Time-reversal symmetry breaking in the noncentrosymmetric superconductor ${\mathrm{Re}}_6\mathrm{Hf}$: Further evidence for unconventional behavior in the $\alpha$-Mn family of materials

The discovery of new families of unconventional superconductors is important both experimentally and theoretically, especially if it challenges current models and thinking. By using muon spin relaxation in zero field, time-reversal symmetry breaking has been observed in ${\mathrm{Re}}_6\mathrm{Hf}$. Moreover, the temperature dependence of the superfluid density exhibits $s$-wave superconductivity with an enhanced electron-phonon coupling. This, coupled with the results from isostructural ${\mathrm{Re}}_6\mathrm{Zr}$, shows that the ${\mathrm{Re}}_{6}X$ family is indeed a new and important group of unconventional superconductors.

Figure 1

(a) ZF- and LF-$\mu \mathrm{SR}$ spectra collected above (circles) and below (squares) $T_c$ with least-squares fits using the model of Eq. (2) (solid lines). In ZF there is a clear difference between the spectra, indicating the presence of spontaneous fields in the superconducting state. The effect of applying a small LF field of 10 mT is also shown (diamonds). (b) Temperature dependence of the Gaussian relaxation parameter $\mathrm{\Delta }$, which clearly shows spontaneous fields appearing below $T_c\sim 6.0$ K. (c) The electronic relaxation rate $\mathrm{\Lambda }$ exhibits a weak temperature dependence, with no appreciable change at $T_c$.

Figure 2

(a) Representative TF-$\mu \mathrm{SR}$ signals collected at (a) 300 mK and (b) 10 K in an applied magnetic field of 25 mT. The solid lines are fits using Eq. (4). The effect of the flux line lattice can be seen in the top panel as the strong Gaussian decay envelope of the oscillatory function. Above $T_c$, the depolarization is reduced and is due to the randomly oriented array of nuclear magnetic moments. (b) Temperature dependence of the TF-$\mu \mathrm{SR}$ depolarization rate collected in a field of 40 mT. The data point with the red outline has been masked from the fitting as an outlier.