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Review of Single Crystal Synthesis of 11 Iron-Based Superconductors

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06 June 2023

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06 June 2023

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Abstract
The 11 system in iron-based superconducting family has become one of the most extensively studied materials in the research of high-temperature superconductivity due to their simple structure and rich physical properties. However, the research on 11 iron-based superconductors faces numerous obstacles, mainly stemming from the challenges associated with producing high-quality single crystals. Since the discovery of FeSe superconductivity in 2008, researchers have made significant progress in crystal growth, overcoming the hurdles that initially impeded their studies. Consequently, they have successfully established the complete phase diagrams of 11 iron-based superconductors, including FeSe1-xTex, FeSe1-xSx and FeTe1-xSx. In this paper, we aim to provide a comprehensive summary of the preparation methods employed for 11 iron-based single crystals over the past decade. Specifically, we will focus on hydrothermal, chemical vapor transport (CVT), self-flux, and annealing methods. Additionally, we will discuss the quality, size, and superconductivity properties exhibited by single crystals obtained through different preparation methods. By exploring these aspects, we can gain a better understanding of the advantages and limitations associated with each technique.
Keywords: 
single crystal
;  
hydrothermal
;  
CVT
;  
self-flux
;  
annealing
;  
11 iron-based superconductors
;  
superconductivity
Subject: 
Physical Sciences  -   Condensed Matter Physics

1. Introduction

Compared with FeAs-based superconductors, the 11 iron-based superconductors have the advantages of simplest crystal structure and non-toxicity. FeSe consists solely of edge-sharing trtrahedral FeSe4 layers stacked along the c-axis, without charge storage layer [1,2,3]. A structural transition from tetragonal to orthorhombic occurs at about Ts ~ 90 K accompanied by the nematic phase [4,5,6,7]. Despite having a relatively low superconducting critical temperature (Tc) of approximately 9 K, high tunability and nematicity without magnetic order have garnered significant attention and research interest. Under high pressure, the Tc of FeSe can be elevated to approximately 38 K, and a new magnetic order emerges within a specific pressure range once the nematic phase is suppressed [8,9,10,11]. Chemical methods, such as intercalation [12,13], ionic liquid gating [14,15,16] and potassium deposition [17,18], have been employed to raise Tc to over 40 K. Remarkably, monolayer FeSe films on doped SrTiO3 substrates have exhibited superconductivity with Tc surpassing 65 K [19,20].
The substitution of isovalent sulfur (S) in FeSe, equivalent to applying positive chemical pressure, has proven to be an effective method for tuning superconductivity and nematic order. With S doping, the nematic transition temperature Ts gradually decreases until it vanished at x ~ 0.17, marking a nonmagnetic nematic quantum critical point (QCP) [21,22,23,24]. Nuclear magnetic resonance (NMR) measurements indicate a strong suppression of antiferromagnetic (AFM) fluctuations with S substitution, resulting in negligible AFM fluctuations near the QCP [23]. Within the nematic regions, Tc exhibits a small superconducting dome, reaching a maximum of 11 K at x ~ 0.11. Beyond the nematic regions, superconductivity is gradually suppressed, reaching a minimum at x ~ 0.45, after which Tc slowly increases until x = 1 [25]. Notably, unlike when external pressure is applied, no new magnetic order emerges after the nematic phase [25,26,27].
Similarly, the substitution of isovalent tellurium (Te) in FeSe, equivalent to applying negative chemical pressure, is an effective method for tuning the superconductivity and various ordered states. In FeSe1-xTex single crystals phase diagram, Ts linearly decreases until it disappears at x = 0.5 with Te doping [28,29,30]. Tc initially decreases to a minimum at x ~ 0.3 and then increases to a maximum at x ~ 0.6; subsequently, Tc is gradually suppressed and antiferromagnetic (AFM) behavior emerges when x > 0.9 [28,29,31,32,33]. FeTe undergoes a tetragonal-to-monoclinic structural transition at around 70 K, exhibiting AFM behavior without superconductivity, reminiscent of the emergence of superconductivity from AFM in the cuprate superconductors [34,35,36,37,38]. The unique phase diagram of 11 iron-based superconductors, with its interplay of competing orders, nematic phase, magnetic order and superconductivity, provides important insights for exploring the mechanism of high-temperature superconductivity.
Unfortunately, preparing high-quality single crystals is one of the challenges in the study of the 11 iron-based superconducting system, particularly FeSe1-xTex and FeSe1-xSx. This difficulty is also commonly encountered in the study of other iron-based superconducting families. On the one hand, the low chemical stability of FeSe1-xSx and the issue of phase separation in FeSe1-xTex (0 < x < 0.5) make it arduous to obtain single crystals or single phase samples using traditional solid-state reactions [39,40,41,42,43]. On the other hand, even though the preparation of single crystals of FeSe1-xTex (0.5 ≤ x ≤ 1) is relatively straightforward using the self-flux method, the presence of excess Fe significantly affects the investigation of their intrinsic properties, such as the localization of charge carriers [44,45,46], spin glass phase [47] and incoherent electronic states [45,48]. It is difficult to prepare high-quality single crystals of the 11 system using traditional solid-state reaction methods, and new methods are gradually developed.
To synthesize high quality single crystals across the entire doping range, different methods need to be employed. In this review, we provide an overview of the common synthesis methods for 11 iron-based system, focusing on the optimal method for different doping regions, along with a relevant phase diagram of the entire region. Initially, we discuss the conventional methods of obtaining FeSe single crystals, namely the flux method and chemical vapor transport (CVT). In section 3, we describe the preparation of FeSe1-xSx single crystals using CVT for range 0 ≤ x ≤ 0.29 and the hydrothermal method for the entire region. In section 4, we explain how high quality FeSe1-xTex (0 ≤ x ≤ 0.5) single crystals can be directly synthesized via CVT. For the Te-high doping region (0.5 < x ≤ 1), it becomes necessary to anneal the as-grown single crystals in O2 or Te vapor. Finally, we conclude the review with a summary and outlook in section 5.

2. Single Crystal Growth and Superconductivity of FeSe

2.1. Flux Method for Growing FeSe Single Crystals

Maw-Kuen Wu’s group reported the observation of superconductivity with zero-resistance transition temperature at 8 K in the FeSe polycrystalline bulk for the first time [1]. The crystal of FeSe is composed of a stack of edge-sharing FeSe4-tetrahedra layer by layer, as shown schematically in Figure 1. FeSe single crystal with a size about 500 μm was firstly synthesized using the flux method employing a NaCl/KCl mixed eutectic [49]. The preparation process can be divided into two stages. Firstly, Fe1.2Se polycrystalline with nominal stoichiometry was prepared through a traditional solid-state reaction using high purity Fe and Se powders as the raw materials. Then the obtained Fe1.2Se polycrystal powder and NaCl/KCl mixed eutectic with mole ratio 1:1 were ground and sealed in an evacuated quartz tube. The quartz tube was slowly heated to 850 °C and kept two hours for sufficient solution of the raw materials and flux, Afterward, the temperature was gradually reduced at a rate of 3 °C/h down to 600 °C, followed by furnace cooling. FeSe single crystals were separated from the flux by dissolving the NaCl/KCl mixed eutectic in deionized water.
Figure 2 illustrates the basic physical properties of the obtained single crystals. In Figure 2(a), the optical image of FeSe reveals two different shapes present in all the grown single crystals: rectangular and hexagonal, both with a size of approximately 500 μm. The X-ray diffraction (XRD) pattern in Figure 2(b) shows two sets of peaks corresponding to two distinct crystal structures, tetragonal (with space groups P4/nmm) and hexagonal (with space groups P63/mmc). This indicates the presence of non-superconducting impurities in the single crystals. The temperature dependence of resistance and magnetic susceptibility is presented in Figure 2(c) and (d), respectively. The large superconducting transition width (ΔTc) and the small superconducting volume fraction observed suggest a low-quality superconducting tetragonal phase.
Subsequently, several research groups successfully synthesized FeSe single crystals using similar methods [50,51,52,53,54]. While superconductivity has improved, the presence of impurities remains a significant concern. Impurities such as hexagonal FeSe, Fe7Se8 and Fe3O4 exist in all as-grown single crystals, posing a major obstacle in understanding the intrinsic properties of FeSe. The strong magnetism of these impurities, often results in a prominent ferromagnetic background in the superconducting magnetization-field (M-H) loop [51]. FeSe single crystals with no impurity have been synthesized using the LiCl/CsCl flux method where the ferromagnetic background in M-H loop is nearly absent below Tc [55]. However, even with this method, the superconducting volume fraction remains below 60 %, indicating the need for further improvements

2.2. Chemical Vapor Transport (CVT) Method for Growing FeSe Single Crystals

Despite the successful growth of large-sized FeSe single crystals using the flux method, the quality of the crystals and the presence of impurities hindered related research. The iodine vapor transport method did not effectively improved the crystal quality [52]. However, a breakthrough was achieved through the preparation of high-quality FeSe single crystals using the CVT method with KCl/AlCl3 transport agent [5,56]. A distinct kink at approximately 90 K was observed in the temperature dependence of resistance R(T) and confirmed to be a structural(nematic) transition from tetragonal to orthorhombic phase [4,56,57,58,59,60,61,62]. The temperature dependence of resistance and magnetic susceptibility confirmed the presence of a superconducting transition around 9.4 K. The superconducting transition width of about 1.5 K and a nearly 100 % superconducting volume fraction demonstrated good superconductivity [56].
The synthesis process is as follows: High-purity Fe and Se powders were sealed in an evacuated quartz tube along with KCl and AlCl3 powders. The quartz tube was horizontally placed in a tube furnace with double-temperature zone. The hot part of the tube containing the raw materials was heated to 390 °C while the cold part for single crystal growth was kept at 240 °C. After approximately 30 days of transport growth, a large number of single crystals with tetragonal morphology could be observed in the cold part. Similarly to the flux method, FeSe single crystals need to be separated from the flux by dissolving the KCl/AlCl3 mixed eutectic in deionized water. The schematic representation of the typical CVT growth assembly is shown in Figure 3(a). The scanning electron microscope image in Figure 3(b) displays the clear layered structure of a tetragonal FeSe single crystal [56]. Temperature dependence of resistivity (ρ - T) and magnetization (M - T), shown in Figure 3(c) and inset, indicate high quality crystallization and good bulk superconductivity [63].
Since then, the preparation of FeSe single crystals using similar methods has become more prevalent, leading to a flourishing research landscape due to the availability of high-quality single crystals. However, the quality of these single crystals is highly sensitive to the preparation conditions, primarily influenced by the complex binary Fe-Se composition-temperature phase diagram [64].
A study conducted by A. E. Böhmer et al. explored the relationship between transition temperatures and residual resistivity ratio (RRR) in vapor-grown FeSe [65]. Their findings revealed that the inclusion of some excess Fe, with an Fe:Se ratio of 1.1:1 as nominal compositions, effectively suppressed the formation of the hexagonal Fe7Se8 phase. Additionally, the temperature conditions during growth strongly influenced the single crystal quality, with an optimal temperature gradient of 350-390 °C observed in their work. In addition, the tilt angle of the quartz tube can also have some impact on the growth. Figure 4 (a) shows the single crystals under the optimal growth conditions and the schematic picture. Figure 4(b) and (c) provides a summary of the correlation between RRR (ratio of resistance at 250 K to resistance just above Tc), Ts and Tc. Both Ts and Tc decrease as the RRR increases. Composition analysis using wavelength dispersive X-ray spectroscopy (WDS) indicated no correlation between Tc and sample composition. Extrapolating the linear relation between Ts and Tc suggests that superconductivity would be completely suppressed when Ts reaches 64 K.

3. Single Crystal Growth and Superconductivity of FeSe1-xSx

3.1. CVT Growth of FeSe1-xSx single crystals with Low S Doping

FeSe1−xSx single crystals are typically grown by CVT from FeSe up to x ∼ 0.4, using similar preparation methods as FeSe [23,66,67,68,69]. Figure 5(a) displays the temperature dependence of the resistivity normalized to the value at 300 K value for x = 0 to 0.25. With S doping, a clear kink in resistivity is gradually decreases to lower temperatures and disappears at a nonmagnetic nematic QCP, x = 0.17, as shown more clearly in Figure 5(b), depicting the temperature dependence of the first derivative dρ/dT. The discovery of QCP with nonmagnetic nematicity in 11 system has raised the prospect of investigating the role of relationship between nematicity and superconductivity [24,70].

3.2. Hydrothermal Method for Growing FeSe1−xSx single Crystals across the Entire Doping Range

While the CVT method allows the synthesis of FeSe1−xSx single crystals with x ≤ 0.29, the hydrothermal method has been employed to overcome this limitation. Xiaofang Lai et al. successfully synthesized tetragonal FeS through the hydrothermal reaction of Fe powder with a sulfide solution and observed bulk superconductivity for the first time at 5 K [26]. Subsequently, a hydrothermal ion release/introduction technique involving the de-intercalation of K ions from K0.8Fe1.6Se2−xSx precursors has been widely utilized for the preparation of FeS and FeSe1−xSx single crystals [25,71,72,73,74,75,76,77], as schematically depicted in Figure 6(a). The process involves the growth of K0.8Fe1.6Se2−xSx precursors using the self-flux method, followed by the addition of Fe powder, selenourea, thiourea, and K0.8Fe1.6Se2−xSx single crystals pieces to a solution containing dissolved NaOH in deionized water within a Teflon-linked stainless-steel autoclave (25 mL). The autoclave is then sealed and heated to 130-150°C for 50-70 h resulting in the formation of FeSe1−xSx single crystals, shown in Figure 6(b).
Figure 7 presents a comprehensive phase diagram of FeSe1−xSx single crystals, encompassing the entire region obtained from hydrothermal method [25] and a partial region (0 ≤ x ≤ 0.29) obtained from CVT method [23,67,68]. The values of Ts and Tc obtained from the hydrothermal method are slightly lower than those from the CVT method, possibly due to disorder effects in the crystals [65]. The exponent “n” in the contour plot corresponds to the power law, ρ (T) = ρ0 + ATn, where ρ0 represents the residual resistivity. In the nematic phase, the resistivity exhibits a non-Fermi liquid behavior characterized by sublinear temperature dependence. Outside the nematic phase, the resistivity at low temperatures follows a prefect Fermi liquid behavior, i.e. T2 dependence. In the Fermi liquid region, the coefficient A decreases monotonically with S doping, indicating a reduction in effective mass since A is proportional to the carrier effective mass according to the Landau Fermi liquid theory. Below the characteristic temperature T*, the resistivity displays an anomalous upturn just before the superconducting transition. The origin of this anomaly may be attributed to local magnetic impurity scattering or inelastic scattering due to crystallographic disorder.

4. Single Crystal Growth and Superconductivity of FeSe1-xTex

4.1. CVT Growth of FeSe1-xTex (0 < x < 0.5) Single Crystals

While high-quality single crystals of FeSe1−xSx have been successfully obtained, achieving homogenous Te-doping single crystals remains challenging due to strict preparation conditions and the phase separation in the region of 0.1 ≲ x ≲ 0.4 [30,42,43]. In recent years, significant efforts have been made in crystal growth, leading to several studies on phase separation regions. The synthesis of FeSe1-xTex (0 ≤ x ≤ 0.41) single crystals using the flux mothed with temperature gradient, including the phase separation regions, has been reported for the first time [28].
Figure8 (a) illustrates the schematic diagram of the growth setup, where a horizontal quartz tube is placed in a two-temperature zone tube furnace. The mixture of high-purity Fe, Se and Te powders, pre-sintered at 450 °C, along with a flux mixture of AlCl3/KCl was placed in high-temperature zone of quartz tube. After 20–30 days, flake-like single crystals were obtained in the low-temperature zone and the residual flux was removed by dissolving it in distilled water, shown in Figure 8(b). Then, FeSe0.67Te0.33 single crystal was grown using a flux method with single temperature zone in a box furnace [30].
The results of these two works are summarized in a phase diagram, shown in Figure 8(c). Tc exhibits a minimum around x ~ 0.2, which is attributed to the effect of sample disorder, as indicated by the relatively small RRR value [28,65]. Ts decreases linearly with increasing Te doping and disappears at approximately x ~ 0.5. Tc exhibits a maximum around x ~ 0.6, and the Néel temperature (TN) starts to appear when x > 0.9, accompanied by the suppression of superconductivity [78]. The breakthrough in the phase separation region provides a promising approach for preparation of high-quality single crystals, particularly in the phase separation region, enabling the investigation of the evolution of the intrinsic properties of FeSe1-xTex with Te doping.
Recently, significant progress has been made in the growth of high-quality FeSe1-xTex (0 ≤ x ≤ 0.5) single crystals using CVT method, and the temperature-composition phase diagrams have been established, shown in Figure 9 [29]. Similar to the flux method with two temperature zone described earlier, the mixture of Fe, Se, and Te powders was sealed in a quartz ampoule with transport agents AlCl3/KCl and the growth time was 1–2 weeks. The temperatures of the hot and cold sides were controlled at 420 and 250 °C for 0 ≤ x ≤ 0.25 (620 and 450 °C for 0.25 ≤ x ≤ 0.55), respectively, which play a significant role in the crystal growth process.
Despite the similar synthesis methods employed by different research groups, there is considerable variation in the quality of the obtained single crystals, including RRR, superconducting transition temperature Tc and transition width ΔT. In this systematic study, a comprehensive analysis of RRR with a large number of data points, represented by ρ(200 K)/ρ(15 K), reveals a monotonous decrease with increasing Te concentration, shown in Figure 9(c). This suggests an intrinsic origin of the minimum Tc observed at x = 0.3. Additionally, when considering the temperature-pressure-composition phase diagrams of FeSe1-xTex (0 ≤ x ≤ 0.5) single crystals, it is proposed that nematic fluctuations play a role in enhancing Tc above x = 0.3 and contribute to the formation of the observed Tc-dip.

4.2. Self-Flux plus Annealing Method for Growing FeSe1-xTex (0.5 < x ≤ 1) Single Crystals

FeSe1-xTex (0.5 < x ≤ 1) single crystals can be grown using standard melting methods, such as Bridgeman method [41], self-flux method (a modified Bridgeman method, similar each other) [79,80] and optical zone-melting [81]. In the self-flux method, high-purity Fe, Se and Te powders with nominal ratios were loaded into a quartz tube, which is then evacuated and sealed. To prevent cracking during the growth process, it is necessary to seal the quartz tube into a lager quartz tube. The assembly was slowly heated to 1050 °C and sustained for 24 h, followed by cooling down to 710 °C at a rate of 3 °C/h and furnace cooling. The obtained single crystals have a mirror-like surface and can reach the centimeter scale sizes, shown in Figure 10(a).
The position of excess iron in the crystal structure is shown in Figure 10(b) marked by the orange ball. Excess Fe in the crystal structure of FeSe1-xTex significantly affects its intrinsic properties, such as localization of the charge carriers [44,45,46], spin glass phase [47] and incoherent electronic states [45,48]. Annealing processes have been developed to effectively remove excess Fe. FeTe0.61Se0.39 single crystals was successfully annealed in vacuum environment for the first time at 400 °C for more than 10 days resulting a sharp superconducting transition at around 14 K [83]. Subsequently, vacuum annealing technique have been applied to remove excess Fe from FeSe1-xTex (0.5 < x ≤ 1) single crystals [78,84]. It was reported that N2 annealing can also effectively remove excess Fe [85]. However, it was later discovered that vacuum and N2 annealing have no effect on the excess Fe, and the observed improvement was actually due to the action of a small amount of residual O2 present during the annealing process [86,87,88]. Apart from O2 annealing, elements such as Te, Se, S, P, As, I, and Sb have been proved to be effectively remove excess Fe through vapor annealing for FeSe1-xTex (0.5 < x ≤ 1) single crystals [89,90,91,92,93,94,95]. For efficiency and nontoxicity, we focus on providing a detailed introduction using O2 annealing to remove excess Fe.
Figure 11 shows the schematic picture of the annealing system used for O2 [33]. To perform the O2 annealing, as-grown single crystals were cut and cleaved into thin slices with dimensions of about 2.0 × 1.0 × 0.05 mm3. These slices were then weighed and loaded into a quartz tube with an inner diameter of 10 mm. The quartz tube was carefully evacuated using a diffusion pump, and the pressure in the tube was detected using a diaphragm-type manometer with an accuracy greater than 1 mTorr. Once the gas was fully removed, the quartz tube was filled with Ar/O2 (1% Ar) mixed gas and sealed to a length of 100 mm. The pressure in the system is continuously monitored during the sealing process to prevent gas leakage and control the O2 pressure in the quartz tube. The crystals were then annealed at 400 °C for various periods of time and subsequently quenched in water.
The doping-temperature phase diagram for the as-grown and annealed Fe1+yTe1−xSex (0 ≤ x ≤ 0.43, y represents excess Fe) were established based on the magnetization, magnetic susceptibility, resistivity, and Hall effects, as shown in Figure12 (a) and (b), respectively [31]. In the as-grown, there is a clear spin glass state originating from excess Fe in the interstitial site before the onset of superconductivity. The superconductivity observed in the as-grown crystals is not of bulk nature and can only be obviously detected through the temperature dependence of resistivity. After annealing, significant changes in superconductivity and magnetic order are observed. The AFM phase is suppressed into a very narrow regions for x (Se) < 0.05, and the spin glass state completely disappears. This confirms the effective removal of excess Fe through annealing. The superconducting state exhibits a clear bulk effect and can be easily detected by magnetic measurements.
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Figure 12. The doping-temperature (x-T) phase diagrams for Fe1+yTe1−xSex (0 ≤ x ≤ 0.43, y represents excess Fe) single crystals (a) before and (b) after O2 -annealing obtained from magnetization, magnetic susceptibility, resistivity, and Hall effect measurements [31].
Figure 12. The doping-temperature (x-T) phase diagrams for Fe1+yTe1−xSex (0 ≤ x ≤ 0.43, y represents excess Fe) single crystals (a) before and (b) after O2 -annealing obtained from magnetization, magnetic susceptibility, resistivity, and Hall effect measurements [31].
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In our recent work, we have successfully prepared high-quality full-range FeSe1-xTex single crystals, with varying Te doping levels (0 ≤ x ≤ 0.5 by CVT and 0.5 < x ≤ 1 by the flux method plus annealing). The corresponding phase diagram is illustrated in Figure 13. Notably, Te doping gradually suppresses the nematic phase until it completely disappears at x = 0.5. Our results also reveal that Tc reaches its minimum at x = 0.3, which aligns with the findings of Mukasa et al. [29], further supporting the intrinsic nature of the Tc-dip phenomenon observed in FeSe1-xTex. Subsequently, Tc increases and reaches a maximum at x = 0.6 but gradually decreases upon further Te doping, eventually leading to a transition into a non-superconducting antiferromagnetic state.
The high chemical stability, high Tc, and strong upper critical field exhibited by FeSe1-xTex single crystals make them excellent candidates for investigating the pairing mechanism underlying high-temperature superconductivity. Consequently, the comprehensive phase diagram we have established for FeSe1-xTex provides valuable support for the ongoing exploration of the superconducting pairing mechanism in high-temperature superconductors.

4.3. Optical Zone-Melting Technique for Growing FeSe1-xTex Single Crystals

FeSe1-xTex single crystals also can be grown using the optical zone-melting technique [81,96]. This method allows for real-time observation of single crystal growth and precise control of the growth rate by visualizing the melting zone. Figure 14 illustrates the schematic picture of single crystal growth and shows a large-sized single crystal obtained using this technique. The growth process is as follows:
High purity powders of Fe, Se and Te with nominal ratio were mixed in a ball mill for 4 h. The mixed powders were cold pressed into discs under a uniaxial pressure of 400 kg⋅cm−2, and then heated at 600 °C for 20h under a vacuum. The reacted bulk material was reground into a fine powder and loaded into a double quartz tube. The tube was loaded in an optical zone-melting furnace equipped with two 1500 W halogen lamps as infrared radiation sources, as shown in Figure 14. The tube was rotated at a rate of 20 rpm and moved at a rate of 1–2 mm⋅h−1. After the growth, the as-grown crystals undergo an annealing process: ramping to 700–800 °C in 7 h, holding for 48 h; cool to 420 °C in 4 h, hold for 30 h; and finally shutting down the furnace and cooling to room temperature.
Despite obtaining large-sized and well-crystallized single crystals using the optical zone-melting technique, the upwarping behavior of the R(T) curves before superconducting transition is still apparent, indicating the presence of excess Fe in the crystals [81]. Moreover, due to the complexity of the preparation process and the more established self-flux method, the optical zone-melting method is not commonly used for the growth of FeSe1-xTex single crystals.

5. Single Crystal Growth and Superconductivity of FeTe1-xSx

FeTe1-xSx system also exhibits superconductivity. Yoshikazu Mizuguchi et al. first reported the superconductivity in FeTe1-xSx system and found that Tc can reach 10 K when x is 0.2 [97]. FeTe1-xSx single crystals with low S doping were grown using self-flux method, similar to FeSe1-xTex (0.5 < x ≤ 1) single crystals [98,99,100,101,102]. Annealing treatment is also necessary to improve superconductivity for FeTe1-xSx single crystals although the excess Fe cannot be completely removed [103,104,105,106,107,108]. The solubility limit of S in FeTe is about 12% and Chiheng Dong et al. provided the phase diagram in this region [106,109]. With S doping, AFM is suppressed and superconductivity is enhanced.
Caiye Zhao et al. successfully synthesized a series of FeS1-xTex (0 ≤ x ≤ 0.15) single crystals by a hydrothermal method for the first time and provided a phase diagram of FeS1-xTex single crystals, shown in Figure 15 [110]. Tc is rapidly suppressed with the Te doping for FeS1-xTex (0 ≤ x ≤ 0.15) single crystals and finally disappears when x > 0.1. Due to the large solution limited region, only a small amount of doping can be applied at both ends of the phase diagram. The complete phase diagram needs further exploration.

6. Conclusions

In conclusion, significant progress has been made in the preparation of 11 system single crystals, including FeSe1-xTex and FeSe1-xSx, through various methods. A comprehensive phase diagram has been constructed, as depicted in Figure 16, summarizing the superconducting transition temperatures (Tc), the onset of nematic phase (Ts), and the Néel temperature (TN) for the single crystals prepared using the optimal techniques in different intervals.
High quality FeSe1-xSx (0 ≤ x ≤ 0.29) and FeSe1-xTex (0 ≤ x ≤ 0.55) single crystals are typically grown using CVT method with AlCl3/KCl transport agent. It is fortuitous that the range encompassing these single crystals includes the nematic phase without magnetic order. The exceptional quality of these crystals serves as an excellent platform for investigating the interplay between nematicity and superconductivity. FeSe1-xSx (0.29 ≤ x ≤ 1) single crystals, however, can only be synthesized using hydrothermal method. Although the quality of single crystals using hydrothermal is slightly inferior to those grown using CVT, they still hold great significance for studying the complete phase diagram of FeSe1-xSx. By utilizing the self-flux plus annealing technique, single crystals without excess Fe in the highly Te doping region can be obtained. In this particular region, Tc reaches maximum of the entire phase diagram, approximately 15 K, occurring around x (Te) ~ 0.6. Furthermore, AFM state is observed within a narrow region around FeTe. In summary, the establishments of the comprehensive phase diagram for the 11 iron-based system is of utmost importance for unraveling the mechanism behind high-temperature superconductivity and for discovering novel superconducting materials.

Author Contributions

Qiang Hou and Longfei Sun designed and wrote the manuscript with the help of Yue Sun and Zhixiang Shi. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Key R&D Program of China (Grant No. 2018YFA0704300), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB25000000).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data used to support the findings of this study are available upon request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Crystal structure of tetragonal FeSe [1].
Figure 1. Crystal structure of tetragonal FeSe [1].
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Figure 2. (a) Optical image of FeSe with two different shapes, rectangular and hexagonal; (b) XRD pattern from FeSe flake along c-axis, including two sets of peaks; (c) Temperature dependence of resistance for FeSe single crystal in the ab plane, the inset is a magnified plot in the low temperature region; (d) Temperature dependence of magnetic susceptibility for FeSe single crystal at 10 Oe, the inset is a magnified plot in the low temperature region [49].
Figure 2. (a) Optical image of FeSe with two different shapes, rectangular and hexagonal; (b) XRD pattern from FeSe flake along c-axis, including two sets of peaks; (c) Temperature dependence of resistance for FeSe single crystal in the ab plane, the inset is a magnified plot in the low temperature region; (d) Temperature dependence of magnetic susceptibility for FeSe single crystal at 10 Oe, the inset is a magnified plot in the low temperature region [49].
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Figure 3. (a) Schematic image of the typical CVT growth assembly. (b) The scanning electron microscope image of the layered structure of a tetragonal FeSe single crystal [56]. (c) Temperature dependence of resistivity for FeSe single crystal. The inset shows the magnetic susceptibility measured under H = 5 Oe external magnetic field [63].
Figure 3. (a) Schematic image of the typical CVT growth assembly. (b) The scanning electron microscope image of the layered structure of a tetragonal FeSe single crystal [56]. (c) Temperature dependence of resistivity for FeSe single crystal. The inset shows the magnetic susceptibility measured under H = 5 Oe external magnetic field [63].
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Figure 4. (a) Photograph of tetragonal FeSe single crystals under optimal growth conditions and the schematic picture. (b) Structural transition temperature Ts and superconducting transition temperature Tc as a function of residual resistivity ratio (ratio of resistance at 250 K to resistance just above Tc) for different samples. The inset shows the transition temperature as a function of the inverse residual resistivity ratio. (c) Tc as a function of Ts for various samples [65].
Figure 4. (a) Photograph of tetragonal FeSe single crystals under optimal growth conditions and the schematic picture. (b) Structural transition temperature Ts and superconducting transition temperature Tc as a function of residual resistivity ratio (ratio of resistance at 250 K to resistance just above Tc) for different samples. The inset shows the transition temperature as a function of the inverse residual resistivity ratio. (c) Tc as a function of Ts for various samples [65].
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Figure 5. Temperature dependence of the resistivity of FeSe1−xSx. (a) Temperature dependence of resistivity normalized to the 300K value from x = 0 to 0.25. (b) The first derivative of the resistivity with respect to temperature for the same data. The curves for different S concentrations have been offset for clarity. The location of the structural transition, Ts is defined by the intercept of the linear fits on either side of the transition, as indicated by arrows [68].
Figure 5. Temperature dependence of the resistivity of FeSe1−xSx. (a) Temperature dependence of resistivity normalized to the 300K value from x = 0 to 0.25. (b) The first derivative of the resistivity with respect to temperature for the same data. The curves for different S concentrations have been offset for clarity. The location of the structural transition, Ts is defined by the intercept of the linear fits on either side of the transition, as indicated by arrows [68].
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Figure 6. (a) Schematic illustration of the hydrothermal ion release/introduction route for the synthesis of FeSe1−xSx single crystals. (b) Optical image of select FeSe1−xSx single crystals [26].
Figure 6. (a) Schematic illustration of the hydrothermal ion release/introduction route for the synthesis of FeSe1−xSx single crystals. (b) Optical image of select FeSe1−xSx single crystals [26].
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Figure 7. Complete phase diagram of FeSe1−xSx single crystals. Ts represents the nematic transition temperature. Tc zero and Tc M are the SC transition temperatures obtained from resistivity and magnetization measurements, respectively. T∗ is the characteristic temperature at which the ρ-T curves show local minima at low temperatures [25].
Figure 7. Complete phase diagram of FeSe1−xSx single crystals. Ts represents the nematic transition temperature. Tc zero and Tc M are the SC transition temperatures obtained from resistivity and magnetization measurements, respectively. T∗ is the characteristic temperature at which the ρ-T curves show local minima at low temperatures [25].
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Figure 8. (a) Schematic image of the temperature distribution in the horizontal tube furnace for single-crystal growth of FeSe1-xTex by the flux method [28]. (b) Photograph of as-grown single crystals of FeSe1-xTex after removing the flux [28]. (c) Complete Temperature-doping x phase diagram of FeSe1-xTex single crystals [30].
Figure 8. (a) Schematic image of the temperature distribution in the horizontal tube furnace for single-crystal growth of FeSe1-xTex by the flux method [28]. (b) Photograph of as-grown single crystals of FeSe1-xTex after removing the flux [28]. (c) Complete Temperature-doping x phase diagram of FeSe1-xTex single crystals [30].
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Figure 9. (a) Temperature - x (Te) phase diagram of FeSe1-xTex (0 ≤ x ≤ 0.5) single crystals. (b) The same as in (a), but the temperature range is 0–20K. (c) Dependence of ρ(200K)/ρ(15K) on x(Te) extracted from the resistivity data [29].
Figure 9. (a) Temperature - x (Te) phase diagram of FeSe1-xTex (0 ≤ x ≤ 0.5) single crystals. (b) The same as in (a), but the temperature range is 0–20K. (c) Dependence of ρ(200K)/ρ(15K) on x(Te) extracted from the resistivity data [29].
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Figure 10. (a) Photograph of the as-grown FeTe0.6Se0.4 single crystal. (b) Crystal structure of FeSe1-xTex. The orange ball represents the excess Fe [33,82].
Figure 10. (a) Photograph of the as-grown FeTe0.6Se0.4 single crystal. (b) Crystal structure of FeSe1-xTex. The orange ball represents the excess Fe [33,82].
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Figure 11. Schematic picture of the annealing system for sealing the crystal in quartz tube with a controlled amount of O2 [33].
Figure 11. Schematic picture of the annealing system for sealing the crystal in quartz tube with a controlled amount of O2 [33].
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Figure 13. Complete phase diagram of FeSe1-xTex (0 ≤ x ≤ 1) single crystals in our recent work.
Figure 13. Complete phase diagram of FeSe1-xTex (0 ≤ x ≤ 1) single crystals in our recent work.
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Figure 14. (a) Schematic diagram of apparatus setup of the optical zone-melting method. (b) Single crystal boule of as-grown FeTe0.7Se0.3 single crystal on a 1mm grid. The shiny surface is the a–b plane. (c) The crystal flakes with the (001) face. Crystals from A-F represent FeSexTe1-x single crystals of x = 0.3, 0.5, 0.6, 0.7, 0.9, and 1.0, respectively [81].
Figure 14. (a) Schematic diagram of apparatus setup of the optical zone-melting method. (b) Single crystal boule of as-grown FeTe0.7Se0.3 single crystal on a 1mm grid. The shiny surface is the a–b plane. (c) The crystal flakes with the (001) face. Crystals from A-F represent FeSexTe1-x single crystals of x = 0.3, 0.5, 0.6, 0.7, 0.9, and 1.0, respectively [81].
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Figure 15. The doping phase diagram of FeS1-xTex single crystals [106,110].
Figure 15. The doping phase diagram of FeS1-xTex single crystals [106,110].
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Figure 16. The entire phase diagram of FeSe1-xTex and FeSe1-xSx single crystals synthesized by the optimal methods, hydrothermal for FeSe1-xSx (0.29 ≤ x ≤ 1) [25], CVT for FeSe1-xSx (0 ≤ x ≤ 0.29) [23,67,68] and FeSe1-xTex (0 ≤ x ≤ 0.55) [29] and self-flux plus annealing for FeSe1-xTex (0.55 ≤ x ≤ 1) [31].
Figure 16. The entire phase diagram of FeSe1-xTex and FeSe1-xSx single crystals synthesized by the optimal methods, hydrothermal for FeSe1-xSx (0.29 ≤ x ≤ 1) [25], CVT for FeSe1-xSx (0 ≤ x ≤ 0.29) [23,67,68] and FeSe1-xTex (0 ≤ x ≤ 0.55) [29] and self-flux plus annealing for FeSe1-xTex (0.55 ≤ x ≤ 1) [31].
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