Introduction

The discovery of superconductivity in BiS2-based compounds1,2 such as Bi4O4S3 and REO1-xFxBiS2 has triggered numerous studies focusing on identifying new superconductors featuring a higher transition temperatures (Tc) and elucidating the mechanisms of superconductivity in BiS2-based compounds. Due to the similarity of the crystal structure among the BiS2-based, cuprates and iron-based compounds3,4, BiS2-based compounds have been considered as a new example of layered superconductor family. Thus far, various types of BiS2-based compounds have been synthesized by replacing different blocking layers1,2,5,6,7,8,9,10,11,12,13,14,15,16,17, such as the Bi4O4(SO4)1−x layer, the REO layer (RE: La, Ce, Pr, Nd, and Sm), or the AEF layer (AE: Sr or Eu). Notably, some BiS2-based compounds do not exhibit bulk superconductivity even after electron doping. To induce bulk superconductivity in BiS2-based compounds, various chemical substitutions have been attempted (see review articles)14,18. Among these, the iso-valent substitutions, such as Nd3+ substitutions for La3+ or Se2− substitutions for S2−, were found to be effective for inducing bulk superconductivity. Based on systematic structural analyses, we have revealed that the in-plane chemical pressure is one of the essential parameters that facilitate the emergence of bulk superconductivity in BiCh2-based (Ch: S, Se) systems18,19. By applying in-plane chemical pressure, the local structural disorder in the tetragonal structure is removed, and bulk superconductivity is induced20,21. To induce bulk superconductivity, external pressure effects are also effective22,23,24,25,26,27,28,29,30,31,32. For REO0.5F0.5BiS2 and EuFBiS2, the Tc at ambient condition (~ 2.5 K and ~ 0.5 K) dramatically increase to ~ 10 K under high pressure23,24,25,26, and the origin of the increase in Tc was explained by a structural transition from tetragonal (P4/nmm) to monoclinic (P21/m) at around 1 GPa for LaO0.5F0.5BiS2 and EuFBiS223,24. In spite of the interesting phenomena under high pressure in those BiS2-based compounds, the pressure studies have been performed by electrical resistivity measurements. To the best of our knowledge, only two works have used magnetization as a probe for the pressure studies, which confirmed bulk superconductivity in LaO0.5F0.5BiS2 and EuFBiS2 under high pressure23,24. Therefore, further experiments on how the bulk characteristics of superconductivity could be achieved under pressures are needed. In addition, as summarized above, there are two ways, chemical and external pressure effects, to induce bulk superconductivity. Note that those two bulk superconducting phases have a different crystal structure system of tetragonal (under chemical pressure) and monoclinic (under external pressure). Therefore, in order to further investigate the interplay among superconducting characteristics (Tc and bulk nature), external pressure, and chemical pressure, it is essential to establish a new system where discussion about the relationships among those factors is possible. In this study, to search for a system which enables us to study such relationships, we have studied the chemical and external pressure effects for the Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm) system.

SrFBiS2 is a parent phase of those target materials and a semiconductor with a band gap. The substitution of Sr2+ with RE3+ induces electron carriers in the BiS2 layer, and filamentary superconductivity appears at approximately 2.8 K in La-, Ce-, and Pr-doped compounds12,13,14,15,29,30,31,32. Based on electrical resistivity measurements conducted under high pressures, a considerable increase in Tc was observed in previous pressure experiments22,29,30,31,32. The highest Tc in Sr0.5RE0.5FBiS2 is approximately 10 K, and the pressure dependences of Tc exhibits a sharp increase at the critical pressure (~ 1 GPa). Since there has been no further report on the pressure-induced superconductivity in Sr0.5RE0.5FBiS2, we have studied the superconducting phase diagrams for Sr0.5RE0.5FBiS2 from magnetization experiments under high pressure and discussed the interplay among superconducting characteristics, chemical pressure, and external pressure. Two bulk superconducting phases with a lower Tc (low-P phase) and a higher Tc (high-P phase) were confirmed.

Results

Sample characterization and physical properties at ambient pressure

Figure 1 depicts the powder synchrotron X-ray diffraction (XRD) patterns for Sr0.5La0.5FBiS2. For Sr1-xRExFBiS2 (RE = Ce, Pr, Nd, and Sm), see Supplemental Fig. S1a–d. The crystal structure of the obtained samples was well refined using the Rietveld method. They were well refined using a tetragonal structure with the P4/nmm space group. Small impurity peaks due to REF3 (RE: La, Ce) and Bi2S3 were also detected in the case of the Pr-, Nd-, and Sm-based samples. As shown in Fig. 2, we observed that the lattice constant a decreased with decreasing RE ionic radius; however, the lattice constant c increased under these conditions. The obtained values were in agreement with previous reports12,30,31. The chemical composition ratios of the samples were determined using energy dispersive X-ray spectroscopy (EDX). These results showed that the chemical compositions of the obtained samples were in reasonable agreement with the nominal compositions (Table 1). The electrical resistivity of the samples at ambient pressure was measured down to 1.6 K (Fig. 3). In all the samples, semiconducting behaviour was observed; moreover, the resistivity-temperature (ρ-T) curve indicated a slight increase in ρ on cooling, which implied that the conduction electrons were weakly localized due to the in-plane local disorder in the BiS2 layer18,19,20,21. A superconducting transition was observed at Tc = 2.7, 2.7, 2.6, 2.6, and 2.1 K for RE = La, Ce, Pr, Nd, and Sm, respectively (see the inset of Fig. 3). In addition, a superconducting transition was also observed in the temperature dependence of magnetization, as plotted in Fig. 4. The Tc estimated based on magnetization was in agreement with that obtained based on the resistivity measurements. This is the first study to report on the observation of superconductivity in Sr0.5Nd0.5FBiS2 and Sr0.5Sm0.5FBiS2 under ambient pressure. However, in these samples, the estimated shielding volume fraction was less than 6%. This indicates that chemical pressure effects, which is expected to be generated by the substitution of smaller RE such as Nd and Sm, are insufficient to induce bulk superconductivity in the Sr1−xRExFBiS2 system. To obtain bulk superconductivity, which is essentially important for describing intrinsic superconducting properties, we applied external pressure on the samples.

Figure 1
figure 1

Synchrotron powder XRD patterns for Sr0.5La0.5FBiS2. Symbol of + indicates the impurity of LaF3.

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Figure 2
figure 2

Dependences of the lattice constants a and c as a function of the RE3+ (RE: La, Ce, Pr, Nd, and Sm) ionic radius.

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Table 1 Actual composition (mol%) from the EDX analysis against the nominal composition (mol%). Fluorine amount is regarded as 1.
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Figure 3
figure 3

Temperature dependence of resistivity for Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm) at ambient pressure. A. P. denotes an ambient pressure condition.

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Figure 4
figure 4

Temperature dependence of magnetization for Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm) at ambient pressure. Dashed and dotted lines indicate a field cooling (FC) and zero-field cooling (ZFC), respectively. A. P. denotes an ambient pressure condition.

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External pressure effect

Figure 5a shows the temperature dependences of the magnetization of Sr0.5La0.5FBiS2 when increasing the applied pressure to 1.15 GPa. The Tc of approximately 2.7 K (low-P phase) remained almost unchanged up to 0.84 GPa; alternatively, there was an evident increase in the shielding volume fraction. This result indicates that the external pressure effectively enhances the shielding volume fraction, which corresponds to the emergence of bulk nature of the superconducting states in the Sr0.5La0.5FBiS2 samples at a low-P regime. A remarkable increase in Tc up to Tcmax = 10.8 K (high-P phase) was observed at P > 0.95 GPa. The enhancement in the shielding volume fraction was also observed in the high-P phase, which was achieved by increasing applied pressure to the maximum pressure, without a noticeable change in the Tc. The drastic increase in Tc is explained by a tetragonal to a monoclinic phase.

Figure 5
figure 5

(a–e) Temperature dependences of magnetization under various pressure (PLa = 0, 0.01, 0.19, 0.51, 0.836, 0.840, 0.95, 1.02, and 1.15 GPa; PCe = 0, 0.28, 0. 53 0.94, 1.11, and 1.15 GPa; PPr = 0.0, 0.40, 0.64, 0.93, 1.17, and 1.43 GPa; PNdr = 0.0, 0.20, 0.44, 0.87, 1.17, and 1.33 GPa; PSm = 0.0, 0.375, 0.716, 1.03, 1.12, and 1.28 GPa) for Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm), (f–j) pressure dependence of Tc for Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm) when a magnetic field of 10 Oe was applied for all samples. The superconducting transition around 7 K indicates the superconducting transition of Pb manometer.

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Figure 6a presents the laboratory X-ray diffraction patterns of Sr0.5La0.5FBiS2 at room temperature under various applied pressures of up to 3.4 GPa. Shifts of the (001) and (004) peaks to higher angles clearly indicate the shrinkage of the lattice along the c-axis due to the pressure. In contrast, a relatively smaller shift of the (110) peak was detected, which indicates that the in-plane size remains almost unchanged. Strong peak broadening was observed for the (200) peak above 1.1 GPa, indicating peak splitting due to the lowering of in-plane structural symmetry. Similar peak splitting on the (200) peak was observed for isostructural LaO0.5F0.5BiS2 and EuFBiS2 samples under high pressure23,24, and a resultant structural transition from a tetragonal to monoclinic phase was detected. We noticed that the (200) peak asymmetrically split into two or more peaks, as depicted in Fig. 6b. This unexpected evolutions of the XRD pattern may be due to the inhomogeneity of applied pressure and the flexible nature of the in-plane structure of BiS2-based compounds. The critical pressure of 1.1 GPa estimated from the XRD corresponds satisfactorily with the Pc estimated from the magnetization measurements. To further analyse crystal structure of this phase under pressure, synchrotron XRD experiments under homogeneous pressure conditions are needed.

Figure 6
figure 6

(a) XRD patterns (Mo Kα) of Sr0.5La0.5FBiS2 under various pressure at room temperature. (b) Zoomed XRD patterns near the 020 and 200 peaks.

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The pressure dependence of Tc is summarized in Fig. 5f; the light blue, blue, and pink regions indicate the filamentary superconductivity, bulk superconductivity in the low-P phase, and bulk superconductivity in the high-P phase, respectively. The low-P phase shifts to the high-P phase when a pressure slightly exceeding the critical pressure (Pc) for the high-P phase is applied. In regard to this, a phase diagram was created using the shielding volume fraction of 20% or more as a bulk state in order to discuss the phase transition. In the pressure range of 0–0.84 GPa, Tc(P) remains almost constant (~ 2.7 K). The bulk superconductivity of the sample was induced by the pressure for the low-P phase region; eventually, the high-P phase region emerged at approximately P = 0.95 GPa with the bulk superconducting states. The Tc(P) for the high-P phase region is almost constant (10.8 K).

The temperature dependence of magnetization under pressure and the pressure dependence of Tc phases for all the samples with different RE are summarized in Fig. 5a–j and respectively. The high-P phase of Sr0.5Sm0.5FBiS2 was not observed up to 1.28 GPa, which is nearly the upper limit of the pressure measurement apparatus used in this experiment. This is the first report offering evidence of the bulk nature of two different (low-P and high-P) phases of the Sr1-xRExFBiS2 (RE: La, Ce, Pr, and Nd) superconductors when subjected to pressure.

Discussion

In this section, we discuss the relationship between external pressure effects, chemical pressure effects, and evolution of superconductivity in Sr0.5RE0.5FBiS2. On comparing the evolutions of superconductivity for RE = Ce–Sm and that for RE = La, a slight decrease in Tc for the low-P phase was observed with increasing pressure for the RE = Ce, Pr, Nd and, Sm samples. Similar trend was observed in a phase diagram of tetragonal phase of BiCh2-based systems examined as a function of chemical pressure18,19,33. Moreover, we observed that the Tc of the high-P phase showed a trend of decreasing with decreasing RE ionic radius. This trend is also common to that observed in high-pressure studies for REO0.5F0.5BiS2 with different RE22. The Pc increased with decreasing RE ionic radius. Specifically, Pc was roughly estimated as 0.95, 1.11, 1.17, and 1.33 GPa for La3+ (with an ionic radius of 1.16 Å), Ce3+ (with an ionic radius of 1.14 Å), Pr3+ (with an ionic radius of 1.13 Å), and Nd3+ (with an ionic radius of 1.11 Å), respectively, where those ionic radii are values for a coordination number of 8. We noticed that the shift in Pc by replacing RE in Sr0.5RE0.5FBiS2 is clearly small as compared to the case of REO0.5F0.5BiS2; Pc was ~ 2 GPa for NdO0.5F0.5BiS228. These trends, the increase in Pc and the decrease in Tc with a decrease in RE ionic radius, were also observed for REO0.5F0.5BiS2 compounds22,26,28; specifically, the Tc varied from approximately 10 to 6 K. The different pressure evolutions of superconducting phases in between the Sr0.5RE0.5FBiS2 and REO0.5F0.5BiS2 systems would be understood by the difference in the substitution sites. For Sr0.5RE0.5FBiS2, the Sr site is partly (50%) substituted by RE, and hence the Sr-F bonds are partly remained. In the case of REO0.5F0.5BiS2, all the RE site is replaced by different RE, and hence the RE-(O,F) bond length should systematically decrease according to the RE ionic radius. Therefore, the different sensitivity of the crystal structure and superconductivity to external pressures were observed between Sr0.5RE0.5FBiS2 and REO0.5F0.5BiS2. The difference should be caused by the chemical bonding states of the SrF-based and REO-based layers and the interlayer interaction between the blocking layers and BiS2 conducting layers. Our results suggest that the structure of the blocking layer largely affects the evolution of superconducting phases under high pressures. The results obtained in this study will be useful for material design of BiCh2-based superconductors with a higher Tc.

Conclusion

We showed the results of the synthesis, crystal structure analysis, resistivity, and magnetic susceptibility measurements investigated under ambient and high pressures for Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm). The effects of external pressure on magnetization resulted in abrupt increments in Tc up to 10–10.8 K for the samples with RE = La, Ce, Pr, and Nd. Based on the analyses of the shielding volume fraction estimated via magnetic susceptibility measurements, we found that two bulk superconducting phases (low-P and high-P phases) can be induced by external pressure for Sr0.5RE0.5FBiS2. For RE = La, we have confirmed a structural transition from laboratory XRD under high pressure, which is a common trend with those observed for LaO0.5F0.5BiS2 and EuFBiS2. The critical pressure, where Tc sharply increased to the high-P phase, shifted to a higher pressure with decreasing RE ionic radius. This implied that both the external and chemical pressures were affecting Tc. In addition, we have compared the obtained phase diagrams for Sr0.5RE0.5FBiS2 and REO0.5F0.5BiS2. We found differences in the sensitivity of the crystal structure and superconducting characteristics to external pressure effects between Sr0.5RE0.5FBiS2 and REO0.5F0.5BiS2, which should be caused by the different chemical bonding states in the blocking layers and the interlayer interaction between the blocking layers and BiS2 conducting layers.

Methods

Polycrystalline Sr0.5RE0.5FBiS (RE: La, Ce, Pr, Nd, and Sm) samples were synthesized by solid state reaction method in an evacuated quartz tube. Powders of RE2S3 (RE: La (99.9%), Ce (99.9%), Pr (99%), Nd (99%), and Sm (99.9%)), SrF2 (99%), Bi (99.999%), and S (99.9999%) were weighed for Sr0.5RE0.5FBiS2. The mixed powder was subsequently pelletized, sintered in an evacuated quartz tube at 700 °C for 20 h, followed by furnace cooling to room temperature. The obtained compounds were thoroughly mixed and ground, then sintered in the same conditions as the first sintering.

The phase purity and the crystal structure of the Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm) samples were examined by powder synchrotron XRD (ambient pressure XRD) with an energy of 25 keV (λ = 0.49657 Å) at the beamline BL02B2 of SPring-8 under a proposal No. 2019A1101. The synchrotron XRD experiments were performed at room temperature with a sample rotator system, and the diffraction data were collected using a high-resolution one-dimensional semiconductor detector MYTHEN [Multiple mythen system] with a step of 2θ = 0.006°. To investigate the evolution of crystal structure of Sr0.5La0.5FBiS2, laboratory XRD experiments under high pressure up to 3.4 GPa were performed at room temperature using a Mo-Kα radiation on a Rigaku (MicroMax-007HF) rotating anode generator equipped with a 100 µm collimator. Daphne 7474 was used as a pressure medium.

The crystal structure parameters were refined using the Rietveld method with a RIETAN-FP software34. The actual compositions of the obtained samples were analysed using an energy dispersive X-ray spectroscopy (EDX) on TM-3030 (Hitachi).

The temperature dependence of magnetic susceptibility at ambient pressure and under high pressures were measured using a superconducting quantum interference devise (SQUID) with MPMS-3 (Quantum Design). Hydrostatic pressures were generated by the MPMS high pressure Capsule Cell. The sample was immersed in a pressure transmitting medium (Daphene 7373) covered with a Teflon cell. The pressure at low temperature was calibrated from the superconducting transition temperature of Pb manometer. The electrical resistivity was measured on a GM refrigerator system (Made by Axis) using a conventional four-probe method. For the resistivity measurements, gold wires were connected to the samples with a silver paste.