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FAMU is an INFN-led muonic atom physics experiment based at the RIKEN-RAL muon facility at the ISIS Neutron and Muon Source (United Kingdom). The aim of FAMU is to measure the hyperfine splitting in muonic hydrogen to determine the value of the proton Zemach radius with accuracy better than 1%.The experiment has a scintillating-fibre hodoscope for beam monitoring and data normalisation. In order to carry out muon flux estimation, low-rate measurements were performed to extract the single-muon average deposited charge. Then, detector simulation in Geant4 and FLUKA allowed a thorough understanding of the single-muon response function, crucial for determining the muon flux. This work presents the design features of the FAMU beam monitor, along with the simulation and absolute calibration measurements in order to enable flux determination and enable data normalisation.

We investigated the Re-based kagome superconductor Re$_2$Zr through various measurements, including resistivity, magnetization, specific heat, and muon spin rotation and relaxation spectroscopy. These results suggest that Re$_2$Zr is a moderately coupled potential two-gap superconductor. Zero-field muon relaxation data indicate the possible presence of a time-reversal symmetry-breaking state in the superconducting ground state. Our investigation identifies Re$_{2}$Zr as a new unconventional superconductor with a potential complex order parameter that warrants considerable experimental and theoretical interest., Comment: 9 pages, 6 figures

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

Relaxor-ferroelectrics display exceptional dielectric properties resulting from the underlying random dipolar fields induced by strong chemical inhomogeneity. An unusual structural aspect of relaxors is a skin-effect where the near-surface region in single crystals exhibit structures and critical phenomena that differ from the bulk. Relaxors are unique in that this skin effect extends over a macroscopic lengthscale of $\sim$ 100$\mu$m whereas usual surface layers only extend over a few unit cells (or $\sim$ nm). We present a muon spectroscopy study of Pb(Fe$_{1/2}$Nb$_{1/2}$)O$_{3}$ (PFN) which displays ferroelectric order, including many relaxor-like dielectric properties such as a frequency broadened dielectric response, and antiferromagnetism with spatially short-range polar correlations and hence can be termed a multiferroic. In terms of the magnetic behavior determined by the Fe$^{3+}$ ($S=5/2$, $L\approx0$) ions, PFN has been characterized as a unique example of a "cluster spin-glass". We use variable momentum muon spectroscopy to study the depth dependence of the slow magnetic relaxations in a large 1 cm$^{3}$ crystal of PFN. Zero-field positive muon spin relaxation is parameterized using a stretched exponential, indicative of a distribution of relaxation rates of the Fe$^{3+}$ spins. This bandwidth of frequencies changes as a function of muon momentum, indicative of a change in the Fe$^{3+}$ relaxation rates as a function of muon implantation depth in our single crystal. Using negative muon elemental analysis, we find small-to-no measurable change in the Fe$^{3+}$/Nb$^{5+}$ concentration with depth implying that chemical concentration alone cannot account for the change in the relaxational dynamics. PFN displays an analogous magnetic skin effect reported to exist in the structural properties of relaxor-ferroelectrics., Comment: 32 pages, 13 figures

The layered triangular lattice owing to $1:2$ order of $B$ and $B'$ sites in the triple perovskite $A_3 B B'_2$O$_9$ family provides an enticing domain for exploring the complex phenomena of quantum spin liquids (QSLs). We report a comprehensive investigation of the ground state properties of Sr$_3$CuTa$_2$O$_9$ that belongs to the above family, by employing magnetization, specific heat, and muon spin relaxation ($\mu$SR) experiments down to the lowest temperature of 0.1~K. Analysis of the magnetic susceptibility indicates that the spin-lattice is a nearly isotropic $S = 1/2$ triangular lattice. We illustrate the observation of a gapless QSL, in which conventional spin ordering or freezing effects are absent, even at temperatures more than two orders of magnitude smaller than the exchange energy ($J_{\rm CW}/k_{\rm B} \simeq -5.04$~K). Magnetic specific heat in zero-field follows a power law, $C_{\rm m} \sim T^\eta$, below 1.2~K with $\eta \approx 2/3$, which is consistent with a theoretical proposal of the presence of spinon Fermi surface. Below 1.2~K, the $\mu$SR relaxation rate shows no temperature dependence, suggesting persistent spin dynamics as expected for a QSL state. Delving deeper, we also analyze longitudinal field $\mu$SR spectra revealing strong dynamical correlations in the spin-disordered ground state. All of these highlight the characteristics of spin entanglement in the QSL state., Comment: 7 pages, 4 figures. Accepted for publication at Physical Review B (Letter)

In this study, we present a thorough investigation into the superconducting state of the ruthenium-based ternary equiatomic compound ScRuSi. Our analysis combines experimental techniques, including muon spin rotation/relaxation ($\mu$SR) and low-temperature resistivity measurements, with theoretical insights derived from first-principles calculations. The low-temperature resistivity measurements reveal a distinct superconducting phase transition in the orthorhombic structure of ScRuSi at a critical temperature ($T_\text{C}$) of $2.5$ K. Further, the TF-$\mu$SR analysis yields a gap-to-critical-temperature ratio of $2\Delta/k_\mathrm{B}T_\mathrm{C} = 2.71$, a value consistent with results obtained from previous heat capacity measurements. The temperature dependence of the superconducting normalized depolarization rate is fully described by the isotropic $s$-wave gap model. Additionally, zero-field $\mu$SR measurements indicate that the relaxation rate remains nearly identical below and above $T_\text{C}$. This observation strongly suggests the preservation of time-reversal symmetry within the superconducting state. By employing the McMillan-Allen-Dynes equation, we calculate a $T_\text{C}$ of $2.11$ K from first-principles calculations within the density functional theory framework. This calculated value aligns closely with the experimentally determined critical temperature. The coupling between the low-frequency phonon modes and the transition metal d-orbital states play an important role in governing the superconducting pairing in ScRuSi. The combination of experimental and theoretical approaches provides a comprehensive microscopic understanding of the superconducting nature of ScRuSi, offering insights into its critical temperature, pairing symmetry, and the underlying electron-phonon coupling mechanism., Comment: 10 pages, 7 figures

CeNiSn is a Kondo semimetal where a gap opens at low temperatures due to hybridization between 4$f$ and conduction electrons, but a full insulating state fails to develop. Upon the insertion of hydrogen, long range magnetic order is induced. Here we report zero-field muon-spin relaxation and inelastic neutron scattering measurements of polycrystalline samples of the deuterides CeNiSnD$_x$ ($x$=1.0, 1.8). The muon-spin relaxation results confirm magnetic ordering in the whole sample of CeNiSnD below around 4.7 K, while inelastic neutron scattering reveals two well-defined crystalline-electric field (CEF) excitations at around 13 meV and 34 meV in CeNiSnD, and 5 meV and 27 meV for CeNiSnD$_{1.8}$. These results suggest that hydrogenation leads to the localization of the Ce-4$f$ electrons, giving rise to long-range magnetic order. We propose CEF level schemes for both systems, which predict a ground state moment of 0.96$\mu_{\rm B}$/Ce within the $ab$-plane for CeNiSnD$_{1.8}$ and a saturated moment of 1.26$\mu_{\rm B}$/Ce along the easy $c$ axis for CeNiSnD, that account for the observed magnetic properties., Comment: 8 pages, 5 figures

The article gives the motivations for the measurement of the hyperfine splitting (hfs) in the ground state of muonic hydrogen to explore the properties of the proton at low momentum transfer. It summarizes these proposed measurement methods and finally describes the FAMU experiment in more detail.

The recently discovered (Ba,Sr)Ni$_2$As$_2$ family provides an ideal platform for investigating the interaction between electronic nematicity and superconductivity. Here we report the muon spin relaxation ($\mu$SR) measurements on BaNi$_2$As$_2$. Transverse-field $\mu$SR experiments indicate that the temperature dependence of superfluid density is best fitted with a single-band $s$-wave model. On the other hand, the magnetic penetration depth $\lambda$ shows magnetic field dependence, which contradicts with the single-band fully-gapped scenario. Zero-field $\mu$SR experiments indicate the absence of spontaneous magnetic field in the superconducting state, showing the preservation of time-reversal symmetry in the superconducting state. Our $\mu$SR experiments suggest that BaNi$_2$As$_2$ is a fully-gapped multiband superconductor. The superconducting gap amplitudes of each band are nearly the same while different bands exhibit different coherence lengths. The present work helps to elucidate the controversial superconducting property of this parent compound, paving the way for further research on doping the system with Sr to enhance superconductivity., Comment: Accepted by Phys. Rev. B

The FAMU experiment at RIKEN-RAL is a muonic atom experiment with the aim to determine the Zemach radius of the proton by measuring the 1s hyperfine splitting in muonic hydrogen. The activity of the FAMU Collaboration in the years 2015-2023 enabled the final optimisation of the detector-target setup as well as the gas working condition in terms of temperature, pressure and gas mixture composition. The experiment has started its data taking in July 2023. The status of the detector setup for the 2023 experimental runs, for the beam characterisation and muonic X-ray detection in the 100-200 keV energy range, is presented and discussed., Comment: Submitted to JINST

The spin-chain compound Sr3NiPtO6 is known to have a nonmagnetic ground state. We have investigated the nature of ground state of Sr3NiPtO6 using magnetic susceptibility $\chi(T)$, heat capacity $C_{\rm p}(T)$, muon spin relaxation ($\mu$SR) and inelastic neutron scattering (INS) measurements. The $\chi(T)$ and $C_{\rm p}(T)$ do not exhibit any pronounced anomaly that can be associated with a phase transition to a magnetically ordered state. Our $\mu$SR data confirm the absence of long-range magnetic ordering down to 0.04 K. Furthermore, the muon spin relaxation rate increases below 20 K and exhibits temperature independent behavior at low temperature, very similar to that observed in a quantum spin-liquid system. The INS data show a large excitation near 8~meV, and the analysis of the INS data reveals a singlet CEF ground state with a first excited CEF doublet state at $\Delta_{\rm CEF}$ = 7.7 meV. The estimated CEF parameters reveal a strong planar anisotropy in the calculated $\chi(T)$, consistent with the reported behavior of the $\chi(T)$ of single crystal Sr3NiPtO6. We propose that the nonmagnetic singlet ground state and a large $\Delta_{\rm CEF}$ (much larger than the exchange interaction $\mathcal{J}_{\rm ex}$) are responsible for the absence of long-range magnetic ordering and can mimic a classical spin-liquid behavior in this quasi-1D spin chain system Sr3NiPtO6. The classical spin-liquid ground state observed in Sr3NiPtO6 is due to the single-ion property, which is different from the quantum spin-liquid ground state observed in geometrically frustrated systems, where two-ion exchanges play an important role., Comment: 11 pages, 10 figures, 1 table

The silicide superconductors (Ta, Nb, Zr)OsSi are among the best candidate materials for investigating the interplay of topological order and superconductivity. Here, we investigate in detail the normal-state topological properties of (Ta, Nb, Zr)OsSi, focusing on ZrOsSi, by employing a combination of $^{29}$Si nuclear magnetic resonance (NMR) measurements and first-principles band-structure calculations. We show that, while (Ta, Nb)OsSi behave as almost ideal metals, characterized by weak electronic correlations and a relatively low density of states, the replacement of Ta (or Nb) with Zr expands the crystal lattice and shifts ZrOsSi towards an insulator. Our ab initio calculations indicate that ZrOsSi is a $Z_2$ topological metal with clear surface Dirac cones and properties similar to a doped strong topological insulator., Comment: 15 pages, 9 figures

The structure and magnetic properties of rare-earth ions Tm$^{3+}$ kagom\'{e} lattice Tm$_3$Sb$_3$Mg$_2$O$_{14}$ are studied by X-ray diffraction, magnetic susceptibility and muon spin relaxation ($\mu$SR) experiments. The existence of a small amount of Tm/Mg site-mixing disorder is revealed. DC magnetic susceptibility measurement shows that Tm$^{3+}$ magnetic moments are antiferromagnetically correlated with a negative Curie-Weiss temperature of -26.3 K. Neither long-range magnetic order nor spin-glass transition is observed by DC and AC magnetic susceptibility, and confirmed by $\mu$SR experiment down to 0.1 K. However, the emergence of short-range magnetic order is indicated by the zero-field $\mu$SR experiments, and the absence of spin dynamics at low temperatures is evidenced by the longitudinal-field $\mu$SR technique. Compared with the results of Tm$_3$Sb$_3$Zn$_2$O$_{14}$, another Tm-based kagom\'{e} lattice with much more site-mixing disorder, the gapless spin liquid like behaviors in Tm$_3$Sb$_3$Zn$_2$O$_{14}$ can be induced by disorder effect. Samples with perfect geometrical frustration are in urgent demand to establish whether QSL exits in this kind of materials with rare-earth kagom\'{e} lattice.

The microscopic properties of superconducting cubic skutterudite-like material Y$_3$Ru$_4$Ge$_{13}$ are investigated using muon spin relaxation and rotation ($\mu$SR) measurements. Zero-field $\mu$SR measurements reveal the presence of a spontaneous internal field with a magnitude of $\approx$ 0.18~mT below the superconducting transition temperature, indicating broken time-reversal symmetry in the ground state. In line with previous experiments, transverse-field $\mu$SR measurements are consistent with a fully developed superconductivity gap in Y$_3$Ru$_4$Ge$_{13}$. Our observations point towards the relevance of electronic correlations beyond electron-phonon coupling as origin and indicate that spin-orbit coupling is likely not the key driving force behind the spontaneous breaking of time-reversal symmetry in this system., Comment: 7 pages, 3 figures

Filled skutterudite compounds have gained attention recently as an innovative platforms for studying intriguing low-temperature superconducting properties. Regarding the symmetry of the superconducting gap, contradicting findings from several experiments have been made for LaRu$_{4}$As$_{12}$ and its isoelectronic counterpart, LaOs$_{4}$As$_{12}$. In this vein, we report comprehensive bulk and microscopic results on LaOs$_{4}$As$_{12}$ utilizing specific heat analysis and muon-spin rotation/relaxation ($\mu$SR) measurements. Bulk superconductivity with $T_C$ = 3.2 K was confirmed by heat capacity. The superconducting ground state of the filled-skutterudite LaOs$_{4}$As$_{12}$ compound is found to have two key characteristics: superfluid density exhibits saturation type behavior at low temperature, which points to a fully gapped superconductivity with gap value of $2\Delta/k_BT_C$ = 3.26; additionally, the superconducting state does not show any sign of spontaneous magnetic field, supporting the preservation of time-reversal symmetry. These results open the door for the development of La-based skutterudites as special probes for examining the interplay of single- and multiband superconductivity in classical electron-phonon systems., Comment: 5 pages, 4 figures

We report the first experimental determination of the collision-energy dependence of the muon transfer rate from the ground state of muonic hydrogen to oxygen at near-thermal energies. A sharp increase by nearly an order of magnitude in the energy range 0 - 70 meV was found that is not observed in other gases. The results set a reliable reference for quantum-mechanical calculations of low-energy processes with exotic atoms, and provide firm ground for the measurement of the hyperfine splitting in muonic hydrogen and the determination of the Zemach radius of the proton by the FAMU collaboration., Comment: 30 pages, 10 figures

The superconducting order parameter of the noncentrosymmetric superconductor LaRhSn is investigated by means of low temperature measurements of the specific heat, muon-spin relaxation/rotation ($\mu$SR) and the tunnel-diode oscillator (TDO) based method. The specific heat and magnetic penetration depth [$\lambda(T)$] show an exponentially activated temperature dependence, demonstrating fully gapped superconductivity in LaRhSn. The temperature dependence of $\lambda^{-2}(T)$ deduced from the TDO based method and $\mu$SR show nearly identical behavior, which can be well described by a single-gap $s$-wave model, with a zero temperature gap value of $\Delta(0)=1.77(4)k_BT_c$. The zero-field $\mu$SR spectra do not show detectable changes upon cooling below $T_c$, and therefore there is no evidence for time-reversal-symmetry breaking in the superconducting state., Comment: 9 pages, 8 figures

The complex structure of the Remeika phases, the intriguing quantum states they display, and their low carrier concentrations are a strong motivation to study the nature of their superconducting phases. In this work, the microscopic properties of the superconducting phase of single-crystalline Lu$_3$Os$_4$Ge$_{13}$ are investigated by muon-spin relaxation and rotation ($\mu$SR) measurements. The zero-field $\mu$SR data reveal the presence of spontaneous static or quasi-static magnetic fields in the superconducting state, breaking time-reversal symmetry; the associated internal magnetic field scale is found to be exceptionally large ($\approx$ 0.18~mT). Furthermore, transverse-field $\mu$SR measurements in the vortex state of Lu$_3$Os$_4$Ge$_{13}$ imply a complex gap function with significantly different strengths on different parts of the Fermi surface. While our measurements do not completely determine the order parameter, they strongly indicate that electron-electron interactions are essential to stabilizing pairing in the system, thus, demonstrating its unconventional nature., Comment: 7 pages, 2 figures

Muon spin rotation ($\mu$SR) and inelastic X-ray scattering (IXS) were used to investigate the superconducting properties of the filled-skutterudite compound LaRu$_{4}$As$_{12}$. A two-gap isotropic ($s+s$)-wave model can explain the temperature dependence of the superfluid density. Zero field $\mu$SR measurements confirm that the time-reversal symmetry does not break upon entering the superconducting state. The measurements of lattice dynamics at 2, 20 and 300 K revealed temperature dependencies of the phonon modes that do not follow strictly a hardening of phonon frequencies upon cooling as expected within the quasi-harmonic picture. The 20~K data rather mark a turning point for the majority of the phonon frequencies. Indeed a hardening is observed approaching 20~K from above, while for a few branches a weak softening is visible upon further cooling to 2~K. The observed dispersion relations of phonon modes throughout the Brillouin zone matches with the DFT prediction quite closely. Our results point out that cubic LaRu$_{4}$As$_{12}$ is a good reference material for studying multiband superconductivity, including those with lower crystallographic symmetries such as iron arsenide-based superconductors., Comment: 8 pages, 8 figures

We present the results of muon spin relaxation ($\mu$SR) and neutron scattering on the Ce-based quasikagome lattice CeRh$_{1-x}$Pd$_{x}$Sn ($x=0.1$ to 0.75). Our ZF-$\mu$SR results reveal the absence of static long-range magnetic order down to 0.05~K in $x = 0.1$ single crystals. The weak temperature-dependent plateaus of the dynamic spin fluctuations below 0.2~K in ZF-$\mu$SR together with its longitudinal-field (LF) dependence between 0 and 3~kG indicate the presence of dynamic spin fluctuations persisting even at $T$ = 0.05~K without static magnetic order. On the other hand, $C_{\text{4f}}$/$T$ increases as --log $T$ on cooling below 0.9~K, passes through a broad maximum at 0.13~K and slightly decreases on further cooling. The ac-susceptibility also exhibits a frequency independent broad peak at 0.16~K, which is prominent with an applied field $H$ along $c$-direction. We, therefore, argue that such a behavior for $x=0.1$ (namely, a plateau in spin relaxation rate ($\lambda$) below 0.2~K and a linear $T$ dependence in $C_{\text{4f}}$ below 0.13~K) can be attributed to a metallic spin-liquid (SL) ground state near the quantum critical point in the frustrated Kondo lattice. The LF-$\mu$SR study suggests that the out of kagome plane spin fluctuations are responsible for the SL behavior. Low energy inelastic neutron scattering (INS) of $x$ = 0.1 reveals gapless magnetic excitations, which are also supported by the behavior of $C_{\text{4f}}$ proportional to $T^{1.1}$ down to 0.06~K., Comment: 19 pages and 9 figures

We have studied the electronic properties of ScS, a transition-metal monochalcogenide with rocksalt crystal structure, using magnetization, specific heat, transport, and muon spin rotation/relaxation ($\mu$SR) measurements. All measurements confirm the bulk superconducting in ScS with a transition temperature of $T_{C}$ = 5.1(5) K. Specific heat together with transverse-field $\mu$SR measurements indicate a full gap, while our zero-field $\mu$SR study reveals the presence of spontaneous static or quasi-static magnetic fields emerging when entering the superconducting state. We discuss various possible microscopic origins of the observed time-reversal-symmetry breaking. As none of them can be readily reconciled with a conventional pairing mechanism, this introduces ScS as a novel candidate material for unconventional superconductivity., Comment: 6 Pages, 3 figures

The ${\mathbb{Z}}_{2}$ topological metals $R$V$_3$Sb$_5$ ($R$ = K, Rb, Cs) with a layered kagome structure provide a unique opportunity to investigate the interplay between charge order, superconductivity and topology. Here, we report muon-spin relaxation/rotation ($\mu$SR) measurements performed on CsV$_3$Sb$_5$ across a broad temperature range, in order to uncover the nature of the charge-density wave order and superconductivity in this material. From zero-field $\mu$SR, we find that spontaneous magnetic fields appear below 50 K which is well below the charge-density wave transition ($T^* \sim 93$ K). We show that these spontaneous fields are dynamic in nature making it difficult to associate them with a hidden static order. The superconducting state of CsV$_3$Sb$_5$ is found to preserve time-reversal symmetry and the transverse-field $\mu$SR results are consistent with a superconducting state that has two fully open gaps., Comment: 8 pages, 6 figures

Elemental rhenium exhibiting type-II superconductivity has been previously reported to break time-reversal symmetry in the superconducting state. We have investigated an arc-melted sample of rhenium exhibiting type-I superconductivity. Low temperature zero-field muon-spin relaxation measurements indicate that time-reversal symmetry is preserved in the superconducting state. Muon diffusion is observed, which is due to quantum mechanical tunneling between interstitial sites. The normal state behavior is characterized by the conduction electrons screening the muons and thermal broadening, and is typical for a metal. Energy asymmetries between muon trapping sites and the superconducting energy gap also characterize the superconducting state behavior., Comment: 8 pages, 7 figures

Superconductors with broken time-reversal symmetry represent arguably one of the most promising venues for realizing highly sought-after topological superconductivity that is vital to fault-tolerant quantum computation. Here, by using extensive muon-spin relaxation and rotation measurements, we report that the isostructural silicide superconductors (Ta, Nb)OsSi spontaneously break time-reversal symmetry at the superconducting transition while surprisingly showing a fully-gapped superconductivity characteristic of conventional superconductors. The first-principles calculations show that (Ta, Nb)OsSi are three-dimensional Dirac semimetals protected by nonsymmorphic symmetries. Taking advantage of the exceptional low symmetry crystal structure of these materials, we have performed detailed theoretical calculations to establish that the superconducting ground state for both (Ta, Nb)OsSi is most likely a nonunitary triplet state., Comment: 7 pages, 4 figures

The vacancy effect in quantum spin liquid (QSL) has been extensively studied. A finite density of random vacancies in the Kitaev model can lead to a pileup of low-energy density of states (DOS), which is generally experimentally determined by a scaling behavior of thermodynamic or magnetization quantities. Here, we report detailed muon spin relaxation ($\mu$SR) results of H$_3$LiIr$_2$O$_6$, a Kitaev QSL candidate with vacancies. The absence of magnetic order is confirmed down to 80 mK, and the spin fluctuations are found to be persistent at low temperatures. Intriguingly, the time-field scaling law of longitudinal-field (LF)-$\mu$SR polarization is observed down to 0.1 K. This indicates a dynamical scaling, whose critical exponent 0.46 is excellently consistent with the scaling behavior of specific heat and magnetization data. All the observations point to the finite DOS with the form $N(E) \sim E^{-0.5}$ , which is expected for the Kitaev QSL in the presence of vacancies. Our {\mu}SR study provides a dynamical fingerprint of the power-law low-energy DOS, and introduces a crucial new insight into the vacancy effect in QSL.

Magnetic susceptibility, specific heat, and muon spin relaxation ($\mu$SR) measurements have been performed on a newly synthesized three-dimensional sandglass-type lattice Tm$_3$SbO$_7$, where two inequivalent sets of non-Kramers Tm$^{3+}$ ions (Tm$^{3+}_1$ and Tm$^{3+}_2)$ show crystal electrical field effect at different temperature ranges. The existence of an ordered or a glassy state down to 0.1~K in zero field is excluded. The low-energy properties of Tm$_3$SbO$_7$ are dominated by the lowest non-Kramers quasi-doublet of $\rm Tm^{3+}_1$, and the energy splitting is regarded as an intrinsic transverse field. Therefore, the low-temperature paramagnetic phenomenon in Tm$_3$SbO$_7$ is explained by a transverse field Ising model, which is supported by the quantitative simulation of specific heat data. In addition, the perturbation from Tm$^{3+}_2$ may play an important role in accounting for the low temperature spin dynamics behavior observed by $\mu$SR.

Geometrical frustration leads to novel quantum phenomena such as the spin-liquid phase in triangular and Kagom\'e lattices. Intra-band and inter-band Fermi surface (FS) nesting can drive unique superconducting (SC) ground states with $d$-wave and $s^{\pm}$ pairing symmetries, respectively, according to the criterion that the SC gap changes sign across the nesting wavevector. For an odd number of FSs, when multiple inter-band nesting is of comparable strength, the sign-reversal criterion between different FS sheets can leads to frustration, which promotes novel SC order parameters. Here we report the experimental observation of a time-reversal symmetry breaking pairing state in Re$_2$Hf resulting from FS nesting frustration. Furthermore, our electronic specific heat and transverse-field $\mu$SR experiments suggest a fully gaped pairing symmetry. The first-principle electronic structure calculation reveals multiple Fermi surface sheets with comparable inter-band nesting strength. Implementing the {\it ab-initio} band structure, we compute spin-fluctuation mediated SC pairing symmetry which reveals a $s+is'$-pairing state - consistent with experimental observations. Our investigation demonstrates a novel SC state which provides a putative setting for both applied and fundamental study., Comment: 6 pages, 4 figures

Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional data, where it usually outperforms humans. Here we applied a simple ML tool called principal component analysis (PCA) to study data from muon spectroscopy. The measured quantity from this experiment is an asymmetry function, which holds the information about the average intrinsic magnetic field of the sample. A change in the asymmetry function might indicate a phase transition; however, these changes can be very subtle, and existing methods of analyzing the data require knowledge about the specific physics of the material. PCA is an unsupervised ML tool, which means that no assumption about the input data is required, yet we found that it still can be successfully applied to asymmetry curves, and the indications of phase transitions can be recovered. The method was applied to a range of magnetic materials with different underlying physics. We discovered that performing PCA on all those materials simultaneously can have a positive effect on the clarity of phase transition indicators and can also improve the detection of the most important variations of asymmetry functions. For this joint PCA we introduce a simple way to track the contributions from different materials for a more meaningful analysis., Comment: 4 pages, 1 figure, to be published in Journal of Physics: Conference Series, proceedings paper from SCES 2020 conference

The search of quantum spin liquid (QSL), an exotic magnetic state with strongly-fluctuating and highly-entangled spins down to zero temperature, is a main theme in current condensed matter physics. However, there is no smoking-gun evidence for deconfined spinons in any QSL candidate so far. The disorders and competing exchange interactions may prevent the formation of an ideal QSL state on frustrated spin lattices. Here we report comprehensive and systematic measurements of the magnetic susceptibility, ultra-low temperature specific heat, muon spin relaxation (muSR), nuclear magnetic resonance (NMR), and thermal conductivity for NaYbSe2 single crystals, in which Yb3+ ions with effective spin-1/2 form a perfect triangular lattice. All these complementary techniques find no evidence of long-range magnetic order down to their respective base temperatures. Instead, specific heat, muSR and NMR measurements suggest the coexistence of quasi-static and dynamic spins in NaYbSe2. The scattering from these quasi-static spins may cause the absence of magnetic thermal conductivity. Thus, we propose a scenario of fluctuating ferrimagnetic droplets immersed in a sea of QSL. This may be quite common on the way pursuing an ideal QSL, and provides a brand-new platform to study how a QSL state survives impurities and coexists with other magnetically ordered states.

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 ($\mu$SR) experiments on a topological noncentrosymmetric superconductor PbTaSe$_2$ to study its TRS and gap symmetry. Zero-field $\mu$SR experiments indicate the absence of internal magnetic field in the superconducting state, consistent with previous $\mu$SR results. Furthermore, transverse-field $\mu$SR measurements reveals that the superconducting gap of PbTaSe$_2$ is an isotropic three-dimensional fully-gapped single-band. The fully-gapped results can help understand the pairing mechanism and further classify the topological superconductivity in this system.

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 ($\mu$SR) measurements. Bulk superconductivity with transition temperature $T_{C}$ = 5.7 K confirmed by magnetization, resistivity, and heat capacity measurements. Zero-field $\mu$SR measurement shows that the superconducting state preserves time-reversal symmetry, and transverse-field measurements of the superfluid density are well described by an isotropic s-wave model., Comment: 9 pages, 7 figures

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, indicating the preserved time-reversal symmetry. Transverse field muon spin rotation measurements confirms a s-wave nature of the sample with $\Delta(0)/k_{B}T_{c} $ = 1.726. This study urges further investigation on more noncentrosymmetric materials to elucidate the selective appearance of unconventional nature and unveil its dependence on antisymmetric spin-orbit coupling strength., Comment: 7 Pages, 7 fugures

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 ($\alpha$-Mn structure) HEA {(HfNb)}$_{0.10}${(MoReRu)}$_{0.90}$, and {(ZrNb)}$_{0.10}${(MoReRu)}$_{0.90}$ by using magnetization, specific heat, AC transport, and muon-spin relaxation/rotation ($\mu$SR). Despite the disordered nature, low temperature specific heat and transverse-field muon spin rotation measurements suggest nodeless isotropic superconducting gap and Zero-field $\mu$SR measurements confirm that time reversal symmetry is preserved in the superconducting ground state., Comment: 8 pages, 8 figures

Exploring superconductors which can possess pairing mechanism other than the BCS predicted s-wave have continually attracted considerable interest. Superconductors with low-lying phonons may exhibit unconventional superconductivity as the coupling of electrons with these low-lying phonons can potentially affect the nature of the superconducting ground state, resulting in strongly coupled superconductivity. In this work, by using magnetization, AC transport, specific heat, and muon spin rotation/relaxation ($\mu$SR) measurements, we report a detailed investigation on the superconducting ground state of the strongly coupled superconductor, IrGe, that has a transition temperature, T$_{C}$, at 4.7 K. Specific heat (SH), and transverse field $\mu$SR is best described with an isotropic s-wave model with strong electron-phonon coupling, indicated by the values of both $\Delta(0)/k_{B}T_{C}$ = 2.3, 2.1 (SH, $\mu$SR), and $\Delta C_{el}/\gamma_{n}T_{C}$ = 2.7. Zero-field $\mu$SR measurements confirm the presence of time-reversal symmetry in the superconducting state of IrGe., Comment: 8 pages, 7 figures

We report a systematic study of the $5d$-electron-doped system Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$ ($0 \leq x \leq 0.15$). With increasing $x$, the orthorhombic $b$~axis decreases slightly while accompanying changes in $a$ and $c$ leave the unit cell volume almost unchanged. Inelastic neutron scattering, along with thermal and transport measurements, reveal that for the Kondo semiconductor CeFe$_2$Al$_{10}$, the low-temperature energy gap which is proposed to be a consequence of strong $c \mhyphen f$ hybridization, is suppressed by a small amount of Ir substitution for Fe, and that the system adopts a metallic ground state with an increase in the density of states at the Fermi level. The charge or transport gap collapses (at $x=$~0.04) faster than the spin gap with Ir substitution. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements demonstrate that the system undergoes long-range antiferromagnetic order below a N\'eel temperature, $T_{\mathrm{N}}$, of 3.1(2)~K for $x = 0.15$. The ordered moment is estimated to be smaller than 0.07(1)~$\mu_\mathrm{B}$/Ce although the trivalent state of Ce is confirmed by Ce L$_3$-edge x-ray absorption near edge spectroscopy. It is suggested that the $c \mhyphen f$ hybridization gap, which plays an important role in the unusually high ordering temperatures observed in Ce$T_2$Al$_{10}$ ($T$ = Ru and Os), may not be necessary for the onset of magnetic order with a low $T_{\mathrm{N}}$ seen here in Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$., Comment: 12 pages, 11 figures

The nonsymmorphic Zr$_{2}$Ir alloy is a possible topological semimetal candidate material and as such may be part of an exotic class of superconductors. Zr$_{2}$Ir is a superconductor with a transition temperature of 7.4 K with critical fields of 19.6(3) mT and 3.79(3) T, as determined by heat capacity and magnetisation. Zero field muon spin relaxation measurements show that time-reversal symmetry is preserved in these materials. The specific heat and transverse field muon spin rotation measurements rule out any possibility to have a nodal or anisotropic superconducting gap, revealing a conventional s-wave nature in the superconducting ground state. Therefore, this system is found to be conventional nonsymmorphic superconductor, with time-reversal symmetry being preserved and an isotropic superconducting gap., Comment: 7 Pages, 10 figres

CeRh$_6$Ge$_4$ is an unusual example of a stoichiometric heavy fermion ferromagnet, which can be cleanly tuned by hydrostatic pressure to a quantum critical point. In order to understand the origin of this anomalous behavior, we have characterized the magnetic ordering and crystalline electric field (CEF) scheme of this system. While magnetic Bragg peaks are not resolved in neutron powder diffraction, coherent oscillations are observed in zero-field $\mu$SR below $T_{\rm C}$, which are consistent with in-plane ferromagnetic ordering consisting of reduced Ce moments. From analyzing the magnetic susceptibility and inelastic neutron scattering, we propose a CEF-level scheme which accounts for the easy-plane magnetocrystalline anisotropy, where the low lying first excited CEF exhibits significantly stronger hybridization than the ground state. These results suggest that the orbital anisotropy of the ground state and low lying excited state doublets are important for realizing anisotropic electronic coupling between the $f$- and conduction electrons, which gives rise to the highly anisotropic hybridization observed in photoemission experiments., Comment: 7 pages, 4 figures

Topological superconductors (SCs) are novel phases of matter with nontrivial bulk topology. They host at their boundaries and vortex cores zero-energy Majorana bound states, potentially useful in fault-tolerant quantum computation. Chiral SCs are particular examples of topological SCs with finite angular momentum Cooper pairs circulating around a unique chiral axis, thus spontaneously breaking time-reversal symmetry (TRS). They are rather scarce and usually feature triplet pairing: best studied examples in bulk materials are UPt3 and Sr2RuO4 proposed to be f-wave and p-wave SCs respectively, although many open questions still remain. Chiral triplet SCs are, however, topologically fragile with the gapless Majorana modes weakly protected against symmetry preserving perturbations in contrast to chiral singlet SCs. Using muon spin relaxation (muSR) measurements, here we report that the weakly correlated pnictide compound LaPt3P has the two key features of a chiral SC: spontaneous magnetic fields inside the superconducting state indicating broken TRS 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 chiral d-wave singlet., Comment: 12 pages, 12 figures

Time-reversal symmetry breaking (TRSB) with a Bardeen-Cooper-Schrieffer (BCS) -like superconductivity occurs in a small, but growing number of noncentrosymmetric (NCS) materials, although the mechanism is poorly understood. We present heat capacity, magnetization, resistivity, and muon spin resonance/relaxation ($\mu$SR) measurements on polycrystalline samples of NCS La$_{7}$Pd$_{3}$. Transverse-field $\mu$SR and heat capacity data show La$_{7}$Pd$_{3}$ is a type-II superconductor with a BCS-like gap structure, while zero-field $\mu$SR results provide evidence of TRSB. We discuss the implications of these results for both the La$_{7}X_{3}$ (where $X=$ Ni, Pd, Rh, Ir) group of superconductors and other CS and NCS superconductors for which TRSB has been observed., Comment: 12 pages, 7 figures and 2 tables. Accepted in Physical Review B

The Th$_{7}$Fe$_{3}$ family of superconductors provides a rich playground for unconventional superconductivity. La$_7$Ni$_3$ is the latest member of this family, which we here investigate by means of thermodynamic and muon spin rotation and relaxation measurements. Our specific heat data provides evidence for two distinct and approximately isotropic superconducting gaps. The larger gap has a value slightly higher than that of weak-coupling BCS theory, indicating the presence of significant correlations. These observations are confirmed by transverse-field muon-rotation measurements. Furthermore, zero-field measurements reveal small internal fields in the superconducting state, which occur close to the onset of superconductivity and indicate that the superconducting order parameter breaks time-reversal symmetry. We discuss two possible microscopic scenarios -- an unconventional $E_{2}(1,i)$ state and an $s+i\,s$ superconductor, which is reached by two consecutive transitions -- and illustrate which interactions will favor these phases. Our results establish La$_{7}$Ni$_{3}$ as the first member of the Th$_{7}$Fe$_{3}$ family displaying both time-reversal-symmetry-breaking and multigap superconductivity., Comment: 13 Pages, 7 figures

We present a comprehensive study on superconducting properties of Re$_7$B$_3$ and Re$_3$B through specific heat, magnetic susceptibility, resistivity, and transverse and zero-field muon spin rotation/relaxation ($\mu$SR) experiments on polycrystalline samples. Re$_7$B$_3$ (T$_C$ = 3.2~K) is a non-centrosymmetric type-II ($\kappa$ $\approx$ 9.27) superconductor in the weak coupling ($\lambda_{e-ph}$ = 0.54) regime. On the other hand, Re$_3$B (T$_C$ = 5.19~K) is a centrosymmetric type-II ($\kappa$ $\approx$ 34.55) superconductor in the moderate coupling ($\lambda_{e-ph}$ = 0.64) regime. Our transverse-field $\mu$SR measurements show evidence for isotropically gapped BCS type superconductivity with normalized gap ($\Delta_0/k_BT_C$) values of 1.69 (Re$_7$B$_3$) and 1.75 (Re$_3$B)., Comment: 9 pages, 7 figures

The topologically non-trivial band structure of A15 compounds has drawn attention owing to the possible realization of topological superconductivity. Here, we report a microscopic investigation of the superconducting ground state in A15 compound Ti$_{3}$X (X = Ir, Sb) by muon spectroscopy measurements. Zero field muon measurements have shown that time-reversal symmetry is preserved in these materials. Furthermore, specific heat and a transverse field muon spectroscopy measurement rule out any possibility to have a nodal or anisotropic superconducting gap, revealing a conventional s-wave nature in the superconducting ground state. This work classifies A15 compound Ti$_{3}$X (X = Ir, Sb) as a time-reversal preserved topological superconductor., Comment: 7 pages, 9 figures

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, Principal Component Analysis 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., Comment: 11 pages, 7 figures, to be submitted to the Journal of Physics: Condensed Matter special issue on "Machine Learning in Condensed Matter Physics"

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 $T_{\mathrm{K}}\sim 480$\,K. We report a negative in-plane thermal expansion $\alpha/T$ below 2\,K, which passes through a broad minimum near 0.75\,K. Volume and $a$-axis magnetostriction for $B \parallel a$ 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 $T\ll T_{\mathrm{K}}$ result from geometrical frustration., Comment: to be published in Phys. Rev. Lett

We report results of a muon spin relaxation study of slow magnetic fluctuations in the pseudogap phase of underdoped single-crystalline YBa$_{2}$Cu$_{3}$O$_{y}$, $y = 6.77$ and 6.83. The dependence of the dynamic muon spin relaxation rate on applied magnetic field yields the rms magnitude~$B\mathrm{_{loc}^{rms}}$ and correlation time~$\tau_c$ of fluctuating local fields at muon sites. The observed relaxation rates do not decrease with decreasing temperature~$T$ below the pseudogap onset at $T^\ast$, as would be expected for a conventional magnetic transition; both $B\mathrm{_{loc}^{rms}}$ and $\tau_c$ are roughly constant in the pseudogap phase down to the superconducting transition. Corresponding NMR relaxation rates are estimated to be too small to be observable. Our results put strong constraints on theories of the anomalous pseudogap magnetism in YBa$_{2}$Cu$_{3}$O$_{y}$.

The layered bismuth oxy-sulfide materials, which are structurally related to the Fe-pnictides/chalcogenides and cuprates superconductors, have brought substantial attention for understanding the physics of reduced dimensional superconductors. We have examined the pairing symmetry of recently discovered BiCh$_2$-based superconductor, La$_\mathrm{1-x}$Ce$_\mathrm{x}$OBiSSe with $x$ = 0.3, through transverse field (TF) muon spin rotation measurement, in addition we present the results of magnetization, resistivity and zero field (ZF) muon spin relaxation measurements. Bulk superconductivity has been observed below 2.7 K for $x$ = 0.3, verified by resistivity and magnetization data. The temperature dependence of the magnetic penetration depth has been determined from TF-$\mu$SR data can be described by an isotropic two-gap $s+s$ wave model compared to a single gap $s$- or anisotropic $s$-wave models, the resemblance with Fe-pnictides/chalcogenides and MgB$_2$. Furthermore, from the TF-$\mu$SR data, we have determined the London's penetration depth $\lambda_\mathrm{L}(0)$ = 452(3) nm, superconducting carrier's density $n_\mathrm{s}$ = 2.18(1) $\times$10$^{26}$ carriers/m$^{3}$ and effective mass enhancement $m^{*}$ = 1.66(1) $m_\mathrm{e}$, respectively. No signature of spontaneous internal field is found down to 100 mK in ZF-$\mu$SR measurement suggest that time-reversal symmetry is preserved in this system., Comment: 5 pages, 3 figures

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 pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. Zero field measurements suggest a time-reversal symmetry preserved superconductivity in both the systems, though a small increase in muon depolarization is observed upon decreasing temperature. However, this has been attributed to quasi-static magnetic fluctuations., Comment: 8 pages, 8 figures

Rhenium based noncentrosymmetric superconductors crystallizing in $\alpha$-Mn structure have become potential candidates to exhibit an unconventional superconducting ground-state. Here we report a detailed investigation on the superconducting and normal state properties of Re$_{5.5}$Ta, that also has the $\alpha$-Mn structure. Magnetization, specific heat, and transport measurements confirm the bulk superconducting transition \textit{T}$_{C}$ at 8.0 K. Upper critical field value (H$_{C2}$(0)) calculated from magnetization, specific heat and AC transport measurements exceed the Pauli paramagnetic limit (14.7 T), indicating that the superconducting properties of Re$_{5.5}$Ta are probably unconventional in nature. However, low-temperature specific heat and transverse-field muon spin rotation measurements suggest a surprising nodeless isotropic superconducting gap, although with strong electron-phonon coupling., Comment: 10 Pages, 7 Figures Accepted: Physical Review B