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. 2020 Jul 1;5(27):16819–16825. doi: 10.1021/acsomega.0c01969

Growth and Characterization of ROBiS2 High-Entropy Superconducting Single Crystals

Yuma Fujita †, Koki Kinami †, Yuji Hanada †, Masanori Nagao †,*, Akira Miura ‡, Shigeto Hirai §, Yuki Maruyama †, Satoshi Watauchi †, Yoshihiko Takano ∥, Isao Tanaka †
PMCID: PMC7364703  PMID: 32685850

Abstract

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A series of high-entropy superconductors, ROBiS2 (R = La + Ce + Pr + Nd + Sm), have been successfully grown in the form of single crystals using CsCl flux. The obtained single crystals have a platelike shape with a size of 0.5–2.0 mm and a thickness of 70–450 μm, and they are cleavable along the c-plane. The c-axis lattice constants of the obtained ROBiS2 single crystals have similar values of 13.47–13.57 Å. The Ce in the obtained ROBiS2 single crystals was in a mixed-valence state, comprising both Ce3+ and Ce4+. On the other hand, Pr and Sm showed only the trivalent state. The superconducting transition temperatures of ROBiS2 single crystals were approximately 2–4 K. The superconducting transition temperature and superconducting anisotropies of R-site mixed high-entropy samples increased with a decrease in the mean ionic radius of the R-site. Moreover, a deviation in the tendency to exhibit superconducting properties was observed based on the difference in the R-site mixed entropy. R-site mixed entropy in ROBiS2 superconductors may affect their superconducting properties.

1. Introduction

Layered superconductors often exhibit high superconducting transition temperatures, such as cuprate superconductors,1−3 iron-based superconductors,4,5 and nitride-based layered superconductors.6 ROBiS2 (R: rare earth elements) is a BiS2-based layered superconductor7 that is composed of alternating stacking sequences of BiS2 and RO layers. A schematic image of the crystal structure of ROBiS2 is shown in Figure 1. Similar structural features and superconducting properties have been attracted for exploring new superconductors and their origin. Superconductivity of BiS2-based compounds can be induced by carrier doping and/or in-plane chemical pressure.8,9 Their superconducting transition temperatures are approximately 2–5 K. Carrier doping can be achieved by doping of the O2–-sites with F– or by valence fluctuation of the R-site, such as that with Ce3+ and Ce4+.10,11 Moreover, the R-site can be substituted by various rare earth elements.12−16 High-entropy alloys (HEAs) are defined as alloys containing at least five elements with concentrations between 5 and 35 atom %.17,18 In recent years, HEAs have been extensively studied in various fields of structural materials. This concept has been applied as various functional materials including solid electrolytes,19 electrodes,20 and capacitors.21,22 The HEA concept can be useful for developing new superconducting materials containing an HEA site and/or HEA-type layers. To start with, the HEA superconductor Ta–Nb–Hf–Zr–Ti, with a transition temperature of 7.3 K, was discovered.23 In addition, this high-entropy alloy superconductor exhibits extraordinarily robust zero-resistance superconductivity under pressures up to 190 GPa.24 Later, the relationship between superconductivity and the high-entropy effect was investigated. RBa2Cu3O7−δ (R-123) high-Tc cuprate superconducting polycrystalline samples with the HEA concept in the R-site were investigated.25 In an analogous way, previous reports showed the synthesis and superconducting properties of RO0.5F0.5BiS2 polycrystalline samples with the HEA concept in the R-site for the improvement of superconducting properties.26,27 However, in polycrystalline samples, the intrinsic properties were masked by the impurities and grain boundaries. Especially, the anisotropic properties cannot be measured using polycrystalline samples. In this paper, we report the growth and characterization of HEA superconducting single crystals of ROBiS2 (R = La + Ce + Pr + Nd + Sm). The composition, the mean ionic radius of the R-site, and the superconducting properties of the obtained ROBiS2 single crystals indicated the presence of the HEA effect with mixed entropies (ΔSmix) at the R-site.

Figure 1.

Figure 1

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Schematic image of the crystal structure of ROBiS2 with the HEA concept in the R-site.

2. Results

Figure 2 shows the typical scanning electron microscopy (SEM) image and the corresponding energy-dispersive X-ray spectrometry (EDS) mapping of ROBiS2 single crystals. The single crystals have a platelike shape with sizes of 0.5–2.0 mm and thicknesses of 70–450 μm. EDS mapping revealed that La, Ce, Pr, Nd, Sm, Bi, and S are distributed homogenously in the obtained single crystals. Table 1 shows the CLa, CCe, CPr, CNd, CSm, CBi, and CS, and mixed entropies (ΔSmix) of the R-sites of the grown ROBiS2 single crystals. The analyzed values were almost at the same ratios as the nominal composition of all samples. Moreover, the concentrations of La, Ce, Pr, Nd, and Sm in the R-site were 8–34 atom %, which satisfies the definition of the high-entropy alloy by Yeh et al.18 On the other hand, Cs and Cl from the flux were undetectable in the single crystals within the minimum sensitivity limit of ∼1 wt %. The mixed entropies (ΔSmix) of the R-site in the analyzed compositions are calculated using eq 1

2. 1

where R and ln are the gas constant and the natural logarithmic operator, respectively. The estimated mixed entropies had similar values except for those for sample C.

Figure 2.

Figure 2

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Typical SEM image and La, Ce, Pr, Nd, Sm, Bi, and S elemental mapping of ROBiS2 single crystals.

Table 1. Tmax, ΔSmix, and Nominal and Analytical Compositions of ROBiS2 Single Crystals.

    nominal composition
  
analytical composition
sample Tmax (°C) La: a Ce: b Pr: c Nd: d Sm: e Bi S ΔSmix (estimated from analytical composition) (R: gas constant)
CLa CCe CPr CNd CSm CBi CS
A 950 0.30 0.30 0.20 0.10 0.10 1.00 2.00 1.496R
0.28(1) 0.32(1) 0.21(1) 0.09(1) 0.10(1) 1.11(1) 2.21(2)
B 950 0.10 0.30 0.30 0.20 0.10 1.00 2.00 1.487R
0.10(1) 0.29(2) 0.33(1) 0.19(2) 0.09(1) 1.05(1) 2.07(5)
C 950 0.20 0.20 0.20 0.20 0.20 1.00 2.00 1.598R
0.23(1) 0.21(1) 0.19(2) 0.19(1) 0.17(1) 0.96(3) 2.17(3)
D 850 0.10 0.30 0.10 0.20 0.30 1.00 2.00 1.517R
0.09(1) 0.29(2) 0.12(1) 0.21(2) 0.29(1) 1.01(4) 1.91(4)
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Figure 3 shows the X-ray diffraction (XRD) patterns of a well-developed plane in the obtained ROBiS2 single crystals. The appearance of only (00l) diffraction peaks for the CeOBiS2 structure indicates that the c-plane of ROBiS2 is well developed.10 These results confirm that ROBiS2 single crystals were successfully grown. The c-axis lattice constants of the obtained ROBiS2 single crystals were 13.47–13.57 Å between A, B, C, and D, which were similar values despite the different compositions. We assumed that they were maintained at a similar value due to the Ce valence fluctuation.

Figure 3.

Figure 3

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XRD patterns of the well-developed plane of ROBiS2 single crystals.

It is well known that Ce is trivalent and tetravalent in ROBiS2. To know the effect of carrier concentration, it is important to determine the valence of rare earth elements. We examined the valences of Ce, Pr, and Sm, which can adopt a mixed-valence state by X-ray absorption spectroscopy (XAS) analysis. Figure 4 shows the (a) Ce L3-edge, (b) Pr L3-edge, and (c) Sm L3-edge absorption spectra of the ROBiS2 single crystals at room temperature by XAS analysis. The Ce L3-edge of the ROBiS2 single crystals showed a peak at approximately 5726 eV that was assigned as Ce3+, which is consistent with the other XAS result for the trivalent electronic configuration (Ce3+).29 The peaks at approximately 5730 and 5737 eV were assigned to a tetravalent electronic configuration (Ce4+).30 Cerium in the obtained ROBiS2 single crystals was in a mixed-valence state that comprised trivalent (Ce3+) and tetravalent (Ce4+) states. The ratios of Ce3+ and Ce4+ in the Ce-site and the R-site in the obtained ROBiS2 single crystals are shown in Table 2. In contrast, the Pr L3-edge showed a peak at 5966 eV, which can be assigned to a trivalent electronic configuration (Pr3+). This is consistent with the other XAS results for Pr3+.31,32 The tetravalent electronic configuration (Pr4+) shows a signature peak at 5978 eV,31,33 which was undetectable. On the other hand, the Sm L3-edge showed a peak at 6719 eV, which can be assigned to a trivalent electronic configuration (Sm3+). This is consistent with the other XAS results for Sm3+.34 The peak at approximately 6724 eV appeared in the Sm L3-edge absorption spectra, which was consistent with the Nd L2-edge absorption. Table 2 shows a summary of the XAS measurement. While the ratio of Ce3+ in sample C is lower than that in other samples, the ratio of Ce4+ is almost constant. Considering the ion radii of all of the rare earth elements, the average ion radii of the R-site decrease from A (1.112 Å) to D (1.096 Å).35

Figure 4.

Figure 4

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XAS spectra at room temperature for the ROBiS2 single crystals and some standard valence samples at the (a) Ce L3-edge, (b) Pr L3-edge, and (c) Sm L3-edge.

Table 2. Ce3+ and Ce4+ Contents and the Mean R-site Ionic Radii for the Obtained ROBiS2 Single Crystals.

  Ce3+ and Ce4+ contents in R-site
  
sample Ce3+ Ce4+ mean R-site ionic radius (Å) (calculated from the ratio of Ce3+ and Ce4+)
A 0.19 0.13 1.112
B 0.18 0.11 1.108
C 0.12 0.095 1.104
D 0.19 0.096 1.096
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Figure 5 shows the ρ–T characteristics for all samples (A, B, C, and D) in the temperature range of 1.8–10 K. Various superconducting transition temperatures (Tc) and resistivity behaviors were observed despite the similar c-axis lattice constants. The resistivity basically showed semiconducting behavior. The slope of sample C in the normal state is sharp, indicating lower carrier concentration. The Tc values of samples A (Tc: 2.1–3.4 K) and C (Tc: 2.2–3.3 K) are lower than those of samples B (Tc: 3.8–4.3 K) and D (Tc: 4.3–4.6 K). This result suggests a complex relationship between the superconducting properties and the structural property of the ROBiS2 system. Typical superconducting properties of ROBiS2 single crystals were detected in sample D, which has the highest Tc of these samples. Figure 6 shows the temperature dependence of the resistivity for sample D under the magnetic field (H) parallel to the (a) c-plane (H//c-plane, H = 0.01–9.0 T) and to the (b) c-axis (H//c-axis, H = 0.01–9.0 T). The superconducting transition was drastically suppressed by an increase in the magnetic field parallel to the c-axis compared to those of the c-plane. Similar behaviors were observed for other samples (samples A, B, and C). Therefore, we predict that ROBiS2 single crystals would exhibit highly superconducting anisotropy. The magnetic field dependence of the Tconset under the magnetic field (H) parallel to the c-plane (H//c-plane) and to the c-axis (H//c-axis) for sample D is plotted in Figure 7. The linear extrapolation of the Tconset values for the H//c-plane and the H//c-axis approached 23 and 0.6 T, respectively. Then, the upper critical fields for the c-plane (HC2//c-plane) and the c-axis (HC2//c-axis) at zero temperature are estimated to be 16 and 0.42 T, as determined by the Werthamer–Helfand–Hohenberg (WHH) theory36 using eq 2

2. 2

Figure 5.

Figure 5

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Temperature dependences of the electrical resistivity for ROBiS2 single crystals in the temperature range of 1.8–10 K.

Figure 6.

Figure 6

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Temperature dependence of resistivity for sample D under various magnetic fields parallel to the (a) c-plane and (b) c-axis.

Figure 7.

Figure 7

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Data in Figure 6 after plotting of field dependences of Tconset under magnetic fields (H) parallel to the c-plane (H//c-plane) and c-axis (H//c-axis). The solid lines show the linear fits of the data. The dotted line indicates the Werthamer–Helfand–Hohenberg (WHH) theory.

We determined the superconducting anisotropy (γs) to be approximately 38 from the ratio of the upper critical field using eq 3

2. 3

where ξ is the coherence length.

In a conventional (BCS-like) superconductor at the weak-coupling limit, the Pauli limit (Hp) was calculated to be 8.46 T, since Hp = 1.84 Tc, (Tconset = 4.6 K).37 Thus, the upper critical field in the c-plane (HC2//c-plane = 16 T) is significantly higher than the Pauli limit (Hp = 8.46 T), indicating the possibility of an unconventional superconductor. For only sample C, the HC2//c-plane value (4.9 T) was less than Hp (6.07 T from Tconset = 3.3 K).

In contrast, the γs values of ROBiS2 single crystals were estimated by another approach using the effective mass model.28 The angular (θ) dependence of resistivity (ρ) was measured under different magnetic fields (H) in the liquid state flux to estimate the γs. The reduced field (Hred) was calculated using the following equation for an effective mass model (eq 4)

2. 4

where θ is the angle between the c-plane and the magnetic field.38,39Hred is calculated from H and θ. The γs value was estimated from the best scaling of the ρ–Hred relationship. Figure 8 shows the θ dependence of ρ at various magnetic fields (H = 0.01–9.0 T) in the liquid state flux for sample D. The ρ–θ curve was represented by a 2-fold symmetry. The ρ–Hred scaling obtained from the ρ–θ curves in Figure 8 using eq 4 is shown in Figure 9. The scaling was determined for γs = 33, as shown in Figure 9. The superconducting anisotropy (γs) values of sample D were estimated to be 38 and 33 using eqs 3 and eq 1, respectively. These values are comparable, which indicates that both approaches to determine the superconducting anisotropies are consistent for the ROBiS2 system. The superconducting transition temperature (Tc), upper critical field (HC2), and superconducting anisotropy (γs) values for all samples (samples A, B, C, and D) are shown in Table 3.

Figure 8.

Figure 8

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Angular dependence of resistivity in the liquid state flux at 3.5 K under various magnetic fields H = 0.01–9.0 T for a sample D single crystal.

Figure 9.

Figure 9

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Reduced magnetic field Hred dependence of resistivity scaled by the equation, Hred = H(sin2 θ + γs–2 cos2 θ)1/2 using Figure 8 data.

Table 3. Superconducting Properties (Tc, HC2//c-axis, HC2//c-plane, and γs) for All Samples.

          γs
sample Tconset (K) Tczero (K) HC2//c-axis (T) HC2//c-plane (T) HC2//c-plane/HC2//c-axis effective mass model
A 3.4 2.1 0.65 11 17 19–20
B 4.3 3.8 0.69 15 22 20–24
C 3.3 2.2 0.24 4.9 20 15–20
D 4.6 4.3 0.42 16 38 33–35
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3. Discussion

R-sites can affect the carrier concentration, chemical pressure, and high-entropy effect of the ROBiS2 single crystals, that is, superconducting properties are affected by several parameters. Figure 10 shows the mixed entropy (ΔSmix) values, the mean R-site ionic radius, dependencies of superconducting transition temperature (Tc), and superconducting anisotropy (γs) of ROBiS2 (R = La + Ce + Pr + Nd + Sm) (HEA-type) and Ce1–xNdxOBiS2 (R = Ce1–xNdx) single crystals.40,41 Owing to the comparable valence of Ce3+ and Ce4+ along with the slope of resistivity in the normal state region for samples A, B, and D, these carrier concentrations are considered comparable. Therefore, the superconducting properties of A, B, and D can be dominated by either the chemical pressure or the high-entropy effect. While the mixed entropy (ΔSmix) value does not correlate with the superconducting transition temperature (Tc) and superconducting anisotropy (γs), a decrease in mean R-site ionic radius leads to an increase in the chemical pressure,8,9 which also increases Tc and γs. This trend is similar to that in the Ce1–xNdxOBiS2 system,40,41 in which the ΔSmix values are less than half (0.486R–0.619R). Therefore, chemical pressure can affect the superconducting properties and has no significant effect on the high-entropy effect.

Figure 10.

Figure 10

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Mixed entropy (ΔSmix) value dependence of (a) Tc and (b) γs; mean R-site ionic radius dependence of (c) Tc and (d) γs.

Sample C, whose ΔSmix value is higher than that of samples A, B, and D, does not follow this trend; both its Tc and γs are low. This characteristic can be explained by either the carrier concentration or the high-entropy effect. Even though the content of Ce4+ in the case of sample C is similar to that of the other samples, its slope of resistivity in the normal state region indicates that it has the lowest carrier concentration (Figure 5). The carrier concentration may have been reduced by the reduced carrier transfer from the RO layer to the BiS2 layer.42 A low carrier concentration can lower the transition temperature.43 The other possibility is that a high ΔSmix value can reduce Tc and decrease γs; also, a substantial-high-entropy effect can reduce superconducting anisotropy by inducing different local structures near the RO layer. The value of the upper critical field (Hc2) for sample C is the only one less than the Pauli limit (Hp), which is one of the deciding criteria for conventional or unconventional superconductors. This result cannot be explained by carrier concentration only; therefore, we expect that the high ΔSmix value is a possible explanation for this phenomenon. Further investigation, including the growth of other ROBiS2 (R: rare earth elements) single crystals with different ΔSmix values, is required to systematically reveal the relationship between the superconductivity and the high-entropy effect.

4. Conclusions

ROBiS2 (R = La + Ce + Pr + Nd + Sm) HEA superconducting single crystals were grown using CsCl flux. The c-axis lattice constants of the obtained ROBiS2 single crystals were approximately constant (13.47–13.57 Å) regardless of the composition of the R-site. However, there was no relationship between the c-axis lattice constant and Tc. Tc and γs exhibited similar tendencies as the mean R-site ionic radius in both ROBiS2 (HEA-type) and Ce1–xNdxOBiS2 (conventional-type). In ROBiS2 (HEA-type), the Tc and γs in higher ΔSmix single crystals (sample C) deviated from the trend of other samples (samples A, B, and D). The mixed entropy values (ΔSmix) may introduce a high-entropy effect that alters the superconducting properties. Furthermore, we believe that the flexible compositions and various local structures of the R-site can expand the variety of superconducting materials, which can reveal new phenomena and applications of layered superconductors.

5. Experimental Section

ROBiS2 (R = La + Ce + Pr + Nd + Sm) single crystals were grown using CsCl flux. Nominal compositions of the R-site were chosen for implementation in the high-entropy alloys (HEA) composed of five elements with concentrations between 5 and 35 atom %. Table 1 shows the nominal compositions and growth temperatures (Tmax) of all samples. We note that the ionic radius of the R-site can be systematically changed for these samples. The starting materials for the growth of ROBiS2 single crystals were La2S3, Ce2S3, Pr2S3, Nd2S3, Sm2S3, Bi2S3, Bi2O3, and CsCl flux. The raw materials were weighed to obtain a nominal composition, LaaCebPrcNddSmeOBiS2. A mixture of raw materials (0.8 g) and the CsCl flux (5.0 g) was ground using a mortar and pestle and then sealed in an evacuated (∼10 Pa) quartz tube. The quartz tube was heated at Tmax for 10 h, followed by cooling to 650 °C at a rate of 1 °C/h. Then, the quartz tube was cooled to room temperature in the furnace. The heated quartz tube was opened in air, and the obtained materials were washed and filtered with distilled water to remove the CsCl flux.

Scanning electron microscopy (SEM) was conducted using a TM3030 system from Hitachi High-Technologies. The compositional ratio of the grown ROBiS2 single crystals was evaluated using energy-dispersive X-ray spectrometry (EDS, Quantax 70, Bruker). The atomic content of each element was defined as CXX (XX: the symbol of element). The obtained values were normalized using the atomic content obeying La + Ce + Pr + Nd + Sm (CLa + CCe + CPr + CNd + CSm) = 1.00 to clarify the relationship between the nominal and the analytical compositions. Then, Bi and S compositions (CBi and CS) were estimated to the precision of two decimal places. X-ray diffraction (XRD, MultiFlex, Rigaku) using Cu Kα radiation was employed to estimate the c-axis lattice constant. The c-axis lattice constants with an error range were calculated from all (00l) diffraction peaks.

The valence states of the La, Ce, Pr, Nd, and Sm components in the obtained single crystals were estimated by X-ray absorption spectroscopy (XAS) analysis of La L3, Ce L3, Pr L3, Nd L3, and Sm L3 edges using an Aichi XAS beamline with a synchrotron X-ray radiation source (BL05S1: Experimental No. 201905108). For the XAS samples, the obtained single crystals were ground, mixed with boron nitride (BN) powder, and pressed into a pellet with a diameter of 4 mm.

The resistivity–temperature (ρ–T) characteristics of the obtained single crystals were measured using the standard four-probe method in constant current density (J) mode by employing a physical property measurement system (PPMS DynaCool, Quantum Design). The electrical terminals were fabricated using Ag paste. The superconducting transition temperature (Tc) of the ROBiS2 single crystals was estimated using the ρ–T characteristics. The transition temperature corresponding to the onset of superconductivity (Tconset) was defined as the point at which deviation from normal state behavior was reflected in the ρ–T characteristics. The zero-resistivity temperature (Tczero) was determined by considering the criterion of a resistivity of 50 μΩ·cm in terms of the ρ–T characteristics. The ρ–T characteristics of ROBiS2 single crystals were measured under a magnetic field (H) parallel to the c-plane and a c-axis with a range of 0.01–9.0 T in the temperature range of 2.0–10.0 K.

We measured the angular (θ) dependence of the resistivity (ρ) in the liquid state flux under various magnetic fields (H) and calculated the superconducting anisotropy (γs) using the effective mass model.28

Acknowledgments

The XAS experiments were conducted at the BL05S1 of Aichi Synchrotron Radiation Center, Aichi Science & Technology Foundation, Aichi, Japan (Experimental No. 201905108). This research was partially supported by Grants-in-Aid for Scientific Research (C) (JSPS KAKENHI Grant Number JP19K05248). We would like to thank ACS Authoring Services and Editage (www.editage.com) for English language editing.

The authors declare no competing financial interest.

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