Microscopic investigation of the superconducting state in CuCo₂S₄: Evidence for an intermediate-coupling fully gapped superconductor

The thiospinel compound CuCo₂S₄ provides an attractive platform for exploring superconductivity in transition-metal chalcogenide spinels. Here, we report the first microscopic investigation of the superconducting state in CuCo₂S₄ using muon spin rotation and relaxation (μSR) measurements, complemented by magnetization and heat-capacity experiments. The temperature dependence of the superconducting depolarization rate obtained from transverse-field μSR measurements indicates a fully gapped superconducting order parameter. The extracted gap ratio 2Δ(0)/(k_BT_SC)=3.95(2) exceeds the BCS weak-coupling value of 3.53, placing CuCo₂S₄ in the intermediate electron–phonon coupling regime. Zero-field μSR 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_SC. 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 μSR results demonstrate that CuCo₂S₄ exhibits a fully gapped superconducting state with intermediate coupling strength, consistent with conventional s-wave superconductivity in this cobalt-based thiospinel system.