Time-Reversal Symmetry-Breaking Superconductivity in Heavy-Fermion ${\mathrm{P}\mathrm{r}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$ Detected by Muon-Spin Relaxation

We report on muon-spin relaxation measurements of the $4f^2$-based heavy-fermion superconductor filled-skutterudite ${\mathrm{Pr}\mathrm{}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$. The results reveal the spontaneous appearance of static internal magnetic fields below the superconducting transition temperature, providing unambiguous evidence for the breaking of time-reversal symmetry in the superconducting state. A discussion is made on which of the spin or orbital component of Cooper pairs carries a nonzero momentum.

Figure 1

Zero-field $\mu \mathrm{S}\mathrm{R}$ spectra in ${\mathrm{Pr}\mathrm{}\mathrm{O}\mathrm{s}}_4{\mathrm{S}\mathrm{b}}_{12}$ measured across the superconducting transition temperature $T_{c1}=1.82\mathrm{K}$. The corrected asymmetry was obtained by subtracting the temperature-independent contribution from the silver plate (0.057). The curves are fits to model I given by Eq. (1). The relaxation rate becomes stronger below $T_{c1}$.

Figure 2

Temperature dependences of the width of the internal field distribution $\Delta$, the relaxation rate $\Lambda$ in zero field and in ${\mu }_0{H}_{\mathrm{L}\mathrm{F}}=0.01\mathrm{T}$, and the specific heat divided by temperature $C/T$. The vertical lines indicate two consecutive transitions at $T_{c1}$ and $T_{c2}$ determined from the $C/T$ data.

Figure 3

Longitudinal field $H_{\mathrm{L}\mathrm{F}}$ dependence of the relaxation rate $\Lambda$. The curves are fits to the model given by Eq. (3).