Bulk superconductivity and Pauli paramagnetism in nearly stoichiometric CuCo${}_2$S${}_4$

It has long remained elusive whether CuCo${}_2$S${}_4$ thiospinel shows bulk superconductivity. Here we clarify the issue by studying on the samples of sulfur-deficient CuCo${}_2$S${}_{3.7}$ and sulfurized CuCo${}_2$S${}_4$. The sample CuCo${}_2$S${}_{3.7}$ has a smaller lattice constant of $a=9.454$ {\AA}, and it is not superconducting down to 1.8 K. After a full sulfurization, the $a$ axis of the thiospinel phase increases to 9.475 {\AA}, and the thiospinel becomes nearly stoichiometric CuCo${}_2$S${}_4$, although a secondary phase of slightly Cu-doped CoS${}_2$ forms. Bulk superconductivity at 4.2 K and Pauli paramagnetism have been demonstrated for the sulfurized CuCo${}_2$S${}_4$ by the measurements of electrical resistivity, magnetic susceptibility, and specific heat.