Magnetic and superconducting properties of the layered superconducting ferromagnet CeO0.5F0.5BiS2 are investigated by specific heat and magnetization measurements and muon spin rotation/relaxation (mu SR). A specific-heat anomaly, an abrupt increase of magnetic susceptibility, and bifurcation of zero-field-cooled and field-cooled magnetization indicate ferromagnetic (FM) order below 7.5 K. Hysteresis loops yield a Ce3+ ordered moment of 0.22(1)mu B. A low-temperature Schottky specific-heat anomaly indicates a splitting of Ce3+ Kramers-doublet ground states, consistent with Orbach-process Ce3+ spin dynamics observed in zero-field mu SR. Transverse-field mu SR results indicate bulk superconductivity below similar to 2 K and microscopic coexistence of superconductivity and FM order in separate layers. The static local field observed by zero-field mu SR in the FM phase is small (similar to 0.2 mT), indicating that Ce3+ dipolar fields nearly cancel at muon stopping sites.

We report results of specific heat and muon spin relaxation (μSR) measurements on a polycrystalline sample of Pr3Cr10−xN11, which shows superconducting state below Tc = 5.25 K, a large upper critical field Hc2 ~ 20 T and a residual Sommerfeld coefficient γ0. The field dependence of γ0(H) resembles γ of the U-based superconductors UTe2 and URhGe at low temperatures. The temperature-dependent superfluid density measured by transverse-field μSR experiments is consistent with a p-wave pairing symmetry. ZF-μSR experiment suggests a time-reversal symmetry broken superconducting transition, and temperature-independent spin fluctuations at low temperatures are revealed by LF-μSR experiments. These results indicate that Pr3Cr10−xN11 is a candidate of p-wave superconductor which breaks time-reversal symmetry.

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 (μSR) 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 dynamical spin fluctuations are found to be persistent at low temperatures. Intriguingly, the time-field scaling law of longitudinal-field μSR polarization is observed with the critical exponent of 0.46, exhibiting excellent consistency with scaling behavior of specific heat and magnetization data. This points to the finite DOS with the form of N(E) ~ E ν , wihch is expected for the Kitaev QSL in the presence of vacanncies.

We report results of specific heat and muon spin relaxation ( μ SR) measurements on a polycrystalline sample of Pr 3 Cr 10− x N 11 , which shows superconducting state below T c = 5.25 K, a large upper critical field H c2 ~ 20 T and a residual Sommerfeld coefficient γ 0 . The field dependence of γ 0 ( H ) resembles γ of the U-based superconductors UTe 2 and URhGe at low temperatures. The temperature-dependent superfluid density measured by transverse-field μ SR experiments is consistent with a p -wave pairing symmetry. ZF- μ SR experiment suggests a time-reversal symmetry broken superconducting transition, and temperature-independent spin fluctuations at low temperatures are revealed by LF- μ SR experiments. These results indicate that Pr 3 Cr 10− x N 11 is a candidate of p -wave superconductor which breaks time-reversal symmetry.

We report the results of muon spin rotation and relaxation ($\rm \mu$SR) measurements on the recently discovered layered Cu-based superconducting material La$_{2}($Cu$_{1-x}$Ni$_{x}$)$_{5}$As$_{3}$O$_{2}$ ($x =$ 0.40, 0.45). Transverse-field $\rm \mu$SR experiments on both samples show that the temperature dependence of superfluid density is best described by a two-band model. The absolute values of zero-temperature magnetic penetration depth $\lambda_{\rm ab}(0)$ were found to be 427(1.7) nm and 422(1.5) nm for $x =$ 0.40 and 0.45, respectively. Both compounds are located between the unconventional and the standard BCS superconductors in the Uemura plot. No evidence of time-reversal symmetry (TRS) breaking in the superconducting state is suggested by zero-field $\rm \mu$SR measurements.

We report the results of muon spin rotation and relaxation (μSR) measurements on the recently discovered layered Cu-based superconducting material La_2(Cu_1-xNi_x)_5As_3O_2 (x = 0.40, 0.45). Transverse-field μSR experiments on both samples show that the temperature dependence of superfluid density is best described by a two-band model. The absolute values of zero-temperature magnetic penetration depth λ_ ab(0) were found to be 427(1.7) nm and 422(1.5) nm for x = 0.40 and 0.45, respectively. Both compounds are located between the unconventional and the standard BCS superconductors in the Uemura plot. No evidence of time-reversal symmetry (TRS) breaking in the superconducting state is suggested by zero-field μSR measurements.

We report the results of muon spin rotation and relaxation $(\ensuremath{\mu}\mathrm{SR})$ measurements on the recently discovered layered Cu-based superconducting material ${\mathrm{La}}_{2}{({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{5}{\mathrm{As}}_{3}{\mathrm{O}}_{2}$ ($x=0.40$ and 0.45). Transverse-field $\ensuremath{\mu}\mathrm{SR}$ experiments on both samples show that the temperature dependence of superfluid density is best described by a two-band model. The absolute values of zero-temperature magnetic penetration depth ${\ensuremath{\lambda}}_{\mathrm{ab}}(0)$ were found to be 427(1.7) and 422(1.5) nm for $x=0.40$ and 0.45, respectively. Both compounds are located between the unconventional and the standard BCS superconductors in the Uemura plot. No evidence of time-reversal symmetry breaking in the superconducting state is suggested by zero-field $\ensuremath{\mu}\mathrm{SR}$ measurements.

We report the results of muon spin rotation and relaxation (mu SR) measurements on the recently discovered layered Cu-based superconducting material La2(Cu1-xNix)5As3O2 (x = 0.40 and 0.45). Transverse-field mu SR experiments on both samples show that the temperature dependence of superfluid density is best described by a two-band model. The absolute values of zero-temperature magnetic penetration depth lambda ab(0) were found to be 427(1.7) and 422(1.5) nm for x = 0.40 and 0.45, respectively. Both compounds are located between the unconventional and the standard BCS superconductors in the Uemura plot. No evidence of time-reversal symmetry breaking in the superconducting state is suggested by zero-field mu SR measurements.

Quantum fluctuations are expected to lead to highly entangled spin-liquid states in certain two-dimensional spin-1/2 compounds. We have synthesized and measured thermodynamic properties and muon spin relaxation rates in the copper-based two-dimensional triangular-lattice spin liquids Lu_3Cu_2Sb_3O_14 and Lu_3CuZnSb_3O_14. The former is the least disordered of this kind discovered to date. Magnetic entropy generation at high temperatures has been ruled out after carefully correcting for the lattice specific heat. Surprisingly, roughly half of the magnetic entropy is missing down to temperatures of O(10^-3) the exchange energy, independent of magnetic field up to gμ_B H ≳ k_BΘ_W, where Θ_W is the Weiss temperature. The magnetic specific heat divided by temperature C_M(T)/T and muon spin relaxation rate λ(T) are both temperature-independent at low temperatures, followed by logarithmic decreases with increasing temperature. This behavior can be simply characterized by scale-invariant time-dependent fluctuations with a single parameter. Since no cooperative effects due to impurities are observed, the measured properties are intrinsic. They are evidence that in Lu_3Cu_2Sb_3O_14 massive quantum fluctuations lead to either a gigantic specific heat peak from singlet excitations at very low temperatures or, perhaps less likely, an extensively degenerate possibly topological singlet ground state.

We present detail thermodynamic and muon spin relaxation ($\mu$SR) studies of quantum spin liquid (QSL) candidate H$_3$LiIr$_2$O$_6$. In agreement with the low temperature thermodynamic evidence (\textit{e.g.} bulk magnetization and heat capacity) for the absence of magnetic transition, zero-field (ZF)-$\mu$SR measurements indicate the absence of static magnetic ordering or spin freezing down to our lowest temperature of 80~mK. Both ZF- and longitudinal-field (LF)-$\mu$SR measurements reveal persistent spin fluctuations at low temperatures. These results provide well-established evidence of a QSL state in H$_3$LiIr$_2$O$_6$. Furthermore, the observation of the time-field scaling behavior of $\mu$SR spectra $A(t)\sim A(t/H^{0.46})$, and the low temperature power-law specific heat coefficient $C/T \sim T^{-0.57}$, indicate the finite density of state in the form of $N(E) \sim E^{-0.5}$, in a good agreement with the disorder-induced states in the Kitaev spin liquid.

Yan-Xing Yang,1, ∗ Liang-Long Huang,2, ∗ Zi-Hao Zhu,1 Chang-Sheng Chen,1 Qiong Wu,1 Zhao-Feng Ding,1 Cheng Tan,1 Pabi K. Biswas,3 Adrian D. Hillier,3 You-Guo Shi,4, 5 Da-Peng Yu,2, 6 Cai Liu,2, 6 Le Wang,2, 6 Fei Ye,2, 6 Jia-Wei Mei,2, 6, † and Lei Shu1, 7, ‡ State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200438, China Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China ISIS Facility, STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX110QX, United Kingdom Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, PR China. Shanghai Research Center for Quantum Sciences, Shanghai 201315, China (Dated: February 1, 2022)

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 symmetry (TRS), along with their relations with topology, are crucial for topological superconductivity. We report muon spin relaxation/rotation (μSR) experiments on a topological noncentrosymmetric superconductor PbTaSe2 to study its TRS and gap symmetry. Zero-field μSR experiments indicate the absence of internal magnetic field in the superconducting state, consistent with previous μSR results. Furthermore, transverse-field μSR measurements reveals that the superconducting gap of PbTaSe2 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.

The Pr-rich end of the alloy series Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ has been studied using muon spin rotation and relaxation. The end compound PrOs$_4$Sb$_{12}$ is an unconventional heavy-fermion superconductor, which exhibits a spontaneous magnetic field in the superconducting phase associated with broken time-reversal symmetry. No spontaneous field is observed in the Nd-doped alloys for x $>$ 0.05. The superfluid density is insensitive to Nd concentration, and no Nd$^{3+}$ static magnetism is found down to the lowest temperatures of measurement. Together with the slow suppression of the superconducting transition temperature with Nd doping, these results suggest anomalously weak coupling between Nd spins and conduction-band states.

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$_{y}$.

We report results of muon spin relaxation and rotation ($\ensuremath{\mu}\mathrm{SR}$) experiments on the spin-liquid candidate ${\mathrm{YbMgGaO}}_{4}$. No static magnetism $\ensuremath{\gtrsim}0.003{\ensuremath{\mu}}_{B}$ per Yb ion, ordered or disordered, is observed down to 22 mK, a factor of 2 lower in temperature than previous measurements. Persistent (temperature-independent) spin dynamics are observed up to 0.20 K and at least 1 kOe, thus extending previous zero-field $\ensuremath{\mu}\mathrm{SR}$ results over a substantial region of the $H\text{\ensuremath{-}}T$ phase diagram. Knight shift measurements in a 10-kOe transverse field reveal two lines with nearly equal amplitudes. Inhomogeneous muon depolarization in a longitudinal field, previously characterized by stretched-exponential relaxation due to spatial inhomogeneity, is fit equally well with two exponentials, also of equal amplitudes. We attribute these results to two interstitial muon sites in the unit cell rather than disorder or other spatial distribution. Further evidence for this attribution is found from agreement between the ratio of the two measured relaxation rates and calculated mean-square local ${\mathrm{Yb}}^{3+}$ dipolar fields at candidate muon sites. Zero-field data can be understood as a combination of two-exponential dynamic relaxation and quasistatic nuclear dipolar fields.

We report results of muon spin relaxation and rotation (μSR) experiments on the spin-liquid candidate YbMgGaO_4. No static magnetism ≳ 0.003μ_B per Yb ion, ordered or disordered, is observed down to 22 mK, a factor of two lower in temperature than previous measurements. Persistent (temperature-independent) spin dynamics are observed up to 0.20 K and at least 1 kOe, thus extending previous zero-field μSR results over a substantial region of the H-T phase diagram. Knight shift measurements in a 10-kOe transverse field reveal two lines with nearly equal amplitudes. Inhomogeneous muon depolarization in a longitudinal field, previously characterized by stretched-exponential relaxation due to spatial inhomogeneity, is fit equally well with two exponentials, also of equal amplitudes. We attribute these results to two interstitial muon sites in the unit cell, rather than disorder or other spatial distribution. Further evidence for this attribution is found from agreement between the ratio of the two measured relaxation rates and calculated mean-square local Yb^3+ dipolar fields at candidate muon sites. Zero-field data can be understood as a combination of two-exponential dynamic relaxation and quasistatic nuclear dipolar fields.

Hidden magnetic order in the correlated iridate Sr2Ir1-xRhxO4, x = 0.05 and 0.1, has been studied using muon spin relaxation spectroscopy. In zero field (ZF) and weak longitudinal fields (LFs) (less than or similar to 2 mT), the muon spin relaxation data indicate that static and dynamic local fields coexist at each muon site, and can be well described by exponentially damped static Lorentzian Kubo-Toyabe functions. The ZF relaxation rate is dominated by the static-field distribution, and a broad relaxation rate maximum at 175 K for x = 0.1 in ZF is attributed to muon diffusion and trapping. For LF greater than or similar to 2 mT the static rate is completely decoupled, and the exponential decay is due to dynamic spin fluctuations. The temperature dependencies of the relaxation rates exhibit maxima at 215 K (x = 0.05) and 175 K (x = 0.1), in agreement with previous second harmonic generation and polarized neutron diffraction determinations of transition temperatures to a hidden-order state. The maxima are most likely due to critical slowing down of electronic spin fluctuations. The field dependencies of the dynamic spin fluctuation rates can be well described by the Redfield relation, from which the rms width B-loc(rms) and correlation time tau(c) of the fluctuating field are obtained. Values of tau(c) are in the range of 1.5-4 ns for x = 0.1 and shorter than 2 ns for x = 0.05, suggesting an increase with increasing Rh concentration. Values of B-loc(rms) are on the order of 1 mT, consistent with the polarized neutron diffraction cross section.

We report results of a muon spin rotation (mu SR) study of the cuprate-analog nickelate La4Ni3O8, which undergoes a transition at 105 K to a low-temperature phase with charge-stripe and antiferromagnetic (AFM) order on square planar NiO2 layers. Zero-field mu SR shows that the AFM transition is abrupt, commensurate, and has a quasi-two-dimensional character below similar to 25 K. Comparison of observed muon precession frequencies with Ni dipolar field calculations yields Ni moments less than or similar to 0.5 mu(B). Dynamic muon spin relaxation above 105 K suggests critical slowing of Ni spin fluctuations, but is inconsistent with corresponding La-139 NMR results. Critical slowing and an abrupt transition are also observed in the planar cuprate AFM La2CuO4+delta, where they are taken as evidence for weakly interplanar-coupled two-dimensional AFM spin fluctuations, but our mu SR data do not agree quantitatively with theoretical predictions for this scenario when applied to the nickelate.