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We reply to the objections raised in a recent Comment (arXiv:1706.03023) regarding our observation of slow magnetic fluctuations and critical slowing down of magnetic fluctuations in the pseudogap phase of YBa$_2$Cu$_3$O$_y$ by zero-field and longitudinal-field muon spin relaxation (arXiv:1703.06799)., Comment: 4 pages, 3 figures

Evidence for intra-unit-cell (IUC) magnetic order in the pseudogap region of high-$T_c$ cuprates below a temperature $T^\ast$ is found in several studies, but NMR and $\mu$SR experiments do not observe the expected static local magnetic fields. It has been noted, however, that such fields could be averaged by fluctuations. Our measurements of muon spin relaxation rates in single crystals of YBa$_2$Cu$_3$O$_y$ reveal magnetic fluctuations of the expected order of magnitude that exhibit critical slowing down at $T^\ast$. These results are strong evidence for fluctuating IUC magnetic order in the pseudogap phase., Comment: 8 pages 7 figures including supplemental material; added discussion of statistics and other experiments

We report beta-NMR investigations of polarized 8Li implanted in thin Pb and Ag/Nb films. At the critical superconducting temperature, we observe a singular peak in the spin relaxation rate in small longitudinal magnetic fields, which is attributed to fluctuations in the superconducting order parameter. However, the peak is more than an order of magnitude larger than the prediction based on the enhancement of the dynamic electron spin susceptibility by superconducting fluctuations and reflects the presence of unexpected slow fluctuations. Furthermore the fluctuations are rapidly suppressed in a small magnetic field, which may explain why they have not been observed previously with conventional NMR or NQR., Comment: 5 pages, 2 figures

Weak spontaneous magnetic fields are observed near the surface of YBCO films using Beta-detected Nuclear Magnetic Resonance. Below Tc, the magnetic field distribution in a silver film evaporated onto the superconductor shows additional line broadening, indicating the appearance of small disordered magnetic fields. The line broadening increases linearly with a weak external magnetic field applied parallel to the surface, and is depth-independent up to 45 nm from the Ag/YBCO interface. The magnitude of the line broadening at 10 K extrapolated to zero applied field is less than 0.2 G, and is close to nuclear dipolar broadening in the Ag. This indicates that any fields due to broken time-reversal symmetry are less than 0.2 G.

Beta-NMR has been used to study vortex lattice disorder near the surface of the high-Tc superconductor YBCO. The magnetic field distribution from the vortex lattice was detected by implanting a low energy beam of highly polarized 8Li into a thin overlayer of silver on optimally doped, twinned and detwinned YBCO samples. The resonance in Ag broadens significantly below the transition temperature Tc as expected from the emerging field lines of the vortex lattice in YBCO. However, the lineshape is more symmetric and the dependence on the applied magnetic field is much weaker than expected from an ideal vortex lattice, indicating that the vortex density varies across the face of the sample, likely due to pinning at twin boundaries. At low temperatures the broadening from such disorder does not scale with the superfluid density., Comment: 10 pages, 6 figures

The high field superconducting state in CeCoIn5 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 Hc2 = 4.97 T. At magnetic fields >= 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 < H < 4.8 T. In the normal state close to Hc2 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 CeCoIn5 for H directed parallel to the c-axis., Comment: 5 paes, 4 figures

Transverse-field muon spin rotation ($\mu$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $\lambda(T)$ is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency (rf) inductive measurements yield a stronger temperature dependence of $\lambda(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the perturbing effect of the muon charge on the neighboring Pr$^{3+}$ crystalline electric field is negligibly small, and therefore is unlikely to cause the difference between the $\mu$SR and rf results., Comment: 10 pages, 7 figures

We have measured the temperature dependence and magnitude of the superfluid density $\rho_{\rm s}(T)$ via the magnetic field penetration depth $\lambda(T)$ in PuCoGa$_5$ (nominal critical temperature $T_{c0} = 18.5$ K) using the muon spin rotation technique in order to investigate the symmetry of the order parameter, and to study the effects of aging on the superconducting properties of a radioactive material. The same single crystals were measured after 25 days ($T_c = 18.25$ K) and 400 days ($T_c = 15.0$ K) of aging at room temperature. The temperature dependence of the superfluid density is well described in both materials by a model using d-wave gap symmetry. The magnitude of the muon spin relaxation rate $\sigma$ in the aged sample, $\sigma\propto 1/\lambda^2\propto\rho_s/m^*$, where $m^*$ is the effective mass, is reduced by about 70% compared to fresh sample. This indicates that the scattering from self-irradiation induced defects is not in the limit of the conventional Abrikosov-Gor'kov pair-breaking theory, but rather in the limit of short coherence length (about 2 nm in PuCoGa$_5$) superconductivity., Comment: 11 pages

The effective superconducting penetration depth measured in the vortex state of PrOs4Sb12 using transverse-field muon spin rotation (TF-muSR) exhibits an activated temperature dependence at low temperatures, consistent with a nonzero gap for quasiparticle excitations. In contrast, Meissner-state radiofrequency (rf) inductive measurements of the penetration depth yield a T^2 temperature dependence, suggestive of point nodes in the gap. A scenario based on the recent discovery of extreme two-band superconductivity in PrOs4Sb12 is proposed to resolve this difference. In this picture a large difference between large- and small-gap coherence lengths renders the field distribution in the vortex state controlled mainly by supercurrents from a fully-gapped large-gap band. In zero field all bands contribute, yielding a stronger temperature dependence to the rf inductive measurements., Comment: 2 pages, 2 figures, submitted for publication in Proc. Int. Conf. on Strongly Correlated Electron Systems, Houston, May 2007

A low energy radioactive beam of polarized $^8$Li has been used to observe the vortex lattice near the surface of superconducting NbSe$_2$. The inhomogeneous magnetic field distribution associated with the vortex lattice was measured using depth-resolved $\beta$-detected NMR. Below $T_c$ one observes the characteristic lineshape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with magnetic field. In particular in a low field of 10.8 mT the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed., Comment: 5 pages, 3 figures. Submitted to Phys. Rev. Lett

$\beta$-NMR of isolated $^8$Li has been investigated in the normal state of 2H-NbSe$_2$. In a high magnetic field of 3T a single resonance is observed with a Gaussian line width of 3.5 kHz. The line shape varies weakly as function of magnetic field and temperature but has a strong orientation dependence. The nuclear electric quadrupole splitting is unresolved implying that the electric field gradients are 10-100 times smaller than in other non-cubic crystals. The nuclear spin relaxation rate is also anomalously small but varies linearly with temperature as expected for Korringa relaxation in a metal. These results suggest that Li adopts an interstitial position between the weakly coupled NbSe$_2$ layers and away from the conduction band., Comment: accepted for publication in Physica B

Transverse-field muon spin relaxation rates in single crystals of the heavy-fermion superconductor PrOs4Sb12 (Tc = 1.85 K) are nearly constant in the vortex state for temperatures below ~0.5Tc. This suggests that the superconducting penetration depth lambda(T) is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency measurements yield a stronger temperature dependence of lambda(T), indicative of point nodes in the gap. A similar discrepancy exists in superconducting Sr2RuO4 which, like PrOs4Sb12, breaks time-reversal symmetry (TRS) below Tc, but not in a number of non-TRS-breaking superconductors., Comment: 4 pages, 3 figures, submitted to Phys. Rev. Lett

The symmetry of the superconducting order parameter in single-crystalline PuCoGa$_5$ ($T_{\rm c} = 18.5$ K) is investigated via zero- and transverse- field muon spin relaxation ($\mu$SR) measurements, probing the possible existence of orbital and/or spin moments (time reversal-symmetry violation TRV) associated with the superconducting phase and the in-plane magnetic-field penetration depth $\lambda(T)$ in the mixed state, respectively. We find no evidence for TRV, and show that the superfluid density, or alternatively, $\Delta\lambda(T) = \lambda(T) - \lambda(0)$, are $\propto T$ for $T/T_{\rm c} \leq 0.5$. Taken together these measurements are consistent with an even-parity (pseudo-spin singlet), d-wave pairing state., Comment: 4 pages, 5 figures

We report on zero-field muon spin relaxation studies of cerium based heavy-fermion materials CeRh_{1-x}Ir_xIn_5. In the superconducting x=0.75 and 1 compositions muon spin relaxation functions were found to be temperature independent across T_c; no evidence for the presence of electronic magnetic moments was observed. The x=0.5 material is antiferromagnetic below T_N=3.75 K and superconducting below T_c=0.8 K. Muon spin realxation spectra show the gradual onset of damped coherent oscillations characteristic of magnetic order below T_N. At 1.65 K the total oscillating amplitude accounts for at least 85% of the sample volume. No change in muon precession frequency or amplitude is detected on cooling below T_c, indicating the microscopic coexistence of magnetism and superconductivity in this material., Comment: 6 pages with 3 figures. Revision with corrected axis label (mK) in Fig.1

Transverse-field muon spin rotation measurements in the vortex-lattice mixed state of the heavy-fermion (HF) superconductor PrOs4Sb12 yield a temperature dependence of the penetration depth 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) \mu s^-1 yields an estimated penetration depth \lambda(0) = 3440(20) \AA, which is considerably shorter than in other HF superconductors., Comment: 4 pages, 5 figures

Evidence for static alternating magnetic fields in the vortex cores of underdoped YBa$_2$Cu$_3$O$_{6+x}$ is reported. Muon spin rotation measurements of the internal magnetic field distribution of the vortex state of YBa$_2$Cu$_3$O$_{6.50}$ 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 YBa$_2$Cu$_3$O$_{6.95}$ 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., Comment: Submitted to PRL; corresponding author: miller@physics.ubc.ca

Zero-field muon spin relaxation (ZF-$\mu$SR) measurements were undertaken on under- and overdoped samples of superconducting YBa$_2$Cu$_3$O$_{6+x}$ to determine the origin of the weak static magnetism recently reported in this system. The temperature dependence of the muon spin relaxation rate in overdoped crystals displays an unusual behavior in the superconducting state. A comparison to the results of NQR and lattice structure experiments on highly doped samples provides compelling evidence for strong coupling of charge, spin and structural inhomogeneities., Comment: 4 pages, 4 figures, new data, new figures and modified text

A novel high magnetic field (8 T) spectrometer for muon spin rotation has been used to measure the temperature dependence of the in-plane magnetic penetration depth in YBa2Cu3O6.95. At low H and low T, the penetration depth exhibits the characteristic linear T dependence associated with the energy gap of a d_x^2-y^2-wave superconductor. However, at higher fields the penetration depth is essentially temperature independent at low T. We discuss possible interpretations of this surprising new feature in the low-energy excitation spectrum., Comment: 8 pages, 4 figures, 1 RevTex file and 4 postscript figures