Microscopic Investigation of the Superconducting State in CuCo${}_2$S${}_4$: Evidence for an Intermediate-Coupling Fully Gapped Superconductor

Abstract

The thiospinel compound CuCo${}_2$S${}_4$ provides an attractive platform for exploring superconductivity in transition-metal chalcogenide spinels. Here, we report the first microscopic investigation of the superconducting state in CuCo${}_2$S${}_4$ using muon spin rotation and relaxation ($\mu$SR) measurements, complemented by magnetization and heat-capacity experiments. The temperature dependence of the superconducting depolarization rate obtained from transverse-field $\mu$SR measurements indicates a fully gapped superconducting order parameter. The extracted gap ratio $2\Delta (0)/(k_{\mathrm{B}}{T}_{\mathrm{SC}})=3.95(2)$ exceeds the BCS weak-coupling value of 3.53, placing CuCo${}_2$S${}_4$ in the intermediate electron-phonon coupling regime. Zero-field $\mu$SR measurements were performed to probe possible time-reversal symmetry breaking (TRSB) in the superconducting state. Within the experimental resolution, no additional spontaneous internal magnetic fields are observed below $T_c$. However, due to the presence of a ferromagnetic impurity phase and the associated fast-relaxing signal component, the sensitivity of the present measurements to weak spontaneous fields is reduced. Consequently, while no evidence for TRSB is detected, its existence cannot be definitively ruled out. Overall, our combined thermodynamic and $\mu$SR results demonstrate that CuCo${}_2$S${}_4$ exhibits a fully gapped superconducting state with intermediate coupling strength, consistent with conventional $s$-wave superconductivity in this cobalt-based thiospinel system.