Evolution of superconducting order in Pr(Os$_{1-x}$Ru$_{x}$)$_{4}$Sb$_{12}$

TL;DR

This study investigates how the superconducting order evolves in Pr(Os$_{1-x}$Ru$_{x}$)$_{4}$Sb$_{12}$ through magnetic penetration depth measurements, revealing a complex three-phase transition scenario as Ru content varies.

Contribution

It provides the first detailed experimental evidence of a three-phase evolution of superconducting order in Pr(Os$_{1-x}$Ru$_{x}$)$_{4}$Sb$_{12}$, highlighting the transition from fully-gapped to nodal phases.

Findings

Exponential behavior of $ ho_s$ for $x extgreater=0.4$ indicating fully-gapped superconductivity.

Power-law ($T^2$) variation of $ ho_s$ at low temperatures for $x extless=0.2$, suggesting nodal gaps.

Evidence of a three-phase transition scenario with intermediate unconventional phases.

Abstract

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 $x$.