordering. The effect of Ti substitution on the magnetism in CeCrGe3 is presented. A systematic study has been made on polycrystalline CeCr(1-x)Ti(x)Ge3 (0 ⩽ x ⩽ 1) using magnetic susceptibility χ(T), isothermal magnetization M(H), specific heat C(T) and electrical resistivity ρ(T) measurements which clearly reveal that the substitution of Ti for Cr in CeCrGe3 strongly influences the exchange interaction and ferromagnetic ordering of Cr moments. The Cr moment ordering temperature is suppressed gradually with increasing Ti concentration up to x = 0.50 showing Tc = 7 K beyond which Ce moment ordering starts to dominate and a crossover between Cr and Ce moment ordering is observed with a Ce moment ordering Tc = 14 K for x = 1.0. The Kondo lattice behavior is evident from temperature dependence of ρ(T) in all CeCr(1-x)Ti(x)Ge3 samples.

Unconventional Superconductivity in La(7)Ir(3) Revealed by Muon Spin Relaxation: Introducing a New Family of Noncentrosymmetric Superconductor That Breaks Time-Reversal Symmetry.

The superconductivity of the noncentrosymmetric compound La(7)Ir(3) is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature T(c)=2.25 K-a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La(7)Ir(3) may be unconventional and paves the way for further studies of this family of materials.

Investigations of the singlet ground state system: PrIrSi3.

We report our comprehensive study of physical properties of a ternary intermetallic compound PrIrSi3 investigated by dc magnetic susceptibility χ(T), isothermal magnetization M(H), thermo-remnant magnetization M(t), ac magnetic susceptibility χac(T), specific heat Cp(T), electrical resistivity ρ(T), muon spin relaxation (µSR) and inelastic neutron scattering (INS) measurements. A magnetic phase transition is marked by a sharp anomaly at Ttr = 12.2 K in χ(T) measured at low applied fields which is also reflected in the Cp(T) data through a weak anomaly at 12 K. An irreversibility between the zero field cooled and field cooled χ(T) data below 12.2 K and a very large relaxation time of M(t) indicates the presence of ferromagnetic correlation. The magnetic part of specific heat shows a broad Schottky-type anomaly near 40 K due to the crystal electric field (CEF) effect. An extremely small value of magnetic entropy below 12 K suggests a CEF-split singlet ground state which is confirmed from our analysis of INS data. The INS spectra show two prominent inelastic excitations at 8.5 meV and 18.5 meV that could be well accounted by a CEF model. The CEF splitting energy between the ground state singlet and the first excited doublet is found to be 92 K. Our µSR data reveal a possible magnetic ordering below 30 K, which is much higher than that found from the specific heat and magnetic susceptibility measurements. This could be due to the presence of short range correlations well above the long range magnetic ordering or due to the electronic changes induced by muons. The induced moment magnetism in the singlet ground state system PrIrSi3 with such a large splitting energy of 92 K is quite surprising.

Detection of time-reversal symmetry breaking in the noncentrosymmetric superconductor Re6Zr using muon-spin spectroscopy.

We have investigated the superconducting state of the noncentrosymmetric compound Re6Zr using magnetization, heat capacity, and muon-spin relaxation or rotation (µSR) measurements. Re6Zr has a superconducting transition temperature, Tc=6.75±0.05 K. Transverse-field µSR experiments, used to probe the superfluid density, suggest an s-wave character for the superconducting gap. However, zero and longitudinal-field µSR data reveal the presence of spontaneous static magnetic fields below Tc indicating that time-reversal symmetry is broken in the superconducting state and an unconventional pairing mechanism. An analysis of the pairing symmetries identifies the ground states compatible with time-reversal symmetry breaking.

Low-temperature muon spin rotation studies of the monopole charges and currents in Y doped Ho2Ti2O7.

In the ground state of Ho2Ti2O7 spin ice, the disorder of the magnetic moments follows the same rules as the proton disorder in water ice. Excitations take the form of magnetic monopoles that interact via a magnetic Coulomb interaction. Muon spin rotation has been used to probe the low-temperature magnetic behaviour in single crystal Ho2-xYxTi2O7 (x = 0, 0.1, 1, 1.6 and 2). At very low temperatures, a linear field dependence for the relaxation rate of the muon precession λ(B), that in some previous experiments on Dy2Ti2O7 spin ice has been associated with monopole currents, is observed in samples with x = 0, and 0.1. A signal from the magnetic fields penetrating into the silver sample plate due to the magnetization of the crystals is observed for all the samples containing Ho allowing us to study the unusual magnetic dynamics of Y doped spin ice.