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Register a new userEvolution of superconductivity in Pr$_{1-x}$La$_{x}$Os$_{4}$Sb$_{12}$: Upper critical field measurements
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Measurements of the upper critical field $H_{c2}$ near $T_c$ of Pr$_{1- x}$La$_{x}$Os$_{4}$Sb$_{12}$ were performed by specific heat. A positive curvature in $H_{c2}$ versus $T$ was observed in samples and concentrations exhibiting two superconducting transitions. These results argue against this curvature being due to two-band superconductivity. The critical field slope - $dH_{c2}/dT$ suggests the existence of a crossover concentration $x_{cr} approx 0.25$, below which there is a rapid suppression of effective electron mass with La-alloying. This crossover concentration was previously detected in the measurement of the discontinuity of $C/T$ at $T_c$.
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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 $x$.
Resistivity measurements were performed on Pr$_{1-x}$La$_x$Os$_4$Sb$_{12}$ single crystals at temperatures down to 20 mK and in fields up to 18 T. The results for dilute-Pr samples ($x=0.3$ and 0.67) are consistent with model calculations performed assuming a singlet crystalline-electric-field (CEF) ground state. The residual resistivity of these crystals features a smeared step centered around 9 T, the predicted crossing field for the lowest CEF levels. The CEF contribution to the magnetoresistance has a weaker-than-calculated dependence on the field direction, suggesting that interactions omitted from the CEF model lead to avoided crossing in the effective levels of the Pr$^{3+}$ ion. The dome-shaped magnetoresistance observed for $x = 0$ and 0.05 cannot be reproduced by the CEF model, and likely results from fluctuations in the field-induced antiferroquadrupolar phase.
The Pr-rich end of the alloy series Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ has been studied using muon spin rotation and relaxation. The end compound PrOs$_4$Sb$_{12}$ is an unconventional heavy-fermion superconductor, which exhibits a spontaneous magnetic field in the superconducting phase associated with broken time-reversal symmetry. No spontaneous field is observed in the Nd-doped alloys for x $>$ 0.05. The superfluid density is insensitive to Nd concentration, and no Nd$^{3+}$ static magnetism is found down to the lowest temperatures of measurement. Together with the slow suppression of the superconducting transition temperature with Nd doping, these results suggest anomalously weak coupling between Nd spins and conduction-band states.
The superconducting state of the filled skutterudite alloy series Pr$_{1-x}$La$_{x}$Pt$_{4}$Ge$_{12}$ has been systematically studied by specific heat, zero-field muon spin relaxation ($mu$SR), and superconducting critical field measurements. An additional inhomogeneous local magnetic field, indicative of broken time-reversal symmetry (TRS), is observed in the superconducting states of the alloys. For $x lesssim 0.5$ the broken-TRS phase sets in below a temperature $T_m$ distinctly lower than the superconducting transition temperature $T_c$. For $x gtrsim 0.5$ $T_m approx T_c$. The local field strength decreases as $x to 1$, where LaPt$_{4}$Ge$_{12}$ is characterized by conventional pairing. The lower critical field $H_{c1}(T)$ of PrPt$_{4}$Ge$_{12}$ shows the onset of a second quadratic temperature region below $T_q sim T_m$. Upper critical field $H_{c2}(T)$ measurements suggest multiband superconductivity, and point gap nodes are consistent with the specific heat data. In Pr$_{1-x}$La$_{x}$Pt$_{4}$Ge$_{12}$ only a single specific heat discontinuity is observed at $T_c$, in contrast to the second jump seen in PrOs$_{4}$Sb$_{12}$ below $T_c$. These results suggest that superconductivity in PrPt$_{4}$Ge$_{12}$ is characterized by a complex order parameter.
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.
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