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Register a new userMulti-symmetry and Multi-band Superconductivity in Filled-skutterudites PrOs$_4$Sb$_{12}$ and PrRu$_4$Sb$_{12}$
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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.
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The filled skutterudite compound PrOsSb{} exhibits superconductivity below a critical temperature $T_mathrm{c} = 1.85$ K that develops out of a nonmagnetic heavy Fermi liquid with an effective mass $m^{*} approx 50 m_mathrm{e}$, where $m_mathrm{e}$ is the free electron mass. Analysis of magnetic susceptibility, specific heat, electrical resistivity and inelastic neutron scattering measurements within the context of a cubic crystalline electric field yields a Pr$^{3+}$ energy level scheme that consists of a $Gamma_{3}$ nonmagnetic doublet ground state that carries an electric quadrupole moment, a low lying $Gamma_{5}$ triplet excited state at $sim 10$ K, and $Gamma_{4}$ triplet and $Gamma_{1}$ singlet excited states at much higher temperatures. The superconducting state appears to be unconventional and to consist of two distinct superconducting phases. An ordered phase of magnetic or quadrupolar origin occurs at high fields and low temperatures, suggesting that the superconductivity may occur in the vicinity of a magnetic or electric quadrupolar quantum critical point.
MHz conductivity, torque magnetometer and magnetization measurements are reported on single crystals of CeOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$ using temperatures down to 0.5~K and magnetic fields of up to 60~tesla. The field-orientation dependence of the de Haas-van Alphen and Shubnikov-de Haas oscillations is deduced by rotating the samples about the $[010]$ and $[0bar{1}1]$ directions. The results indicate that NdOs$_4$Sb$_{12}$ has a similar Fermi surface topology to that of the unusual superconductor PrOs$_4$Sb$_{12}$, but with significantly smaller effective masses, supporting the importance of local phonon modes in contributing to the low-temperature heat capacity of NdOs$_4$Sb$_{12}$. By contrast, CeOs$_4$Sb$_{12}$ undergoes a field-induced transition from an unusual semimetal into a high-field, high-temperature state characterized by a single, almost spherical Fermi-surface section. The behavior of the phase boundary and comparisons with models of the bandstructure lead us to propose that the field-induced phase transition in CeOs$_4$Sb$_{12}$ is similar in origin to the well-known $alpha-gamma$ transition in Ce and its alloys.
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.
We present polar Kerr effect measurements of the filled skutterudite superconductor PrOs$_4$Sb$_{12}$. Simultaneous AC susceptibility measurements allow us to observe the superconducting transition under the influence of heating from the optical beam. A nonzero Kerr angle $theta_K$ develops below the superconducting transition, saturating at $sim 300$ nrad at low temperatures. This result is repeated across several measurements of multiple samples. By extrapolating the measured $theta_K(T)$ to zero optical power, we are able to show that the Kerr angle onset temperature in one set of measurements is consistent with the transition to the B phase at $T_{C2}$. We discuss the possible explanations for this result and its impact on the understanding of multi-phase and inhomogeneous superconductivity in PrOs$_4$Sb$_{12}$.
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.
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