Evolution of superconducting order in Pr(Os${}_{1-x}$Ru${}_x$)${}_4$Sb${}_{12}$

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$$\ge$0.4 samples, going from weak ($x$=0.4,0.6), to moderate, coupling ($x$=0.8). For the $x$$\le$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 $x$.

Changed title, enlarged numbering in figures 5 pages, 4 figures, 1 table