Muon Spin Relaxation and Isotropic Pairing in Superconducting ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$

Transverse-field muon-spin rotation measurements in the vortex-lattice of the heavy-fermion (HF) superconductor ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$ yield a temperature dependence of the magnetic penetration depth $\lambda$ indicative of an isotropic or nearly isotropic energy gap. This is not seen to date in any other HF superconductor and is a signature of isotropic pairing symmetry, possibly related to a novel nonmagnetic “quadrupolar Kondo” HF mechanism in ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$. The $T=0$ relaxation rate ${\sigma }_s(0)=0.91(1)\mu {\mathrm{s}}^{-1}$ yields an estimated magnetic penetration depth $\lambda (0)=3440(20)\AA$, which is considerably shorter than in other HF superconductors.

Figure 1

Damped Kubo-Toyabe ZF-$\mu$SR relaxation in ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$. Circles: Kubo-Toyabe relaxation rate ${\Delta }_{\mathrm{K}\mathrm{T}}(T)$. Triangles: exponential damping rate $W(T)$.

Figure 2

TF-$\mu$SR spin precession signals in ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$ ($T_c=1.82\mathrm{K}$), applied field 20 mT. (a) Normal state ($T=2.1\mathrm{K}$). (b) Superconducting state ($T=0.1\mathrm{K}$). The weak nonrelaxing signal in (b) is due to muons that do not stop in the sample.

Figure 3

Temperature dependence of vortex state ${\mu }^{+}$ relaxation rate ${\sigma }_s(T)$ in the superconducting state of ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$. Curve: ${\sigma }_s(T)={\sigma }_s(0)[1-(T/T_c{)}^y]$, ${\sigma }_s(0)=0.91(1)\mu {\mathrm{s}}^{-1}$, $T_c=1.83(2)\mathrm{K}$, $y=3.6(2)$. Inset: low-temperature penetration depth $\lambda (T)$ derived from ${\sigma }_s(T)$. Curve: $\lambda (T)=\lambda (0)[1+(\pi \Delta /2T{)}^{1/2}\exp (-\Delta /T)]$, $\lambda (0)=3440(20)\AA$, $\Delta /T_c=2.1(2)$, from fit to data for $T\le 0.8\mathrm{K}$.

Figure 4

Dependence of TF-$\mu$SR relaxation rate ${\sigma }_s(H)$ on applied field in ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$, $T=0.1\mathrm{K}$.

Figure 5

Uemura plot of superconducting transition temperature $T_c$ versus muon relaxation rate ${\sigma }_s(0)$ for ${\mathrm{U}\mathrm{B}\mathrm{e}}_{13}$ [20], ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2$ [9], ${\mathrm{U}\mathrm{P}\mathrm{d}}_2{\mathrm{A}\mathrm{l}}_3$ [21], $\mathrm{C}\mathrm{e}T{\mathrm{I}\mathrm{n}}_5$, $T=\mathrm{C}\mathrm{o}$ and Ir [22], ${\mathrm{U}\mathrm{P}\mathrm{t}}_3$ [23], and ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$ (this Letter). The “Uemura line” is followed by a number of unconventional superconductors.