Time-reversal symmetry breaking in the noncentrosymmetric superconductor ${\mathrm{Re}}_6\mathrm{Ti}$

We have investigated the superconducting state of the noncentrosymmetric superconductor ${\mathrm{Re}}_6\mathrm{Ti}$ ($T_c=6.0$ K) using a muon-spin rotation/relaxation technique. The zero-field muon experiment shows the presence of spontaneous magnetic fields in the superconducting state, indicating time-reversal symmetry breaking (TRSB). However, the low-temperature transverse-field muon measurements suggest nodeless $s$-wave superconductivity. Similar results were also observed for ${\mathrm{Re}}_{6}X$ ($X=\text{Zr}$, Hf) family of materials which indicates that the pairing symmetry does not depend on the spin-orbital coupling. Altogether, these studies suggest an unconventional nature (TRSB) of superconductivity is intrinsic to the ${\mathrm{Re}}_{6}X$ family of compounds and paves the way for further studies of this family of materials.

Figure 1

Powder x-ray diffraction pattern for the ${\mathrm{Re}}_6\mathrm{Ti}$ sample recorded at room temperature using Cu $K\alpha$ radiation. Rietveld refined calculated pattern for the cubic noncentrosymmetric $\alpha -\text{Mn}$ (217) structure shown by a solid black line.

Figure 2

(a) The superconducting transition temperature appeared around $T_c=6.0\pm 0.2$ from magnetization measurement. (b) The low-temperature specific-heat data in the superconducting state was fitted with a single-gap $s$-wave model for $\mathrm{\Delta }\left(0\right)/k_B{T}_c=1.86.$

Figure 3

(a) Representative TF $\mu \mathrm{SR}$ signals collected at (a) 10 K and (b) 0.3 K in an applied magnetic field of 30 mT. The solid lines are fits using Eq. (1). (b) Temperature dependence of ${\sigma }_{\mathrm{FLL}}$ collected at an applied field of 30 mT was following the single-gap s-wave model in dirty limit for $\mathrm{\Delta }\left(0\right)/k_B{T}_c=1.85\pm 0.01$.

Figure 4

(a) Zero-field $\mu \mathrm{SR}$ spectra collected below (0.3 K) and above (10 K) the superconducting transition temperature. The solid lines are the fits to Gaussian Kubo-Toyabe (KT) function given in Eq. (7). (b) Temperature dependence of nuclear relaxation rate ${\sigma }_{\text{ZF}}$ shows a systematic increase below $T_c$. (c) Temperature dependence of electronic relaxation rate $\mathrm{\Lambda }$ shows no appreciable change at $T_c$.