Absence of Spontaneous Magnetic Fields due to Time-Reversal Symmetry Breaking in Bulk Superconducting UTe_{2}.

We have investigated the low-temperature local magnetic properties in the bulk of molten salt-flux (MSF)-grown single crystals of the candidate odd-parity superconductor UTe_{2} by zero-field muon spin relaxation (µSR). In contrast to previous µSR studies of UTe_{2} single crystals grown by a chemical vapor transport method, we find no evidence of magnetic clusters or electronic moments fluctuating slow enough to cause a discernible relaxation of the zero-field µSR asymmetry spectrum. Consequently, our measurements on MSF-grown single crystals rule out the generation of spontaneous magnetic fields in the bulk that would occur near impurities or lattice defects if the superconducting state of UTe_{2} breaks time-reversal symmetry. This result suggests that UTe_{2} is characterized by a single-component superconducting order parameter.

Intrinsic Low-Temperature Magnetism in SmB_{6}.

By means of new muon spin relaxation experiments, we disentangle extrinsic and intrinsic sources of low-temperature bulk magnetism in the candidate topological Kondo insulator (TKI) SmB_{6}. Results on Al-flux-grown SmB_{6} single crystals are compared to those on a large floating-zone-grown ^{154}Sm ^{11}B_{6} single crystal in which a 14 meV bulk spin exciton has been detected by inelastic neutron scattering. Below ∼10 K, we detect the gradual development of quasistatic magnetism due to rare-earth impurities and Sm vacancies. Our measurements also reveal two additional forms of intrinsic magnetism: (1) underlying low-energy (∼100 meV) weak magnetic moment (∼10^{-2} µ_{B}) fluctuations similar to those detected in the related candidate TKI YbB_{12} that persist down to millikelvin temperatures, and (2) magnetic fluctuations consistent with a 2.6 meV bulk magnetic excitation at zero magnetic field that appears to hinder surface conductivity above ∼4.5 K. We discuss potential origins of the magnetism.

Direct search for a ferromagnetic phase in a heavily overdoped nonsuperconducting copper oxide.

The doping of charge carriers into the CuO(2) 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 La(2-x)Sr(x)CuO(4) 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.

Magnetism and disorder effects on muon spin rotation measurements of the magnetic penetration depth in iron-arsenic superconductors.

It is shown that attempts to accurately deduce the magnetic penetration depth λ of overdoped BaFe(1.82)Co(0.18)As2 single crystals by transverse-field muon spin rotation (TF µSR) are thwarted by field-induced magnetic order and strong vortex-lattice disorder. We explain how substantial deviations from the magnetic field distribution of a nearly perfect vortex lattice by one or both of these factors is also significant for other iron-arsenic superconductors, and this introduces considerable uncertainty in the values of λ obtained by TF µSR.

Detection of the unusual magnetic orders in the pseudogap region of a high-temperature superconducting YBa2Cu3O6.6 crystal by muon-spin relaxation.

We present muon-spin relaxation (muSR) measurements on a large YBa2Cu3O6.6 single crystal in which two kinds of unusual magnetic order have been detected in the pseudogap region by neutron scattering. A comparison is made to measurements on smaller, higher quality YBa2Cu3Oy single crystals. One type of magnetic order is observed in all samples, but does not evolve significantly with hole doping. A second type of unusual magnetic order is observed only in the YBa2Cu3O6.6 single crystal. This magnetism has an ordered magnetic moment that is quantitatively consistent with the neutron experiments, but is confined to just a small volume of the sample ( approximately 3%). Our findings do not support theories that ascribe the pseudogap to a state characterized by loop-current order, but instead indicate that dilute impurity phases are the source of the unusual magnetic orders in YBa2Cu3Oy.

Field-induced coupled superconductivity and spin density wave order in the heavy fermion compound CeCoIn5.

The high-field superconducting state in CeCoIn(5) has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic c axis close to the upper critical field mu(0)H(c2) = 4.97 T. At magnetic fields mu(0)H > or = 4.8 T the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate sigma reveal paramagnetic spin fluctuations in the field regime from 2 T < or = mu(0)H < 4.8 T. In the normal state close to H(c2) correlated spin fluctuations as described by the self-consistent renormalization theory are observed. The results support the formation of a mode-coupled superconducting and antiferromagnetically ordered phase in CeCoIn(5) for H directed parallel to the c axis.

Anomalous weak magnetism in superconducting YBa2Cu3O6+x.

For some time now, there has been considerable experimental and theoretical effort to understand the role of the normal-state "pseudogap" phase in underdoped high-temperature cuprate superconductors. Recent debate has centered on the question of whether the pseudogap is independent of superconductivity. We provide evidence from zero-field muon spin relaxation measurements in YBa2Cu3O6+x for the presence of small spontaneous static magnetic fields of electronic origin intimately related to the pseudogap transition. Our most significant finding is that, for optimal doping, these weak static magnetic fields appear well below the superconducting transition temperature. The two compositions measured suggest the existence of a quantum critical point somewhat above optimal doping.

Coexistence of ferromagnetic fluctuations and superconductivity in the actinide superconductor UTe2.

We report low-temperature muon spin relaxation/rotation (µSR) measurements on single crystals of the actinide superconductor UTe2. Below 5 K we observe a continuous slowing down of magnetic fluctuations that persists through the superconducting transition temperature (T c = 1.6 K), but we find no evidence of long-range or local magnetic order down to 0.025 K. The temperature dependence of the dynamic relaxation rate down to 0.4 K agrees with the self-consistent renormalization theory of spin fluctuations for a three-dimensional weak itinerant ferromagnetic metal. Our µSR measurements also indicate that the superconductivity coexists with the magnetic fluctuations.

Signatures of new d-wave vortex physics in overdoped Tl2Ba2CuO(6+x) revealed by TF-µ(+)SR.

The spontaneous expulsion of applied magnetic field, the Meissner effect, is a defining feature of superconductors; in Type-II superconductors above the lower critical field, this screening takes the form of a lattice of magnetic flux vortices. Using implanted spin-1/2 positive muons, one can measure the vortex lattice field distribution through the spin precession and deduce key parameters of the superconducting ground state, and thereby fundamental properties of the superconducting pairing. Muon spin rotation/relaxation (µSR) experiments have indeed revealed much interesting physics in the underdoped cuprates, where superconductivity is closely related to, or coexistent with, disordered or fluctuating magnetic and charge excitations. Such complications should be absent in overdoped cuprates, which are believed to exhibit conventional Fermi liquid behaviour. These first transverse field (TF)-µ(+)SR experiments on heavily-overdoped single crystals reveal a superfluid density exhibiting a clear inflection point near 0.5Tc, with a striking doping-independent scaling. This reflects hitherto unrecognized physics intrinsic to d-wave vortices, evidently generic to the cuprates, and may offer fundamentally new insights into their still-mysterious superconductivity.

Charge segregation model for superconducting correlations in cuprates above T(c).

We present a theoretical framework for understanding recent transverse field muon spin rotation (TF-µSR) experiments on cuprate superconductors in terms of localized regions of phase-coherent pairing correlations above the bulk superconducting transition temperature Tc. The local regions of phase coherence are associated with a tendency toward charge ordering, a phenomenon found recently in hole-doped cuprates. We use the Cahn-Hilliard equation as a means to phenomenologically model the inhomogeneous charge distribution of the electron system observed experimentally. For this system we perform self-consistent superconducting calculations using the Bogoliubov-deGennes method. Within this context we explore two possible scenarios: (i) the magnetic field is diamagnetically screened by the sum of varying shielding currents of isolated small-sized superconducting domains. (ii) These domains become increasingly correlated by Josephson coupling as the temperature is lowered and the main response to the applied magnetic field is from the sum of all varying tunneling currents. The results indicate that these two approaches may be used to simulate the TF-µSR data but case (ii) yields better agreement.

High-field µSR studies of superconducting and magnetic correlations in cuprates above T(c).

The advent of high transverse field muon spin rotation (TF-µSR) has led to recent µSR investigations of the magnetic field response of cuprates above the superconducting transition temperature T(c). Here the results of such experiments on hole-doped cuprates are reviewed. Although these investigations are currently ongoing, it is clear that the effects of high field on the internal magnetic field distribution of these materials is dependent upon competition between superconductivity and magnetism. In La(2 - x)Sr(x)CuO(4) the response to the external field above T(c) is dominated by heterogeneous spin magnetism. However, the magnetism that dominates the observed inhomogeneous line broadening below x ∼ 0.19 is overwhelmed by the emergence of a completely different kind of magnetism in the heavily overdoped regime. The origin of the magnetism above x ∼ 0.19 is probably related to intrinsic disorder, but the systematic evolution of the magnetism with doping changes in the doping range beyond the superconducting 'dome'. In contrast, the width of the internal field distribution of underdoped Y Ba(2)Cu(3)O(y) above T(c) is observed to track T(c) and the density of superconducting carriers. This observation suggests that the magnetic response above T(c) is not dominated by electronic moments, but rather inhomogeneous fluctuating superconductivity. The spatially inhomogeneous response of Y Ba(2)Cu(3)O(y) to the applied field may be a means of minimizing energy, rather than being caused by intrinsic disorder.

Inhomogeneous magnetic-field response of YBa2Cu3Oy and La2-xSrxCuO4 persisting above the bulk superconducting transition temperature.

We report that in YBa2Cu3Oy and La2-xSrxCuO4 there is a spatially inhomogeneous response to the magnetic field for temperatures T extending well above the bulk-superconducting transition temperature Tc. An inhomogeneous magnetic response is observed above Tc even in ortho-II YBa2Cu3O6.50, which has highly ordered doping. The degree of the field inhomogeneity above Tc tracks the hole-doping dependences of both Tc and the density of the superconducting carriers below Tc, and therefore is apparently coupled to superconductivity.

Field dependence of the vortex core size in a multiband superconductor.

The magnetic field dependence of the vortex core size in the multiband superconductor NbSe2 has been determined from muon spin rotation measurements. The spatially extended nature of the quasiparticle core states associated with the smaller gap leads to a rapid field-induced shrinkage of the core size at low fields, while the more tightly bound nature of the states associated with the larger gap leads to a field-independent core size for fields greater than 4 kOe. A simple model is proposed for the density of delocalized core states that establishes a direct relationship between the field-induced reduction of the vortex core size and the corresponding enhancement of the electronic thermal conductivity. We show that this model accurately describes both NbSe2 and the single-band superconductor V3Si.

Observation of two time scales in the ferromagnetic manganite La1-xCaxMnO3, x approximately 0.3.

We report new zero-field muon spin relaxation and neutron spin echo measurements in ferromagnetic (FM) (La,Ca)MnO3 which suggest at least two spatially separated regions possessing very different Mn-ion spin dynamics. One region displays diffusive relaxation, "critical slowing down" near T(C) and an increasing volume fraction below T(C), suggesting overdamped FM spin waves below T(C). The second region possesses more slowly fluctuating spins, a linewidth independent of q, and a decreasing volume fraction below T(C). The estimated length scale for the inhomogeneity is

Glassy spin dynamics in non-fermi-liquid UCu5-xPdx, x = 1.0 and 1.5.

Local f-electron spin dynamics in the non-Fermi-liquid heavy-fermion alloys UCu5-xPdx, x = 1.0 and 1.5, have been studied using muon spin-lattice relaxation. The sample-averaged asymmetry function G(t) indicates strongly inhomogeneous spin fluctuations and exhibits the scaling G(t,H) = G(t/H(gamma)) expected from glassy dynamics. At 0.05 K gamma(x = 1.0) = 0.35+/-0.1, but gamma(x = 1.5) = 0.7+/-0.1. This is in contrast to inelastic neutron scattering results, which yield gamma = 0.33 for both concentrations. There is no sign of static magnetism approximately greater than 10(-3)(B)/U ion in either material above 0.05 K. Our results strongly suggest that both alloys are quantum spin glasses.

Superconductivity and field-induced magnetism in Pr2-xCexCuO4 single crystals.

We report muon-spin rotation and relaxation (muSR) measurements on single crystals of the electron-doped high-T(c) superconductor Pr2-xCexCuO4. In a zero external magnetic field, superconductivity is found to coexist with dilute Cu spins that are static on the muSR time scale. In an applied field, we observe a mu(+)-Knight shift that is primarily due to the magnetic moment induced on the Pr ions. Below the superconducting transition temperature T(c), an additional source of local magnetic field appears throughout the volume of the sample. This finding is shown to be consistent with field-induced antiferromagnetic ordering of the Cu spins. Measurements of the temperature dependence of the in-plane magnetic penetration depth lambda(ab) in the vortex state are also presented.

Local magnetic susceptibility of the positive muon in the quasi-one-dimensional S=1/2 antiferromagnet dichlorobis (pyridine) copper (II).

We report muon spin rotation measurements of the local magnetic susceptibility around a positive muon in the paramagnetic state of the quasi-one-dimensional spin 1/2 antiferromagnet dichlorobis (pyridine) copper (II). Signals from three distinct sites are resolved and have a temperature dependent frequency shift which is significantly different than the magnetic susceptibility. This difference is attributed to a muon induced perturbation of the spin 1/2 chain. The obtained frequency shifts are compared with transfer matrix density-matrix renormalization-group numerical simulations.

Muon spin relaxation and isotropic pairing in superconducting PrOs4Sb12.

Transverse-field muon-spin rotation measurements in the vortex-lattice of the heavy-fermion (HF) superconductor PrOs4Sb12 yield a temperature dependence of the magnetic penetration depth lambda indicative of an isotropic or nearly isotropic energy gap. This is not seen to date in any other HF superconductor and is a signature of isotropic pairing symmetry, possibly related to a novel nonmagnetic "quadrupolar Kondo" HF mechanism in PrOs4Sb12. The T=0 relaxation rate sigma(s)(0)=0.91(1) micros(-1) yields an estimated magnetic penetration depth lambda(0)=3440(20) A, which is considerably shorter than in other HF superconductors.

Temperature dependence of the magnetic penetration depth in the vortex state of the pyrochlore superconductor, Cd2Re2O7.

We report transverse-field and zero-field muon spin rotation and relaxation studies of the superconducting rhenium oxide pyrochlore, Cd2Re2O7. Transverse-field measurements (H=0.007 T) show line broadening below T(c), which is characteristic of a vortex state, demonstrating conclusively the type-II nature of this superconductor. The penetration depth is seen to level off below about 400 mK (T/T(c) approximately 0.4), with a rather large value of lambda(T=0) approximately 7500 A. The temperature independent behavior below approximately 400 mK is consistent with a nodeless superconducting energy gap. Zero-field measurements indicate no static magnetic fields developing below the transition temperature.

Evidence for static magnetism in the vortex cores of ortho-II YBa2Cu3O6.50.

Evidence for static alternating magnetic fields in the vortex cores of underdoped YBa2Cu3O6+x is reported. Muon spin rotation measurements of the internal magnetic field distribution of the vortex state of YBa2Cu3O6.50 in applied fields of H = 1 T and H = 4 T reveal a feature in the high-field tail of the field distribution which is not present in optimally doped YBa2Cu3O6.95 and which fits well to a model with static magnetic fields in the vortex cores. The magnitude of the fields is estimated to be 18(2) G and decreases above T = 10 K. We discuss possible origins of the additional vortex core magnetism within the context of existing theories.