Bulk superconductivity and Pauli paramagnetism in nearly stoichiometric CuCo₂S₄

The discoveries of superconductivity (SC) in the complex copper oxide [1] and the iron-based pnictide [2] stimulate enthusiasm to search for SC especially in late 3d-transition-metal (Fe, Co, Ni, and Cu) compounds [3, 4, 5, 6, 7]. Among them, the Co-based superconductors are very limited so far. One example is the cobalt oxyhydrate Na_xCoO${}_{2}\cdot y$H₂O ($x\approx 0.35,y\approx 1.3$), which shows SC at $T_{\mathrm{c}}\approx$ 4.5 K [8]. The Co-based thiospinel CuCo₂S₄ shows similarities with Na_xCoO${}_{2}\cdot y$H₂O in the Co coordination, geometrical frustration, and formal Co valence. However, it is not clear whether CuCo₂S₄ superconducts or not. Besides, the magnetism of CuCo₂S₄ also remains elusive up to present.

Earlier studies in 1960s suggested Pauli paramagnetism in CuCo₂S₄ [9, 10], and no superconducting transition was observed down to 0.05 K [11]. In 1990s, however, it was reported that CuCo₂S₄ shows a Curie-Weiss (CW) paramagnetism with an effective magnetic moment of 0.89 $\mu_{\mathrm{B}}$ per formula unit (f.u.) [12]. A cusp in the magnetic susceptibility appears at $T_{\mathrm{N}}=$ 18 K, which was attributed to an antiferromagnetic spin ordering. In a multiphasic sample with the nominal composition of Cu_1.5Co_1.5S₄, SC or superconductor-like behavior was observed with an onset transition temperature of $T_{\mathrm{c}}^{\mathrm{onset}}=$ 4.0 K and a zero-resistance temperature of $T_{\mathrm{c}}^{\mathrm{zero}}=$ 2.3 K. Investigations on the ⁶³Cu and ⁵⁹Co NMR suggested a gapless superconducting state as well as antiferromagnetic spin correlations, and SC was considered to be in line with the growth of antiferromagnetic spin correlation [13]. Contrastingly, later NMR study on the Co-rich series samples of (Cu_xCo_1-x)Co₂S₄ indicated a full superconducting gap without long-range magnetic ordering for CuCo₂S₄ [14]. It was concluded that SC and the antiferromagnetic spin correlation are associated with the Co-3d and Cu-3d holes, respectively.

One of the present authors (G.-H.C.) and coworkers [15] attempted to reproduce SC in CuCo₂S₄ in 2003. However, no SC was observed above 1.8 K in the single-phase sample of CuCo₂S₄, although signature of SC at $T_{\mathrm{c}}=$ 3.5 K was detected in a multiphasic sample. Aito and Sato [16] reported the resistivity data of five CuCo₂S₄ samples from different batches. Two of them showed a superconducting transition, and the higher $T_{\mathrm{c}}$ value is 3.8 K. Fang et al. [17] synthesized an unusual K-doped sample Cu_1.3K_0.2Co_1.5S₄ which showed SC at 4.4 K together with a CW-like susceptibility but without any antiferromagnetic transition down to 9 K. A very recent work [18] showed absence of SC with a weak antiferromagnetic transition at about 4 K in CuCo₂S₄. In a word, the previous reports on CuCo₂S₄ appear to be highly dispersive and even contradictive. To our knowledge, evidence of bulk SC with specific-heat measurements has not been reported so far in the Cu-Co-S system.

The contradictive results above strongly suggest that the physical properties are sensitive to the synthesis of samples, and a controlled preparation of nearly stoichiometric samples of CuCo₂S₄ is crucial to clarify the intrinsic properties. Previous studies showed difficulties in obtaining desired samples of CuCo₂S₄ [12, 19, 20, 21, 15, 16]. They were commonly synthesized by direct reacting copper and cobalt powders with sulfur in a sealed evacuated silica tube at an elevated temperatures. While relatively low reaction temperatures (500 ^∘C - 600 ^∘C) were suggested for the preparation of monophasic CuCo₂S₄ [22], however, a following-up work [19] failed to obtain the single-phase sample. The synthesized sample tends to form CoS₂ impurity, as revealed by the phase-relation study in the Cu-Co-S system [20, 21]. Indeed, later studies [12, 14, 15, 16] also showed presence of the CoS₂ impurity for the reaction temperatures from 500 ^∘C to 800 ^∘C. Note that CoS₂ is a ferromagnet with a Curie temperature of $\sim$120 K [23, 24, 25], which makes it more easily to be detected by the magnetic measurement [15].

Here we report a novel two-step strategy for the controlled synthesis of stoichiometric CuCo₂S₄. First, to minimize the formation of CoS₂ impurity, we prepared sulfur-deficient CuCo₂S_4-δ with $\delta=$ 0.3. Then, the S-deficient sample was sulfurized by annealing in the presence of appropriate amount of sulfur. As a result, the main phase of the annealed sample was found to be nearly stoichiometric CuCo₂S₄. Bulk SC at 4.2 K and Pauli paramagnetism in the normal state were demonstrated in the S-compensated CuCo₂S₄.

Polycrystalline sample of S-deficient CuCo₂S_3.7 was first prepared by high-temperature reactions of the constituent elements in a sealed evacuated silica tube. The source materials were powders of copper (99.997%), cobalt (99.998%), and sulfur (99.999%). The homogenized mixture with the composition of CuCo₂S_3.7 was allowed to fire at 750 ^∘C for 72 hours. This procedure was repeated to improve the quality of the sample. In the second step, the synthesized CuCo₂S_3.7 was sulfurized in the presence of compensatory sulfur (0.35 S/f.u.) by annealing at 450 ^∘C for 144 hours in a sealed evacuated silica ampoule. Note that excess of sulfur was necessary to ensure a full sulfurization. This is because, during the sulfurization, a side reaction that forms CoS₂ always takes place, which additionally consumes sulfur. Besides, in order to quantize the amount of the CoS₂ impurity in the sulfurized sample, we additionally prepared CoS₂ by reacting Co with S in an evacuated silica tube. The sample is of single phase with the lattice constant of $a=5.535$ Å (consistent with the previous report [23]), as determined by the powder x-ray diffractions (XRD).

Powder XRD were carried out using a PANalytical diffractometer (Empyrean Series 2) with a monochromatic Cu-$K_{\alpha 1}$ radiation. The crystal structure were refined by a Rietveld analysis using the GSAS+EXPGUI package [26]. The sulfur content in the crystallites was examined by energy-dispersive x-ray spectroscopy (EDS, Oxford Instruments X-Max) equipped in a scanning electron microscope (SEM, Hitachi S-3700N).

The electrical resistivity and specific heat were measured on a Quantum Design Physical Properties Measurement System, and the magnetic properties were measured on a Quantum Design Magnetic Property Measurement System. The resistivity measurement employed a standard four-terminal method. The heat-capacity measurement utilized a thermal relaxation technique. In the magnetic measurements, the applied magnetic fields were set to be 20 Oe and 10,000 Oe, respectively, to detect SC and to study the normal-state magnetism. In the case of the low-field measurements, both zero-field-cooling and field-cooling protocols were employed.

Figure 1(a) shows the XRD profile for the sulfur-deficient sample of CuCo₂S_3.7. Most of the reflections can be well indexed with a face-centered cubic unit cell of the thiospinel. As is seen in the inset, no reflections associated with CoS₂ are detectable, while tiny amount of Cu₂S is possibly presented. Therefore, with a lack of sulfur we succeeded in avoiding the appearance of the CoS₂ secondary phase. The Rietveld refinement ($R_{\mathrm{wp}}$ = 2.3% and $\chi^{2}$ = 1.31) confirms the normal spinel structure with $a=9.4544(1)$ Å and $u=0.3865(1)$ for the main phase. Note that the lattice constant is the smallest among those reported previously for CuCo₂S₄ [$9.461(2)$ Å [22], $9.478(5)$ Å [19], and $9.472(1)$ Å [20]]. This may be attributed the apparent sulfur deficiency and/or the partial substitution of Cu by Co (hereafter denoted as Co/Cu substitution) [14]. The latter is implied by the presence of small amount of Cu₂S. As a matter of fact, the Rietveld refinement does not support a significant sulfur vacancy.

The XRD pattern of the sulfurized CuCo₂S₄ is displayed in Fig. 1(b). The main phase remains to be the cubic thiospinel, although small amount of CoS₂-like phase emerges. With the two-phase Rietveld refinement ($R_{\mathrm{wp}}$ = 2.2% and $\chi^{2}$ = 1.13), the weight percentage of the CoS₂-like impurity was determined to be 14.8(6)%. The lattice constant of the pyrite phase is refined to be 5.538(1) Å, which is slightly larger than that of CoS₂ (5.534 Å [23]), suggesting that Cu is slightly incorporated. The structural parameters of the main phase were fitted to be $a=9.4750(2)$ Å and $u=0.3851(1)$. The $a$ axis is remarkably larger than that of the sulfur-deficient CuCo₂S_3.7, suggesting a successful sulfurization.

The two samples above were examined by SEM observations in combination with the EDS measurements. As shown in Fig. 2(a), the crystallites of S-deficient CuCo₂S_3.7 are similar in shape. The sulfur content, measured on the basis of the Co content, is consistent with the nominal composition. However, the Cu content is substantially lower than the nominal one. The result suggests that the real composition of the thiospinel phase is something like (Cu_1-x-yCo${}_{x}\Box_{y}$)Co₂S_4-δ. The SEM image of the sulfurized sample [Fig. 2(b)] shows additional round-shape crystallites which were identified to be slightly Cu-doped CoS₂ (1-2% Cu) by the EDS analysis. Furthermore, the sulfur deficiency is fully compensated, and the Cu content is also increased, as is indicated by the atomic ratio measured. Therefore, we conclude that the sulfurized sample mainly ($\sim$85% by weight) contains nearly stoichiometric CuCo₂S₄.

Figure 3(a) shows the temperature dependence of magnetic susceptibility under a magnetic field of $H=$ 10 kOe for the sulfur-deficient CuCo₂S_3.7. The magnetic susceptibility is nearly temperature independent at high temperatures. No anomaly at $\sim$120 K can be seen, indicating free of the ferromagnetic impurity of CoS₂. There is an upturn tail at low temperatures. Fitting of the data with the CW formula, $\chi=\chi_{0}+C/(T-\theta_{\mathrm{CW}})$, yields a temperature-independent term of $\chi_{0}$ = 0.00047 emu mol-f.u.^-1, a Curie constant of $C$ = 0.0043 emu K mol-f.u.^-1, and a paramagnetic CW temperature of $\theta_{\mathrm{CW}}=-1.9$ K. Such a small value of the Curie constant (corresponding to 0.13 $\mu_{\mathrm{B}}$/Co) is commonly originated from tiny paramagnetic impurities. Additionally, the positive temperature coefficient of susceptibility at high temperatures, shown in the inset of Fig. 3(a), also rules out the possible CW-type paramagnetism in CuCo₂S_3.7.

Figure 3(b) shows the temperature dependence of magnetization (in the unit of $\mu_{\mathrm{B}}$/f.u.) of the sulfurized CuCo₂S₄ under the same magnetic field of $H=$ 10 kOe. A ferromagnetic transition is seen at about 120 K, which is attributed to the ferromagnetic impurity of slightly Cu-doped CoS₂ that was identified by the XRD experiment above. To quantify the amount of (Co,Cu)S₂ independently, the magnetization data of pure CoS₂ are shown for comparison. One sees that the Curie temperature of (Co,Cu)S₂ is slightly lower than that of CoS₂ due to the Cu incorporation. The low-temperature saturation magnetization is about 19% of that CoS₂. At the same time, the high-temperature magnetic susceptibility basically coincides. Since the Cu content in (Co,Cu)S₂ is only 1-2% according to the EDS measurement, the amount of the (Co,Cu)S₂ impurity should be also around 19%, basically consistent with the XRD result above.

The high-temperature magnetic susceptibility data are highlighted in the inset of Fig. 3(b), which shows a CW-type paramagnetism. The CW paramagnetism is attributed to the (Co,Cu)S₂ impurity, because the magnetic susceptibility of the sulfurized CuCo₂S₄ shows a similar temperature dependence with that of 18.8% CoS₂. The magnetic susceptibility of S-compensated CuCo₂S₄ phase can be roughly obtained by a simple substraction. The result indicates a small value of magnetic susceptibility that is almost temperature independent. Therefore, CuCo₂S₄ should be intrinsically Pauli paramagnetic. Nevertheless, the accurate value of the Pauli-paramagnetic susceptibility cannot be reliably extracted not only because of the influence of the magnetic impurity, but also due to the possible Van Vleck paramagnetism involved [10]. According to the bandstructure calculation of CuCo₂S₄ which gives the density of states at Fermi level of 31.88 states/eV/f.u. [27], the calculated Pauli-paramagnetic susceptibility is derived to be $\chi_{\mathrm{P}}=\mu_{\mathrm{B}}^{2}N(E_{\mathrm{F}})=1.03\times 10^{-3}$ cm³/mol.

Figure 4 shows the low-temperature susceptibility data for the samples of CuCo₂S_3.7 as well as sulfurized CuCo₂S₄. The S-deficient CuCo₂S_3.7 exhibits low values of magnetic susceptibility, and no signal of SC can be detected down to 1.8 K. By contrast, the sulfurized sample shows a steep decrease in the magnetic susceptibility at 4.2 K, suggesting a superconducting transition. Note that the high value of the susceptibility above $T_{\mathrm{c}}$ is due to the ferromagnetic impurity (Co,Cu)S₂. The large magnitude of the ZFC diamagnetism (exceeding $-100$%) below $T_{\mathrm{c}}$ could also be due to the extra magnetic field generated by the ferromagnetic (Co,Cu)S₂. The inset shows the field dependence of magnetization at 2 K for the superconducting sample. An extremely type-II superconductivity with $H_{\mathrm{c2}}\gg H_{\mathrm{c1}}$ can be concluded. As expected also, the ferromagnetic signal from (Co,Cu)S₂ is superposed on the superconducting loop.

Figure 5(a) shows the temperature dependence of resistivity for the sulfur-deficient CuCo₂S_3.7 and the sulfurized CuCo₂S₄. Both samples show a metallic behavior, yet the sulfurized CuCo₂S₄ sample exhibits a lower room-temperature resistivity with a higher residual resistivity ratio (RRR). The RRR values are 1.4 and 6.4 for CuCo₂S_3.7 and CuCo₂S₄, respectively. Although there are about 19% (Co,Cu)S₂ impurity in the sulfurized CuCo₂S₄ sample, no anomaly at $\sim$120 K associated with the ferromagnetic transition can be detected. At lower temperatures, while no superconducting transition appears down to 1.8 K for CuCo₂S_3.7, a sharp superconducting transition is seen at $T_{\mathrm{c}}^{\mathrm{onset}}=$ 4.3 K for the S-compensated CuCo₂S₄. The observation of SC in relation with a high RRR value was also reported previously [16]. This could suggest that the nonmagnetic scattering, measured by the residual resistivity, may destroy SC in the system, resembling the scenario in Sr₂RuO₄ [28] and K₂Cr₃As₃ [29]. Besides, the low-temperature resistivity of CuCo₂S₄ essentially shows a $T^{2}$ temperature dependence (see the inset), suggesting dominant electron-electron scattering in the system.

The resistive superconducting transitions are more clearly shown in Fig. 5(b). One sees that the superconducting transition shifts to lower temperatures with increasing magnetic fields. Using the criterion of 50% normal-state resistivity just above $T_{\mathrm{c}}$ for determining $T_{\mathrm{c}}(H)$, the upper critical magnetic fields $H_{\mathrm{c2}}$ can be extracted. The resultant $H_{\mathrm{c2}}(T)$ data are shown in the inset of Fig. 5(b), which shows an essentially linear temperature dependence down to 0.42$T_{\mathrm{c}}$. This result suggests dominant orbital pair-breaking mechanism over a paramagnetic pair-breaking mechanism. The zero-temperature upper critical field is estimated to be $H_{\mathrm{c2}}(0)=$ 24.6 kOe from the linear extrapolation, far below the Pauli-paramagnetic limit $H_{\mathrm{P}}\approx$ 77 kOe. The coherence length can thus be derived as $\xi_{0}=$ 11.6 nm using the relation $H_{\mathrm{c2}}(0)=\Phi_{0}/[2\pi\xi(0)^{2}]$, where $\Phi_{0}(=2.07\times 10^{-15}$ Wb) denotes a magnetic flux quantum.

Figure 6(a) shows the temperature dependence of specific heat for the sulfurized CuCo₂S₄ sample. The specific heat tends to approach the value of $3NR=$ 174.6 J K^-1 mol^-1 at high temperatures, in accordance with the Dulong-Petit law. No obvious anomaly is seen at around 120 K where the CoS₂ impurity undergoes a ferromagnetic transition. This observation verifies that the CoS₂ impurity is the minor phase. As is seen in the inset of Fig. 6(a), at low temperatures, a remarkable specific-heat jump is observable at around 4 K, confirming bulk SC in the sulfurized sample which dominantly contains nearly stoichiometric CuCo₂S₄.

Figure 6(b) shows the plot of $C/T$ versus $T^{2}$, from which the low-temperature electronic specific heat can be separated out. The linear fit gives an intercept of $\gamma$ = 32.2 mJ K^-2 mol-f.u.^-1, corresponding to a bare density of states of $N(E_{\mathrm{F}})=3\gamma/(\pi^{2}k_{\mathrm{B}}^{2})=$ 13.6 states/eV/f.u., consistent with the electronic structure calculation [27]. Note that the Sommerfeld constant of CoS₂ is 21 mJ K^-2 mol^-1 [24, 25], somewhat smaller than the above $\gamma$ value, yet it turns out to be larger on the basis of Co content. Furthermore, the CoS₂ impurity is the minor phase after all. Therefore, the Sommerfeld coefficient of the CuCo₂S₄ phase will not change very much even if corrections due to the existence of CoS₂ impurity could be reliably made. Note that the

Assuming the $\gamma$ value of 32.2 mJ K^-2 mol-f.u.^-1 and with the electronic specific heat of $C_{\mathrm{e}}=C-\beta T^{3}$, figure 6(c) was plotted using $C_{\mathrm{e}}/(\gamma T)$ and $T/T_{\mathrm{c}}$ as the coordinates. Under the constrain of entropy conservation, i.e. $\int_{0}^{T_{\mathrm{c}}}[(C_{\mathrm{e}}-\gamma T)/T]\mathrm{d}T=0$, a full-gap BCS $\alpha$ model [30] can basically fit the data with $\alpha\equiv\Delta(0)/(k_{\mathrm{B}}T_{\mathrm{c}})=$ 1.5 if a residual electronic specific-heat coefficient of $\gamma_{0}=0.25\gamma$ due to the existence of non-superconducting impurity phase of CoS₂ is taken into account. In this circumstance, the superconducting fraction is fitted to be 77(1)%, which is conversely consistent with $\sim$19% non-superconducting phase.

Here we note that the single-gap BCS model does not account for the data exclusively. Other models with line energy-gap nodes are also applicable. However, the present limited data cannot distinguish which model applies. Interestingly, previous NMR investigations concluded contrasting superconducting properties in the Cu-Co-S system: one suggested a gapless superconducting state [13], the other indicated a full superconducting gap [14]. This discrepancy seems to be due to the big difference in the sample’s quality. Our present specific-heat result excludes the possibility of gapless superconductivity in the nearly stoichiometric sample of CuCo₂S₄. We expect that future measurements of specific-heat, NMR, and other techniques down to lower temperatures with using better samples (with less impurity) will be able to clarify the issue of the superconducting gap.

Above we have clarified that the nearly stoichiometric CuCo₂S₄ thiospinel is a superconductor with Pauli paramagnetism. Now let us comment on the previous dispersive results about “CuCo₂S₄” [11, 12, 15, 16, 18]. They can be accounted for in terms of the deviations from the stoichiometry. The actual composition of the synthesized thiospinel phase should be written as (Cu_1-xCo_x)Co₂S_4-δ (because impurity phases such as CoS₂ and Cu₂S appeared). The S deficiency obviously decreases the hole concentration in (Cu_1-xCo_x)Co₂S_4-δ, which suppresses SC. The Co/Cu substitution (Co²⁺ partially substitutes Cu⁺) not only decreases the hole concentration, but also possibly induces magnetic impurity of Co²⁺ at the Cu site, both of which are detrimental to SC. This could be the main reason for the difficulty to observe SC in the sample with nominally stoichiometric composition. In the Cu-rich sample of “Cu_1.5Co_1.5S₄” [13, 14], however, the Co/Cu substitution at the Cu site is greatly reduced because Co is poor. The possible Cu occupation at the Co site may not destroy SC because of nonmagnetic Cu⁺. Thus SC is easily observed in the Cu-rich samples.

To summarize, with a novel two-step synthesis strategy, we were able to prepare nearly stoichiometric CuCo₂S₄ phase which shows bulk SC at 4.2 K with Pauli paramagnetism in the normal state. We have also revealed that sulfur deficiency and Co/Cu substitution is detrimental to SC, which may explain the contradictive results in previous reports. The result calls for further investigations on the rare Co-based superconductor by optimizing the sample quality (with the CoS₂ impurity as less as possible) and with various measurements down to lower temperatures.

SC in Co-based compounds is very rare. This work corroborates that CuCo₂S₄ is another Co-based superconductor in addition to Na_xCoO${}_{2}\cdot y$H₂O [8]. Albeit of different crystal structures, interestingly, the two systems show many similarities including the $T_{\mathrm{c}}$ value, Co coordination, formal Co valence, and the geometrical frustration. It is of great interest to clarify whether CuCo₂S₄ is an unconventional superconductor [31]. On the other hand, SC is not frequently found in the thiospinel compounds. However, the Cu$M_{2}$S₄ ($M=$ Co, Rh, or Ir) family seem to be the only exception. CuRh₂S₄ was first discovered to be a superconductor in 1967 with $T_{\mathrm{c}}$ = 4.35-4.8 K [11, 32], which was confirmed in 1990s [33]. CuIr₂S₄ [34] itself is not a superconductor, yet it undergoes a metal-insulator transition at 230 K accompanied with a charge ordering as well as a spin dimerization [35]. SC with $T_{\mathrm{c}}$ up to 3.4 K can be induced by the suppression of the metal-insulator transition via Zn/Cu substitution [36, 37]. For the spinel selenides, SC was reported in CuRh₂Se₄ ($T_{\mathrm{c}}=$ 3.5 K [11, 32]) and Cu(Ir_0.8Pt_0.2)₂Se₄ ($T_{\mathrm{c}}=$ 1.76 K [38]). Therefore, one may expect that CuCo₂Se₄ could be also a superconductor if it can be synthesized with the stoichiometric composition.