1 Introduction

The discovery of superconductivity in LaFeAsO1-xFx with superconducting transition temperature (Tc) about 26 K opens up a new route for both searching high-temperature superconductor and probing their mechanism [1]. Tetragonal FeSe is an iron-based superconductor with the simplest layered structure. Its Tc ~9 K [2] can be obviously enhanced to 37 K under high pressure [3], and over 40 K by intercalating space layers between the FeSe layers [4, 5]. Meanwhile, bulk FeSe exhibits a structural transition at 87 K without a long-range magnetic order at ambient pressure [6]. The physical properties of FeS and FeTe are significantly different from FeSe, although they display the same anti-PbO structure. FeS was synthesized by hydrothermal method with Tc ~ 4.5 K [7] and remained its tetragonal structure from room temperature to Tc [8]. High pressure or chemical intercalation provides limited contribution to superconductivity, probably due to its peculiar structural characteristics and topology of Fermi surface [9,10,11,12,13,14]. Pure FeTe is non-superconducting, but exhibits antiferromagnetic ordering around 70 K [15]. However, the doping among them can obviously regulate Tc, and shows rich physical properties.

A lot of previous work has been focused on the isovalent S doping in FeSe, which is equivalent to internal positive chemical pressure. The nematic order is gradually suppressed by S doping in FeSe1-xSx and a non-magnetic nematic quantum critical point (QCP) appears at x ~ 0.17. However, these samples synthesized by chemical vapor transport (CVT) [16, 17] or solid state reaction [18, 19] were limited to the low sulfur content of x < 0.29, which hindered the study of high sulfur doping region. The successful synthesis of FeS single crystal by the hydrothermal method can provide reference for the growth of FeSe1-xSx [7]. Recently, a series of FeSe1-xSx superconducting single crystals were prepared by the same method, especially the high-S doping region (0.3 ≤ x ≤ 1) for the first time [20]. The complete phase diagram exhibits presents a dome-shaped behavior of anomalously resistive characteristic temperature T∗ competing with superconductivity in the moderate-S doping region, resulting from the weak localization effect or possible magnetic transition.

According to isovalent substitution of Se, accompanying with the suppression of the antiferromagnetic ordering, non-superconducting FeTe could generate superconductivity under internal positive chemical pressure. The maximum value of Tc can reach up to 14 K when x = 0.6 in FeSe1-xTex [21]. Recently, the high-quality FeSe1-xTex (0 ≤ x ≤ 0.5) single crystals were grown by the self-flux method, which addresses the lack of single crystals in the phase separation region, and Tc exhibits a minimum value at x = 0.2 [22]. Thus, a complete doping phase diagram of FeSe1-xTex (0 ≤ x ≤ 1) was established. Similarly, a partial substitution of S by Te can also induce superconductivity with Tc around 10 K. However, the superconducting volume fraction of FeS1-xTex (x = 0.8, 0.9) was less than 20% [23]. Meanwhile, it is difficult to synthesize FeS1-xTex single crystals with higher sulfur content by solid state reaction due to the low solubility limit of S for the Te [24]. The preparation of high-quality FeS1-xTex single crystals with S-rich part is still a great challenge until now. Therefore, it is desirable to investigate how the transport properties of FeS evolve with the larger ion radius of Te substitutes the S site.

In this work, a series of FeS1-xTex (0 ≤ x ≤ 0.15) single crystals were successfully synthesized by a hydrothermal method for the first time. We find that the superconductivity of FeS is continuously suppressed upon Te doping. Furthermore, the field-dependent of Hall resistivity ρxy evolves from non-linear to linear behavior at low-temperature region with Te substitution, and accompanied by an obvious reduction of magnetoresistance (MR). All these results can be explained by introducing more impurity scattering. The negative values of RH for FeS1-xTex reveal that the conduction is dominated by electron-like charge carriers.

2 Experimental Section

The single crystals of FeS1-xTex were synthesized by de-intercalation of K+ from K0.8Fe1.6(S1-xTex)2 using a hydrothermal method. The precursors of K0.8Fe1.6(S1-xTex)2 single crystals with x = 0, 0.06, and 0.13 were grown by a self-flux method. Stoichiometric mixtures of K, Fe, S, and Te were sealed in an evacuated quartz tube. All steps were carried out in an argon-filled glove box with the water and oxygen content less than 0.1 ppm. The samples were slowly heated to 1070 °C and kept at this temperature for 10 h, then slowly cooled down to 750 °C at a rate of 3 K/h, and then followed by the furnace cooling. The hydrothermal reactions were performed in a Teflon-lined stainless steel autoclave with Teflon liners (25 mL). One gram of Fe powder (Aladdin Industrial, 99.99% purity), 0.42 g thiourea (Aladdin Industrial, 99.9% purity), 0.1 g Na2Te (which was prepared mixed by elements of Na and Te in a molar ratio of 2:1, loaded into an aluminum crucible, sealed in an evacuated quartz tube, and heated at 700 °C for 24 h), a certain amount of NaOH (Aladdin Industrial, 99% purity), and several pieces of K0.8Fe1.6(S1-xTex)2 (x = 0, 0.06, 0.13) crystals were added into 10 mL de-ionized water. The autoclave loaded with the mixture solution was tightly sealed and heated at 130 °C for 3 days to ensure the K release and Fe introduction. Silver colored FeS1-xTex single crystals were obtained by washing the powder with de-ionized water.

The single crystal X-ray diffraction (XRD) data were performed using Rigaku diffractometer with Cu-Kα radiation. The average stoichiometries of Fe, S, and Te of the single crystal samples were determined from energy-dispersive X-ray spectroscopy (EDX) analysis. The actual Te content x was obtained by EDX to be 0, 0.02, 0.03, 0.04, 0.05, 0.11, and 0.15, respectively. No trace of K element is detected for all single crystals, indicating the interlayer K ions are completely released from the K0.8Fe1.6(S1-xTex)2 substrates. Electrical resistivity and magnetic measurements were measured on a Quantum Design Physical Property Measurement System (PPMS) and the equipped VSM option. The Hall resistivity and magnetoresistance were measured on the same single crystal using the six-lead method with the applied field parallel to the c-axis and perpendicular to the applied current.

3 Results and Discussion

Figure 1 a shows the XRD patterns of FeS1-xTex (0 ≤ x ≤ 0.15) single crystals. Only (00l) diffraction peaks can be detected, indicating good c-axis orientation. All (00l) peaks can be well indexed by the tetragonal cell structure with P4/nmm space group [25, 26]. As expected, all of the diffraction peaks shift systematically to lower degrees with the increasing of Te concentration due to the larger ionic radius of Te2− than S2−. The corresponding lattice constant c as a function of Te content x is plotted in Fig. 1 b, and it is found that the lattice constant c increases monotonically with the increasing of Te content, indicating that the Te atom is successfully incorporated into the crystal lattice.

Fig. 1
figure 1

a The typical XRD patterns for FeS1-xTex (0 ≤ x ≤ 0.15) single crystals. b The lattice parameter c plotted as a function of the doping concentration x

Full size image

Figure 2 a presents the temperature dependence of the normalized in-plane resistivity ρ(T)/ρ(300 K) of FeS1-xTex single crystals for different doping levels. All of the resistivity reduce monotonically with lowering down of temperature, which exhibits a strongly metallic conductivity. For undoped FeS single crystal, an abrupt resistivity drop and zero resistivity can be observed obviously at Tc = 4.6 K. Upon Te doping, Tc is gradually suppressed from 4.6 K for x = 0, to 4 K for x = 0.02, 3.3 K for x = 0.03, 2.8 K for x = 0.04, and 2.5 K for x = 0.05. The enlarged view of the resistivity in the region of superconducting state is shown in Fig. 2 b. The small superconducting transition width, ΔTc < 0.5 K, shows the excellent quality of our samples. With the further doping, superconductivity is finally killed when x > 0.05, and it do not appear again until x = 0.15. The normal-state resistivity in the vicinity of Tc provides important information on the superconducting properties. In order to gain more insight into the doping effect, we analyze all the normal-state resistivity ρ(T) in low-temperature region by fitting with a power law ρ(T) = ρ0 + ATn, where ρ0 is the residual resistivity, and A and n are the temperature coefficient and the exponent, respectively. In addition, the value of RRR, which is defined as ρ(300 K)/ρ0 and describes the strength of disorder scattering in samples. The RRR values and residual resistivity ρ0 of superconductivity region are plotted in Fig. 2 c. By fitting the resistivity curve, we find that the value of exponent n fluctuates around 2 for all the samples, which is expected for a conventional metal described by Landau Fermi-liquid theory similar with FeS single crystal. Nevertheless, RRR decreases from 48 in undoped FeS single crystal to 11 at x = 0.05, while residual resistivity ρ0 shows the opposite behavior with increasing Te doping. All the characteristics show that the doping of Te leads to more disorder that acts as the impurity scattering center. The superconducting transitions can also be seen in the temperature dependence of the magnetic susceptibility measurements with the zero-field-cooled (ZFC) and field-cooled (FC) modes, as shown in the Fig. 2 d. The onset of the diamagnetism is almost consistent with Tc determined from resistivity measurement. The superconducting shielding fractions are close to 100%, indicating the bulk superconductivity and the high quality.

Fig. 2
figure 2

a Temperature dependence of in-plane resistivity (normalized by corresponding values at T = 300 K) for FeS1-xTex (x = 0, 0.02, 0.03, 0.04, 0.05, and 0.11) single crystal samples. b An enlarged view of the resistivity at low-temperature range for FeS1-xTex with x = 0, 0.02, 0.03, 0.04, and 0.05. c The residual resistivity (ρ0) and the residual resistance ratio (RRR) as a function of Te content x in superconductivity region. d DC magnetization of FeS1-xTex (x = 0, 0.02, 0.03) single crystals under 5 Oe

Full size image

Based on the resistivity and magnetization measurement, we establish the doping phase diagram of FeS1-xTex single crystals, as shown in Fig. 3. For comparison, the corresponding data of FeS1-xTex (1 ≤ x ≤ 0.88) single crystals taken from Ref [27] are also included. For the rich-Te region, the long-ranged AFM phase TN gradually decreases from 70 K with increasing of S doping, and it coexists with the region of the superconducting phase (SC-II) between 0.95 and 0.89 [27], exhibiting a common property of the iron-based superconductors [22, 28]. However, the phase diagram for x < 0.88 is restricted because of the solubility limitation of S. For the rich-S region on the right, superconducting (SC-I) is gradually suppressed from 4.6 K, exhibiting an approximate linear dependence on the Te content. Considering the whole phase diagram of FeS1-xTex, we are surprised to find that the second superconducting phase (SC-II) appears in the high Te-doped region after the SC-I is suppressed until disappears. The similar phenomena of the reemerged second superconducting phase often occurred in many iron-based superconductors under high pressure, such as FeS [29], KxFe2-ySe2 [30], and (Li1-xFex)OHFeSe [31], although Te doping provides the negative chemical pressure.

Fig. 3
figure 3

The doping phase diagram of FeS1-xTex single crystals. The blue solid squares and the red solid circles represents TN and Tc, respectively. The FeS1-xTex single crystals with low-S doping region were reported by a previous report [27]

Full size image

In order to obtain more information about the properties of carrier transport by Te doping, the Hall resistivity ρxy up to 9 T were measured at various temperatures. Hall resistivity ρxy is defined as ρxy(H) = [ρxy(+H) − ρxy(−H)]/2. The field-dependent Hall resistivity for four typical selected samples FeS, FeS0.98Te0.02, FeS0.95Te0.05, and FeS0.89Te0.11 single crystals are shown in Fig. 4 a–d, respectively. For FeS, the ρxy curves exhibit clear non-linear field-dependent behavior at low-temperature region, which is a signature of the multiband effect. With Te doping, this non-linear behavior is gradually suppressed and linear field-dependent behavior is recovered, which means single band dominates the electric conduction. For a single-band system, the Hall coefficient RH is only dependent on the charge density, and exhibits weak temperature dependence. However, mobility should be considered in the multiband system. According to the two-band model, the Hall coefficient RH at low fields can be expressed by \( {R}_{\mathrm{H}}=\left({n}_{\mathrm{h}}{u}_h^2-{n}_{\mathrm{e}}{u}_{\mathrm{e}}^2\right)/\left[e{\left({n}_{\mathrm{h}}{u}_{\mathrm{h}}+{n}_{\mathrm{e}}{u}_{\mathrm{e}}\right)}^2\right] \) [32], where uh(ue) and nh(ne) are the mobility and the charge density of holes (electrons), respectively. Te doping introduces more impurity scattering centers, which reduce the mobility of carriers, and especially the Hall conduction contribution from small band with high mobility. In consequence, multiband effect is suppressed and the singe band effect is recovered gradually. The temperature dependence of RH is shown in Fig. 5, where RH = ρxy/H is determined by the linear part below 1 T. The negative RH of FeS1-xTex below 200 K indicates μe > μh, meaning that the conduction is dominated by electron-like charge carriers. The large change of RH for FeS in the whole temperature range is more obvious than that of doping samples due to the multiband effect.

Fig. 4
figure 4

Magnetic field dependence of the Hall resistivity for a x = 0, b x = 0.02, c x = 0.05, and d x = 0.11 single crystals at various temperatures

Full size image
Fig. 5
figure 5

The temperature dependence of Hall coefficient RH for FeS1-xTex samples. RH is determined by RH = ρxy/H at low fields

Full size image

As we all know, the information of the Fermi surface and the carrier scattering can be obtained by measuring the MR, which is defined as MR = ∆ρ/ρ(0) = (ρ(H) − ρ(0))/ρ(0) . We have measured the field dependence of the MR up to 9 T at various temperatures, and the temperature dependence of MR for FeS1-xTex samples are plotted in Fig. 6 a–d. It is evident that the large value of MR for FeS is suppressed with gradually increasing Te concentration. This result is quite similar to that in S -oped FeSe single crystal [17], where the value of MR for FeSe is obviously larger than that of FeSe0.86S0.14. The similar work has also been reported in α-WP2 single crystals, where the highest RRR exhibits the largest MR [33]. Therefore, the decrease of MR could be attributed to the disorder. Unlike the single-band system, the mobility should be considered in the multiband system, and the mobility is known to be inversely proportional to ρ0 [34]. From Fig. 2 c, we can observe that ρ0 increases with Te doping, which indicates that the mobility decreases by doping. Our results demonstrate that Te doping introduces more impurities scattering, which is consistent with the suppression of the MR value and the non-linear field dependence of ρxy at low temperatures.

Fig. 6
figure 6

Temperature-dependent magnetoresistance at various temperatures for a x = 0, b x = 0.02, c x = 0.05, and d x = 0.11 single crystals

Full size image

For many metallic materials with symmetrical Fermi surface, Kohler’s law is always obeyed. At different temperatures, the MR can be scaled by ∆ρ/ρ0 = f(H/ρ0) = f(ωcτ), known as Kohler’s rule [35]. Figure 7 a–d show the MR as functions of μ0H/ρ(0) at x = 0, 0.02, 0.05, and 0.11, respectively. Clearly, all the curves superimpose into one curve, indicating that Kohler’s rule is obeyed and the scattering rate is isotropic in the Fermi surface [17]. However, Kohler’s law was obviously violated below Ts in FeSe1-xSx (x = 0, 0.14) [17]. The violation of Kohler’s rule may be related to the multiband effect or the anisotropic scattering on the Fermi surface [36, 37].

Fig. 7
figure 7

Kohler’s plots for a x = 0, b x = 0.02, c x = 0.05, and d x = 0.11 single crystals at various temperatures

Full size image

4 Conclusion

In summary, we have investigated the transport properties of FeS1-xTex (0 ≤ x ≤ 0.15) single crystals grown by hydrothermal method. Due to the larger ionic size of Te relative to that of S, the Te substitution leads to the increase of lattice constant c. Magnetic and electric transport properties indicate that Tc is obviously suppressed after Te doping, which also leads to the evolution of Hall coefficient RH from non-linear to linear behavior at low-temperature region, and accompanied by an obvious suppression of the MR. These results can be explained by doping-induced the impurity scattering. The negative RH in the whole temperature range reveals that the conduction is dominated by electron carriers. More advanced experimental synthesis methods need to be explored to further study the physical properties of samples in the unknown restricted region.