We report results of magnetic susceptibility, specific heat, and muon spin relaxation measurements on the polycrystalline titanate Ba6Nd2Ti4O17, an essentially disorder-free triangular-lattice antiferromagnet. The absence of long-range magnetic order or spin freezing is confirmed down to 30 mK, well below the Curie-Weiss temperature -1.8 K. Magnetism and specific heat measurements reveal Ising-like effective-spin-1/2 behavior. Persistent spin dynamics are observed down to 37 mK. Our study has discovered a remarkable example of Ising spins on the triangular lattice, which remains magnetically disordered at low temperatures and potentially hosts a quantum spin liquid ground state.

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.

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 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.

The origin of the pseudogap region below a temperature T* is at the heart of the mysteries of cuprate high-temperature superconductors. Unusual properties of the pseudogap phase, such as broken time-reversal and inversion symmetry are observed in several symmetry-sensitive experiments: polarized neutron diffraction, optical birefringence, dichroic angle-resolved photoemission spectroscopy, second harmonic generation, and polar Kerr effect. These properties suggest that the pseudogap region is a genuine thermodynamic phase and are predicted by theories invoking ordered loop currents or other forms of intra-unit-cell (IUC) magnetic order. However, muon spin rotation (μSR) and nuclear magnetic resonance (NMR) experiments do not see the static local fields expected for magnetic order, leaving room for skepticism. The magnetic resonance probes have much longer time scales, however, over which local fields could be averaged by fluctuations. The observable effect of the fluctuations in magnetic resonance is then dynamic relaxation. We have measured dynamic muon spin relaxation rates in single crystals of YBa2Cu3O y (6.72 < y < 6.95) and have discovered "slow" fluctuating magnetic fields with magnitudes and fluctuation rates of the expected orders of magnitude that set in consistently at temperatures Tmag ≈ T*. The absence of any static field (to which μSR would be linearly sensitive) is consistent with the finite correlation length from neutron diffraction. Equally important, these fluctuations exhibit the critical slowing down at Tmag expected near a time-reversal symmetry breaking transition. Our results explain the absence of static magnetism and provide support for the existence of IUC magnetic order in the pseudogap phase.

Unconventional superconductivity based on the strong correlation of electrons is one of the central issues of solid-state physics. Although many experimental techniques are appropriate for investigating unconventional superconductivity, a complete perspective has not been established yet. The symmetries of electron pairs are crucial properties for understanding the essential state of unconventional superconductivity. In this review, we discuss the investigation of the time-reversal and spin symmetries of superconducting electron pairs using the muon spin rotation and relaxation technique. By detecting a spontaneous magnetic field under zero field and/or the temperature dependence of the muon Knight shift in the superconducting phase, the time-reversal symmetry and spin parity of electron pairs have been determined for several unconventional superconductors.

D. E. MacLaughlin, 2, ∗ O. O. Bernal, Lei Shu, 4, 5 Jun Ishikawa, Yosuke Matsumoto, J.-J. Wen, † M. Mourigal, ‡ C. Stock, 7, § G. Ehlers, C. L. Broholm, 7, 8, 9 Yo Machida, Kenta Kimura, Satoru Nakatsuji, 10, ∗∗ Yasuyuki Shimura, and Toshiro Sakakibara Department of Physics & Astronomy, University of California, Riverside, California 92521, U.S.A. Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581, Japan. Department of Physics & Astronomy, California State University, Los Angeles, California 90032, U.S.A. State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, China Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Quantum Condensed Matter Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan (Dated: August 12, 2015)

Muon spin rotation and relaxation ($\ensuremath{\mu}$SR) experiments have been carried out to characterize magnetic and superconducting ground states in the ${\text{Pr}}_{1\ensuremath{-}x}$${\text{Nd}}_{x}$${\text{Os}}_{4}$${\text{Sb}}_{12}$ alloy series. In the ferromagnetic end compound ${\text{NdOs}}_{4}$${\text{Sb}}_{12}$ the spontaneous local field at positive-muon (${\ensuremath{\mu}}^{+}$) sites below the ordering temperature ${T}_{C}$ is greater than expected from dipolar coupling to ferromagnetically aligned Nd${}^{3+}$ moments, indicating an additional indirect RKKY-like transferred hyperfine mechanism. For $0.45\ensuremath{\le}x\ensuremath{\le}0.75$, ${\ensuremath{\mu}}^{+}$ spin relaxation rates in zero and weak longitudinal applied fields indicate that static fields at ${\ensuremath{\mu}}^{+}$ sites below ${T}_{C}$ are reduced and strongly disordered. We argue this is unlikely to be due to reduction of Nd${}^{3+}$ moments, and speculate that the Nd${}^{3+}$-${\ensuremath{\mu}}^{+}$ interaction is suppressed and disordered by Pr doping. In an $x=0.25$ sample, which is superconducting below ${T}_{c}=1.3$ K, there is no sign of ``spin freezing'' (static Nd${}^{3+}$ magnetism), ordered or disordered, down to 25 mK. Dynamic ${\ensuremath{\mu}}^{+}$ spin relaxation is strong, indicating significant Nd-moment fluctuations. The ${\ensuremath{\mu}}^{+}$ diamagnetic frequency shift and spin relaxation in the superconducting vortex-lattice phase decrease slowly below ${T}_{c}$, suggesting pair breaking and/or possible modification of Fermi-liquid renormalization by Nd spin fluctuations. For $0.25\ensuremath{\le}x\ensuremath{\le}0.75$, the $\ensuremath{\mu}$SR data provide evidence against phase separation; superconductivity and Nd${}^{3+}$ magnetism coexist on the atomic scale.

The doping of charge carriers into the CuO2 planes of copper oxide Mott insulators causes a gradual destruction of antiferromagnetism and the emergence of high-temperature superconductivity. Optimal superconductivity is achieved at a doping concentration p beyond which further increases in doping cause a weakening and eventual disappearance of superconductivity. A potential explanation for this demise is that ferromagnetic fluctuations compete with superconductivity in the overdoped regime. In this case a ferromagnetic phase at very low temperatures is predicted to exist beyond the doping concentration at which superconductivity disappears. Here we report on a direct examination of this scenario in overdoped La2-xSrxCuO4 using the technique of muon spin relaxation. We detect the onset of static magnetic moments of electronic origin at low temperature in the heavily overdoped nonsuperconducting region. However, the magnetism does not exist in a commensurate long-range ordered state. Instead it appears as a dilute concentration of static magnetic moments. This finding places severe restrictions on the form of ferromagnetism that may exist in the overdoped regime. Although an extrinsic impurity cannot be absolutely ruled out as the source of the magnetism that does occur, the results presented here lend support to electronic band calculations that predict the occurrence of weak localized ferromagnetism at high doping.

This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in PrOs4Sb12. After a brief introduction of filled skutterudites, we argue that the normal-state properties of PrOs4Sb12 are quite different from ordinary heavy-fermion superconductors, in the sense that the 4f-electrons seem to be well localized even at low temperatures where the superconductivity appears. This is reflected in the existence of a field-induced antiferro-quadrupole ordering of Pr 4f-electrons. It is shown that the 4f collective excitations can be described as quadrupolar excitons. Their strong temperature dependence in close correlation with the superconductivity suggests a conjecture that the superconducting mechanism may involve quadrupolar-exciton-mediated pairing of some kind. Although the structure of the superconducting order parameter is far from conclusive, outstanding experimental observations reported to date reveal the uniqueness of the unconventional superconducting state. Special focus is given to time-reversal symmetry breaking in the superconducting state. The article concludes with a discussion of some key issues and desirable future work.

We present recent measurements of the magnetic properties of Pu metal and the superconducting properties of PuCoGa5 using the mu SR technique. Our measurements set the most stringent upper limits to date on the magnitude of the ordered moments mu(ord) in alpha-Pu and delta-stabilized Pu (alloyed with 4.3 at. % Ga) in zero applied field: mu(ord) <= 10(-3) mu B at T congruent to 4 K. Measurements of the in-plane magnetic-field penetration depth lambda(T) in PuCoGa5 (T-c = 18.5 K) for 0.06 T applied field (approximate to 2 - 5 x H-c1) show that the temperature dependence of the superfluid density, and therefore Delta lambda(T) = lambda(T) - lambda(0), are proportional to T for T/T-c <= 0.5. We estimate that.(0) = 241(3) nm. We also find no evidence for a time-reversal-symmetry violating superconducting order parameter. Taken together the measurements in PuCoGa5 are, therefore, consistent with an even-parity (pseudo-spin singlet), d-wave pairing state.