Detection of Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor ${\mathrm{Re}}_6\mathrm{Zr}$ Using Muon-Spin Spectroscopy

We have investigated the superconducting state of the noncentrosymmetric compound ${\mathrm{Re}}_6\mathrm{Zr}$ using magnetization, heat capacity, and muon-spin relaxation or rotation ($\mu \mathrm{SR}$) measurements. ${\mathrm{Re}}_6\mathrm{Zr}$ has a superconducting transition temperature, $T_c=6.75\pm 0.05\mathrm{K}$. Transverse-field $\mu \mathrm{SR}$ experiments, used to probe the superfluid density, suggest an $s$-wave character for the superconducting gap. However, zero and longitudinal-field $\mu \mathrm{SR}$ data reveal the presence of spontaneous static magnetic fields below $T_c$ indicating that time-reversal symmetry is broken in the superconducting state and an unconventional pairing mechanism. An analysis of the pairing symmetries identifies the ground states compatible with time-reversal symmetry breaking.

Figure 1

(a) Temperature dependence of the magnetization collected in zero-field-cooled warming (ZFCW) and field-cooled cooling (FCC) modes in an applied field ${\mu }_{0}H=1.0\mathrm{mT}$. (b) $C/T$ versus $T^2$ for ${\mathrm{Re}}_6\mathrm{Zr}$. The line is a fit to the data using $C/T={\gamma }_n+{\beta }_3{T}^2+{\beta }_5{T}^4$ where ${\gamma }_{n}T$ and ${\beta }_3{T}^3+{\beta }_5{T}^5$ are the normal state electronic and lattice contributions to the specific heat, respectively. ${\gamma }_n=26\pm 2m\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-2}$ and the Debye temperature calculated from ${\beta }_3$ is $319\pm 9\mathrm{K}$.

Figure 2

(a) Transverse-field muon time spectra for ${\mathrm{Re}}_6\mathrm{Zr}$ at $T=0.3\mathrm{K}$ in a magnetic field 40 mT. The solid line shows a fit to the data using Eq. (1). For clarity, only the data from one of the two virtual detectors are shown. (b) Temperature dependence of the superconducting muon-spin depolarization rate ${\sigma }_{sc}$ collected in an applied magnetic field ${\mu }_{0}H=40\mathrm{mT}$. The solid line shows a fit to an isotropic $s$-wave gap.

Figure 3

Zero-field $\mu \mathrm{SR}$ time spectra for ${\mathrm{Re}}_6\mathrm{Zr}$ collected at 0.3 (closed symbols) and 8.0 K (open symbols) are shown together with lines that are least squares fits to the data using Eq. (3). These spectra collected below and above $T_c$ are representative of the data collected. A $\mathrm{LF}\text{−}\mu \mathrm{SR}$ time spectrum taken in an applied field of 10 mT at 0.3 K is also shown.

Figure 4

(a) Temperature dependence of $\sigma$ for ${\mathrm{Re}}_6\mathrm{Zr}$ in zero field which clearly shows the spontaneous fields appearing at $T_c=6.78\mathrm{K}$. The solid line is a fit to the data (reduced ${\chi }_{\nu }^2=1.02$) using an approximation [41] to the BCS order parameter for $\sigma$. (b) The electronic relaxation rate $\mathrm{\Lambda }$ versus temperature in zero field shows no temperature dependence.