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

It has long remained elusive whether ${\mathrm{CuCo}}_2{\mathrm{S}}_4$ thiospinel shows bulk superconductivity (SC). Here we clarify the issue by studying the samples of sulfur-deficient ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$ and sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$. The sample ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$ has a smaller lattice constant of $a=9.454$ Å, 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 Å, and the thiospinel becomes nearly stoichiometric ${\mathrm{CuCo}}_2{\mathrm{S}}_4$, although a secondary phase of slightly Cu-doped ${\mathrm{CoS}}_2$ forms. Bulk SC at 4.2 K and Pauli paramagnetism have been demonstrated for the sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$ by the measurements of electrical resistivity, magnetic susceptibility, and specific heat.

Figure 1

Powder XRD with the Rietveld refinement profiles for samples of sulfur-deficient ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$ (a) and sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$ (b). The insets (with a logarithmic scale for the intensity) are a close-up of the marked area, which shows the presence of the secondary phases of ${\mathrm{Cu}}_2\mathrm{S}$ and ${\mathrm{CoS}}_2$, respectively, in ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$ and sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$.

Figure 2

Typical SEM images of sulfur-deficient ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$ (a) and sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$ (b). The lower-right insets are the EDS collected with the electron beam focused on the spots marked. Round-shape grains (indicated by arrows) can be seen in (b), which are identified to be lightly Cu-doped ${\mathrm{CoS}}_2$. The atomic ratios are given by the EDS analysis.

Figure 3

Temperature dependence of magnetic susceptibility or magnetization for sulfur-deficient ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$ (a) and sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$ (b). The inset of (a) is a close-up of the high-temperature data, indicating a positive-temperature-coefficient behavior (dashed line). In (b), the magnetization of ${\mathrm{CoS}}_2$ (multiplied by a factor of 18.8%) is plotted for comparison. The inset of (b) compares the magnetic susceptibilities at high temperatures.

Figure 4

Temperature dependence of magnetic susceptibility for sulfur-deficient ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$, as well as sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$, measured under a magnetic field of 20 Oe in both FC and ZFC modes. The inset shows field dependence of magnetization at 2 K for sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$.

Figure 5

(a) Temperature dependence of electrical resistivity ($\rho$) of the polycrystalline samples of sulfur-deficient ${\mathrm{CuCo}}_2{\mathrm{S}}_{3.7}$ and sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$. The inset plots $\rho$ versus $T^2$ in the temperature range from 4.5 to 50 K. (b) Resistive superconducting transitions under increased magnetic fields from which the upper critical fields $H_{\mathrm{c}2}$ were obtained. The inset plots the resultant $H_{\mathrm{c}2}$ as a function of temperature.

Figure 6

Temperature dependence of specific heat for sulfurized ${\mathrm{CuCo}}_2{\mathrm{S}}_4$. The inset of (a) shows a close-up in the low-temperature region. Panel (b) plots $C/T$ as a function of $T^2$, in which a linear fit ($C/T=\gamma +\beta T^2$) is presented for the normal state. Panel (c) shows $C_{\mathrm{e}}/\left(\gamma T\right)$, where $C_{\mathrm{e}}=C-\beta T^3$ denotes the electronic specific heat as a function of the reduced temperature, $T/T_{\mathrm{c}}$. The data basically agree with a full-gap BCS $\alpha$ model [$\alpha \equiv \mathrm{\Delta }\left(0\right)/\left(k_{\mathrm{B}}{T}_{\mathrm{c}}\right)$, where $\mathrm{\Delta }\left(0\right)$ is the anisotropic superconducting gap at zero temperature] [30] assuming 77% superconducting phase and a residual electronic specific-heat coefficient of ${\gamma }_0=0.25\gamma$.