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Register a new userPenetration depth, multiband superconductivity, and absence of muon-induced perturbation in superconducting PrOs$_{4}$Sb$_{12}$
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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.
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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.
Thermal conductivity measurements were performed on single crystal samples of the superconducting filled skutterudite compounds PrOs$_4$Sb$_{12}$ and PrRu$_4$Sb$_{12}$ both as a function of temperature and magnetic field applied perpendicular to the heat current. In zero magnetic field, the low temperature electronic thermal conductivity of PrRu$_4$Sb$_{12}$ is vanishingly small, consistent with a fully-gapped Fermi surface. For PrOs$_4$Sb$_{12}$, however, we find clear evidence for residual electronic conduction as the temperature tends to zero Kelvin which is consistent with the presence of nodes in the superconducting energy gap. The field dependence of the electronic conductivity for both compounds shows a rapid rise immediately above H$_{c1}$ and significant structure over the entire vortex state. In the fully gapped superconductor PrRu$_4$Sb$_{12}$, this is interpreted in terms of multi-band effects. In PrOs$_4$Sb$_{12}$, we consider the Doppler shift of nodal quasiparticles at low fields and multiband effects at higher fields.
We report on Sb nuclear-quadrupole-resonance (NQR) study in filled-skutterudite compounds (Pr_1-xLa_x)Os_4Sb_12. The Sb-NQR spectra have split into two sets, arising from different Sb_12 cages containing either Pr or La, which enables us to measure two kinds of nuclear spin-lattice relaxation time T_1^Pr and T_1^La. In the normal state, the temperature (T) dependence of 1/T^Pr_1T showed almost the same behavior as that for PrOs_4Sb_12 regardless of. In contrast, 1/T^La_1T markedly decreases with increasing La concentration. In the superconducting state for x=0.05 and 0.2, 1/T_1^Pr exponentially decreases down to T=0.7 K with no coherence peak below T_c as well as in PrOs_4Sb_12. A remarkable finding is that the residual density of states at the Fermi level below T_c is induced by La substitution for Pr. These results are proposed to be understood in terms of a multiband-superconductivity model that assumes a full gap for part of the FS and the presence of point nodes for a small 4f^2-derived FS inherent in PrOs_4Sb_12. For x=0.8 and 1,1/T^La_1 exhibits a coherence peak and the nodeless energy gap characteristic for weak-coupling s-wave superconductors. With increasing Pr content, T_c and the energy gap increases. The novel strong-coupling superconductivity in PrOs_4Sb_12 is inferred to be mediated by the local interaction between 4f^2-derived crystal-electric-field states with the electric quadrupole degree of freedom and conduction electrons. This coupling causes a mass enhancement of quasi-particles for a part of FS and induces a small FS, which is responsible for point nodes in the superconducting gap function. Note that the small FS does not play any primary role for the strong-coupling superconductivity in PrOs_4Sb_12.
Specific heat, dc- and ac-magnetic susceptibility are reported for a large single crystal of PrOs$_4$Sb$_{12}$ and, after grinding, its powder. The room temperature effective paramagnetic moment of the crystal was consistent with the Pr$^{3+}$ ionic configuration and full occupancy of the Pr-sublattice. The crystal showed two distinct anomalies in the specific heat and an overall discontinuity in $C/T$ of more than 1000 mJ/K$^2$mol. The upper transition (at $T_{c1}$) was rounded, in an agreement with previous reports. The anomaly at $T_{c2}$ was very sharp, consistent with a good quality of the crystal. We observed a shoulder in $chi$ and two peaks in $chi$ below $T_{c1}$. However, there were no signatures in $chi$ of the lower temperature transition. PrOs$_4$Sb$_{12}$ is extremely sensitive to grinding, which suppresses the upper superconducting transition in both the specific heat and magnetic susceptibility. $Delta C/T_{c}$ was reduced to 140 mJ/K$^2$ mol in the powdered sample. Existing data on ground, polished, and sliced crystals suggests the existence of a length scale of order 100 $mu$, characterizing the higher temperature superconducting phase.
We report measurements of the magnetic penetration depth $lambda$ in single crystals of Pr(Os$_{1-x}$Ru$_{x}$)$_{4}$Sb$_{12}$ down to 0.1 K. Both $lambda$ and superfluid density $rho_{s}$ exhibit an exponential behavior for the $x$$geq$0.4 samples, going from weak ($x$=0.4,0.6), to moderate, coupling ($x$=0.8). For the $x$$leq$0.2 samples, both $lambda$ and $rho_{s}$ vary as $T^{2}$ at low temperatures, but $rho_{s}$ is s-wave-like at intermediate to high temperatures. Our data are consistent with a three-phase scenario, where a fully-gapped phase at $T_{c1}$ undergoes two transitions: first to an unconventional phase at $T_{c2}$$lesssim$$T_{c1}$, then to a nodal low-$T$ phase at $T_{c3}$$<$$T_{c2}$, for small values of $x$.
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