Positive-muon ($mu^+$) Knight shifts have been measured in the paramagnetic states of Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ alloys, where $x =$ 0, 0.25, 0.45, 0.50, 0.55, 0.75, and 1.00. In Pr-substituted NdOs$_4$Sb$_{12}$ ($x le$ 0.75), but not in NdOs$_4
$Sb$_{12}$, Clogston-Jaccarino plots of $mu^+$ Knight shift~$K$ versus magnetic susceptibility~$chi$ exhibit an anomalous saturation of $K(chi)$ at $sim-$0.5% for large susceptibilities (low temperatures), indicating a reduction of the coupling strength between $mu^+$ spins and $4f$ paramagnetism for temperatures $lesssim$ 15~K. We speculate that itinerant Pr$^{3+}$ quadrupolar excitations, invoked to mediate the superconducting Cooper-pair interaction, might modify the $mu^+$-$4f$ ion indirect spin-spin interaction.
Muon spin rotation and relaxation ($mu$SR) experiments have been carried out to characterize magnetic and superconducting ground states in the Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ alloy series. In the ferromagnetic end compound NdOs$_4$Sb$_{12}$ the spont
aneous local field at positive-muon ($mu^+$) 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 $le x le$ 0.75, $mu^+$ spin relaxation rates in zero and weak longitudinal applied fields indicate that static fields at $mu^+$ 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$^{3+}$-$mu^+$ 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 $mu^+$ spin relaxation is strong, indicating significant Nd-moment fluctuations. The $mu^+$ 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 $le x le$ 0.75, the $mu$SR data provide evidence against phase separation; superconductivity and Nd$^{3+}$ magnetism coexist on the atomic scale.
We report results of a muon spin rotation and relaxation ($mu$SR) study of dilute Pd$_{1-x}$Ni$_x$ alloys, with emphasis on Ni concentrations $x =$ 0.0243 and 0.025. These are close to the critical value $x_mathrm{cr}$ for the onset of ferromagnetic
long-range order (LRO), which is a candidate for a quantum critical point. The 2.43 and 2.5 at.% Ni alloys exhibit similar $mu$SR properties. Both samples are fully magnetic, with average muon local fields $langle B^mathrm{loc}rangle =$ 2.0 and 3.8 mT and Curie temperatures $T_C =$ 1.0 and 2.03 K for 2.43 and 2.5 at.% Ni, respectively, at $T = 0$. The temperature dependence of $langle B^mathrm{loc}rangle$ suggests ordering of Ni spin clusters rather than isolated spins. Just above $T_C$ a two-phase region is found with separate volume fractions of quasistatic short-range order (SRO) and paramagnetism. The SRO fraction decreases to zero with increasing temperature a few kelvin above $T_C$. This mixture of SRO and paramagnetism is consistent with the notion of an inhomogeneous alloy with Ni clustering. The measured values of $T_C$ extrapolate to $x_mathrm{cr}$ = 0.0236 $pm$ 0.0027. The dynamic muon spin relaxation in the vicinity of $T_C$ differs for the two samples: a relaxation-rate maximum at $T_C$ is observed for $x$ = 0.0243, reminiscent of critical slowing down, whereas for $x =$ 0.025 no dynamic relaxation is observed within the $mu$SR time window. The data suggest a mean-field-like transition in this alloy.
Zero-field muon spin relaxation experiments have been carried out in the Pr(Os_{1-x}Ru_x)_4Sb_12 and Pr_{1-y}La_yOs_4Sb_12 alloy systems to investigate broken time-reversal symmetry (TRS) in the superconducting state, signaled by the onset of a spont
aneous static local magnetic field B_s. In both alloy series B_s initially decreases linearly with solute concentration. Ru doping is considerably more efficient than La doping, with a ~50% faster initial decrease. The data suggest that broken TRS is suppressed for Ru concentration x >~ 0.6, but persists for essentially all La concentrations. Our data support a crystal-field excitonic Cooper pairing mechanism for TRS-breaking superconductivity.
Muon spin rotation (muSR) experiments reveal unconventional spin freezing and dynamics in the two-dimensional (2D) triangular lattice antiferromagnet NiGa2S4. Long-lived disordered Ni-spin freezing (correlation time > 10-6 s at 2 K) sets in below T_f
= 8.5 +- 0.5 K with a mean-field-like temperature dependence. The observed exponential temperature dependence of the muon spin relaxation above T_f is strong evidence for 2D critical spin fluctuations. Slow Ni spin fluctuations coexist with quasistatic magnetism at low temperatures but are rapidly suppressed for fields > 10 mT, in marked contrast with the field-independent specific heat. The muSR and bulk susceptibility data indicate a well-defined 2D phase transition at T_f, below which NiGa2S4 is neither a conventional magnet nor a singlet spin liquid.
Muon spin relaxation experiments have been performed in the pyrochlore iridate Pr_2Ir_2O_7 for temperatures in the range 0.025-250 K. Kubo-Toyabe relaxation functions are observed up to > 200 K, indicating static magnetism over this temperature range
. The T -> 0 static muon spin relaxation rate Delta(0) ~ 8 mus^-1 implies a weak quasistatic moment (~0.1 mu_B). The temperature dependence of Delta is highly non-mean-field-like, decreasing smoothly by orders of magnitude but remaining nonzero below ~150 K. The data rule out ordering of the full Pr^3+ CEF ground-state moment (3.0 mu_B) down to 0.025 K. The weak static magnetism is most likely due to hyperfine-enhanced ^141Pr nuclear magnetism. The dynamic relaxation rate lambda increases markedly below ~20 K, probably due to slowing down of spin fluctuations in the spin-liquid state. At low temperatures lambda is strong and temperature-independent, indicative of a high density of low-lying spin excitations as is common in frustrated antiferromagnets.
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 quasipar
ticle 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.
