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Register a new userMagnetoresistance of Pr$_{1-x}$La$_x$Os$_4$Sb$_{12}$: Disentangling local crystalline-electric-field physics and lattice effects
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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.
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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 $T_c$.
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.
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 $x$.
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.
Electrical resistivity measurements of non-magnetic single-crystalline Ce$_{1-x}$La$_x$Os$_4$Sb$_{12}$ alloys, $x=0.02$ and 0.1, are reported for temperatures down to 20 mK and magnetic fields up to 18 T. At the lowest temperatures, the resistivity of Ce$_{0.98}$La$_{0.02}$Os$_4$Sb$_{12}$ has a Fermi-liquid-like temperature variation $rho=rho_0+A T^2$, but with negative $A$ in small fields. The resistivity has an unusually strong magnetic field dependence for a paramagnetic metal. The 20 mK resistivity increases by 75% between H=0 and 4 T and then decreases by 65% between 4 T and 18 T. Similarly, the $A$ coefficient increases with the field from -77 to 29$ muOmega$cmK$^{-2}$ between H=0 and 7 T and then decreases to 18$ muOmega$cmK$^{-2}$ for 18 T. This nontrivial temperature and field variation is attributed to the existence of a very narrow Kondo-hole band in the hybridization gap, which pins the Fermi energy. Due to disorder the Kondo-hole band has localized states close to the band edges. The resistivity for $x=0.1$ has a qualitatively similar behavior to that of $x=0.02$, but with a larger Kondo-hole band.
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