OHFeSe Superconductors : Crystal Growth , Structure , and Electromagnetic Properties

This review focuses on the growth of high-quality (Li1−xFex)OHFeSe single crystals by a hydrothermal method using floating-zone-grown AxFe2−ySe2 (A = K, Rb, and Cs) as precursors. The structure, superconductivity, and magnetic behavior of the obtained crystals are highly influenced by the growth conditions, such as time, temperature, and composition. A phase diagram with temperature against the c-lattice constant is summarized including the antiferromagnetic spin density wave, superconducting, and paramagnetic phases.

The crystal structure of FeSCs characteristically consists of some kind of stacking layers which conduct the SC current [18].In iron-arsenide and iron-selenide, compounds that have been most widely studied, the alternately stacked Fe 2 X 2 (X = As and Se) layers are formed by edge-sharing disordered FeX 4 tetrahedra, which leads to them sharing many similar structures and properties [19].Up to now, several types of iron-arsenide SCs have been discovered, including Fe 2 As-type AFeAs (111-system, A is Li or Na) [20][21][22], ThCr 2 Si 2 -type AeFe 2 As 2 (122-system, Ae is an alkaline or alkaline-earth metal element) [23,24], ZrCuSiAs-type ReFeAsO, Co doped AeFFeAs (1111-system, Re is a rare-earth element) [25][26][27], and the perovskite-based materials such as (Sr 4 M 2 O 6 )(Fe 2 Pn 2 ) (42622-system; M = Sc, Ti, and V; Pn = P and As) [28,29], and (Ca 3 Al 2 O 5-y )(Fe 2 Pn 2 ) (32522-system) [30].At ambient pressure, T c reaches as high as 55 K and 56 K in SmO 1−x F x FeAs and Sr 1−x Sm x FFeAs, respectively [31,32].Since their discovery, iron-selenide SCs have been found to provide a strong platform for the investigation of their high-T c superconductivity, since they possess a simple structure, are nontoxic, and may be fabricated via numerous synthesis methods [2,18,33,34].The simplest tetragonal β-Fe 1+δ Se (11-system) has T c ≈ 8.5 K at ambient pressure and is sensitive to chemical and physical pressure effects [35].It was observed that T c can be increased up to 15 K in the β-Fe 1+δ Se system by partially replacing Se with Te and up to 36.7 K under the application of a hydrostatic pressure of 8.9 GPa [36,37].The positive pressure coefficient dT c /dP reaches as high as 9.1 K/GPa for this system, although smaller than |−(60 ± 3)| K/GPa for Ca(Fe 1−x Co x ) 2 As 2 [38,39].In contrast to the negatively charged FeAs layers in iron arsenide systems, the anti-PbO-type FeSe layers are charge neutral, and the excess Fe is important to the phase diagram and structural stability of the β-Fe 1+δ Se system [40].The two adjacent FeSe layers are weakly coupled and are susceptible to intercalation, which can improve the superconductivity of the system by modulating the crystal lattice constants or even by changing the crystal structure [40,41].A series of new SCs with T c about 30 K have been fabricated by the intercalation of metal ions and small molecules, including A x Fe 2−y Se 2 [A = K, Rb, Cs, (Tl,K), and (Tl,Rb)] [42], M x (NH 3 ) y Fe 2 Se 2 (M: metal elements) [43,44], Li x (NH 2 ) y (NH 3 ) 1−y Fe 2 Se 2 [45], and Li x (C 5 H 5 N) y Fe 2−z Se 2 [46].Besides the coexistence of superconductivity and ferromagnetism, a variety of phase separation phenomena have been observed in these SCs [18].It was reported that two SC phases with T c of 44 K and 30 K coexist in K 0.4 Fe 2 Se 2 (NH 3 ) 0.5 [47].In polycrystalline Fe(Se 1−x Te x ) 0.82 (0.15 ≤ x ≤ 0.3), there are also two different SC phases, arising from two tetragonal structures with the same space group but different lattice parameters [48].In the A x Fe 2−y Se 2 system, intrinsic phase separation in coexisting crystallographic phases is a common feature [18].The majority phase A 0.8 Fe 1.6 Se 2 (the so-called '245' phase) is antiferromagnetic (AFM) with large magnetic moments of 3.31 µ B per Fe and a Néel transition temperature (T N ) up to 560 K.It shows an insulating/semiconducting behavior accompanied by Fe-vacancy orders with a √ 5 × √ 5 superstructure.Embedded in the 245 phase is the minority metallic-SC phase which is Fe vacancy free with the formula A 1−x Fe 2 Se 2 (0 ≤ x ≤ 0.7) [49].Direct observation shows that the phase separation in a K x Fe 2−y Se 2 single crystal at temperatures below 520 K is characterized by the coexistence of the majority tetragonal magnetic phase, minority orthorhombic metallic phase, and an interfacial tetragonal phase which appears below ~300 K [50].However, the coexistence of these complex microstructures makes it difficult to grow bulk SC A x Fe 2 Se 2 single crystals and hinders the determination of their intrinsic electrical and magnetic properties [51].
Recently, (Li 0.8 Fe 0.2 )OHFeSe (11111-system) polycrystalline SCs with T c ~40 K were synthesized using a hydrothermal method [52].This new FeSe-derived SC material has an alternate stacking of anti-PbO-type FeSe layers and (Li 0.8 Fe 0.2 )OH layers, with a weak interlayer hydrogen bonding interaction.Compared with β-Fe 1+δ Se, the FeSe 4 tetrahedron in the ab plane in (Li 0.8 Fe 0.2 )OHFeSe is highly compressed, which is believed to play a key role in enhancing superconductivity.In contrast, the ideal FeAs 4 tetrahedron is favorable for superconductivity in FeAs-based SCs.In (Li 0.8 Fe 0.2 )OHFeSe, the electron-type carriers dominate the conduction, and a canted AFM order occurs at ~8.5 K, coexisting with superconductivity at ~40 K.Moreover, (Li 0.8 Fe 0.2 )OHFeSe is stable in air, unlike other FeSe SCs intercalated with alkali metal ions, NH 3 molecules, or organic molecules, which are extremely air sensitive.Soon after the synthesis of polycrystalline (Li 1−x Fe x )OHFeSe via a hydrothermal method, (Li 1−x Fe x )OHFeSe single crystals with T c above 44 K were successfully synthesized via a hydrothermal ion-exchange process using A x Fe 2−y Se 2 (A = K, Rb, and Cs) as precursors, in which the 245 phase is absent [53].They have a narrow SC transition and 100% shield volume fractions, indicating their excellent bulk superconductivity; in contrast, the shield fractions of A x Fe 2−y Se 2 are only 10-20% [47].These advantages make the (Li 1−x Fe x )OHFeSe crystal an ideal system for investigating the intrinsic mechanism behind its superconductivity and the effect of anisotropy in its crystal structure on its superconducting properties.In this article, we review the growth technology, structure, and physical properties of (Li 1−x Fe x )OHFeSe single crystals.

Crystal Growth
2.1.A x Fe 2−y Se 2 (A = K, Rb, and Cs) Precursor A x Fe 2−y Se 2 (A = K, Rb, and Cs) single crystals used as precursors can be obtained using self-flux, Bridgman, and optical floating-zone (OFZ) crystal growth methods [54][55][56][57][58][59][60][61][62][63]. Figure 1a,b show the schematic illustrations of the self-flux and Bridgman growth methods, respectively.A typical procedure for the self-flux growth method is as follows [56,63].First, the FeSe precursor was prepared by reacting Fe and Se powders at 700 • C for 4 h in an evacuated quartz tube.Then, the obtained FeSe precursor was ground into powder and mixed with A (A = K, Rb, and Cs) pieces at a ratio of A:FeSe = 0.8:2.The mixtures were put into a double-sealed quartz ampule which would protect the raw materials from exposure to air, in case the inner tube broke during growth.The samples were heated to 1030 • C in 4 h and kept at this temperature for 2 h.Before the furnace was shut down at 750 • C, either a cooling rate of 6 • C/h or a quenching method was applied.The actual compositions of K x Fe 2 Se 2 and Cs x Fe 2 Se 2 were determined to be K:Fe:Se = 0.75:1.66:2and Cs:Fe:Se = 0.81:1.61:2,respectively [56].In addition, it was reported that using a Bridgman method, A x Fe 2−y Se 2 single crystals were grown when the melt was soaked at 1070 • C for 5 h and a slow traveling speed of 3 mm/h was applied [62].Using the starting mixture Rb:FeSe = 1:2.5, the actual compositions of the obtained crystal were determined to be Rb:Fe:Se = 0.740(36):1.600(6):2.000(25)[62].
Crystals 2017, 7, 167 3 of 26 = 0.8:2.The mixtures were put into a double-sealed quartz ampule which would protect the raw materials from exposure to air, in case the inner tube broke during growth.The samples were heated to 1030 °C in 4 h and kept at this temperature for 2 h.Before the furnace was shut down at 750 °C, either a cooling rate of 6 °C/h or a quenching method was applied.The actual compositions of KxFe2Se2 and CsxFe2Se2 were determined to be K:Fe:Se = 0.75:1.66:2and Cs:Fe:Se = 0.81:1.61:2,respectively [56].In addition, it was reported that using a Bridgman method, AxFe2−ySe2 single crystals were grown when the melt was soaked at 1070 °C for 5 h and a slow traveling speed of 3 mm/h was applied [62].Using the starting mixture Rb:FeSe = 1:2.5, the actual compositions of the obtained crystal were determined to be Rb:Fe:Se = 0.740(36):1.600(6):2.000(25)[62].
(a) (b) The OFZ crystal growth method is unique in growing both congruent and incongruent melt compounds without contamination of crucible materials.This also allows the production of large crystals that cannot be obtained using solution methods.The relatively high thermal gradient at the crystallization front can be used to control the extent of the constitutional supercooling and has the advantage of a rapid growth of crystals from an incongruent melt.The OFZ method has been successfully used to grow large and high-quality single crystals of high-Tc superconductors, including FeSCs such as AxFe2−ySe2 (A = K, Rb, and Cs) [2,[63][64][65][66][67][68][69][70][71][72][73][74][75][76][77]. Figure 2 shows a schematic illustration of the OFZ growth setup and snapshot of the real growth process.The feed rod was prepared via a one-step conventional solid-state reaction as reported in Ref. [63].Elemental A, Fe, and Se were mixed with the nominal molar ratio of A:Fe:Se = 0.8:2:2 and sintered at 850 °C for 10 h.After sintering, the A0.8Fe2Se2 mixture was uniformly ground into powder, which was pressed into a feed rod of ~70-80 mm in length and ~6-7 mm in diameter using a hydraulic press under an isostatic pressure of 600 bar.The feed rod was used to grow the crystal directly, without the conventional sintering or pre-melting process.A seed rod of 2 cm in length was obtained by cutting the feed rod.The AxFe2−ySe2 single crystals were grown in a four-mirror OFZ furnace (FZ-T-10000-H-III-VPR, Crystal System Inc., Salem, MA, USA) having four 300 W halogen lamps as the heating source.Rotation rates of 20 rpm were employed for both the feed and seed shafts in opposite directions.Growths were carried out at a travelling velocity rate of 0.8 mm/h under an 8 bar argon atmosphere.The obtained crystals were large and homogeneous with a mass of up to 1.8 g. Figure 3a shows a schematic illustration of the OFZ growth process for the AxFe2−ySe2 single crystals.It was found that as the molten zone was slowly moved up along the length of the rotating feed rod, the grown crystal continuously passed through a special temperature zone, Td, where it began to decompose.Therefore, to protect the grown crystal, the four halogen lamps were turned off towards the end of the crystal growth, resulting in un-destroyed crystal phase at the upper portion of the grown ingot.Figure 3bd shows the typical as-grown single-crystal ingots of K0.80Fe1.81Se2,Rb0.80Fe1.81Se2,and Cs0.80Fe1.81Se2,respectively.It can be seen in the inset of Figure 3b that the cleaved ingot displays a large crystal grain with a flat shiny surface.It is interesting to find that although the A ions are different, the iron The OFZ crystal growth method is unique in growing both congruent and incongruent melt compounds without contamination of crucible materials.This also allows the production of large crystals that cannot be obtained using solution methods.The relatively high thermal gradient at the crystallization front can be used to control the extent of the constitutional supercooling and has the advantage of a rapid growth of crystals from an incongruent melt.The OFZ method has been successfully used to grow large and high-quality single crystals of high-T c superconductors, including FeSCs such as A x Fe 2−y Se 2 (A = K, Rb, and Cs) [2,[63][64][65][66][67][68][69][70][71][72][73][74][75][76][77]. Figure 2 shows a schematic illustration of the OFZ growth setup and snapshot of the real growth process.The feed rod was prepared via a one-step conventional solid-state reaction as reported in Ref. [63].Elemental A, Fe, and Se were mixed with the nominal molar ratio of A:Fe:Se = 0.8:2:2 and sintered at 850 • C for 10 h.After sintering, the A 0.8 Fe 2 Se 2 mixture was uniformly ground into powder, which was pressed into a feed rod of ~70-80 mm in length and ~6-7 mm in diameter using a hydraulic press under an isostatic pressure of 600 bar.The feed rod was used to grow the crystal directly, without the conventional sintering or pre-melting process.A seed rod of 2 cm in length was obtained by cutting the feed rod.The A x Fe 2−y Se 2 single crystals were grown in a four-mirror OFZ furnace (FZ-T-10000-H-III-VPR, Crystal System Inc., Salem, MA, USA) having four 300 W halogen lamps as the heating source.Rotation rates of 20 rpm were employed for both the feed and seed shafts in opposite directions.Growths were carried out at a travelling velocity rate of 0.8 mm/h under an 8 bar argon atmosphere.The obtained crystals were large and homogeneous with a mass of up to 1.8 g. Figure 3a shows a schematic illustration of the OFZ growth process for the A x Fe 2−y Se 2 single crystals.It was found that as the molten zone was slowly moved up along the length of the rotating feed rod, the grown crystal continuously passed through a special temperature zone, T d , where it began to decompose.Therefore, to protect the grown crystal, the four halogen lamps were turned off towards the end of the crystal growth, resulting in un-destroyed crystal phase at the upper portion of the grown ingot.Figure 3b-d shows the typical as-grown single-crystal ingots of K 0.80 Fe 1.81 Se 2 , Rb 0.80 Fe 1.81 Se 2 , and Cs 0.80 Fe 1.81 Se 2 , respectively.It can be seen in the inset of Figure 3b that the cleaved ingot displays a large crystal grain with a flat shiny surface.It is interesting to find that although the A ions are different, the iron content in all the A x Fe 2−y Se 2 crystals is approximately 1.81, which is higher than for the ones grown by the self-flux and Bridgman methods.In addition, it was observed that the Fe content in the crystals can be adjusted by changing the growth atmospheres.content in all the AxFe2−ySe2 crystals is approximately 1.81, which is higher than for the ones grown by the self-flux and Bridgman methods.In addition, it was observed that the Fe content in the crystals can be adjusted by changing the growth atmospheres.content in all the AxFe2−ySe2 crystals is approximately 1.81, which is higher than for the ones grown by the self-flux and Bridgman methods.In addition, it was observed that the Fe content in the crystals can be adjusted by changing the growth atmospheres.

Hydrothermal Growth
The hydrothermal method is an important method of crystal growth that is complementary to the classical melt-based or vapor transport methods, being widely used to synthesize new materials, new structures, and new phases for various applications [78].This method is available for preparing novel SCs, such as Ba 1−x K x BiO 3 [79], Ba 1−x K x Bi 1−y Na y O 3 [79], BaPd 1−x Bi x O 3 [80], and La 2 CuO 4+y [81].Recently, the hydrothermal growth of (Li 1−x Fe x )OHFeSe single crystals has been reported [53].The crystal precursors were prepared by cleaving the OFZ-grown single crystals of A x Fe 2−y Se 2 (A = K, Rb, and Cs) [63].C(NH 2 ) 2 Se (99.95%),Fe powder (99.995%),LiOH (99.95%), and 9 mL H 2 O with a mol ratio of Se:Fe:Li = 1:4.38:51.47-154.41 were used for preparing the mixtures.Both the crystal precursors and the mixtures were tightly sealed in a Teflon-lined steel autoclave (30 mL) prior to being heated in a box furnace from room temperature to 120-180 • C at a rate of 60 • C/h.The crystal precursors and mixtures were held at the temperature for up to 4 d, before cooling down naturally to room temperature.The large as-grown (Li 1−x Fe x )OHFeSe single crystals were separated and washed several times with methanol solution to obtain clean surfaces.Figure 4a,b show the Teflon-lined hydrothermal synthesis autoclave reactor and the growth procedure, respectively.Similar hydrothermal growth methods have been used to prepare (Li 1−x Fe x )OHFeSe materials, but, the precursor chosen has significant effects on the final products.Using tetragonal FeSe as the precursor, small (~10 × 10 × 1 µm) crystals were grown [82].Without using any precursor, polycrystalline samples were obtained [52].

Hydrothermal Growth
The hydrothermal method is an important method of crystal growth that is complementary to the classical melt-based or vapor transport methods, being widely used to synthesize new materials, new structures, and new phases for various applications [78].This method is available for preparing novel SCs, such as Ba1−xKxBiO3 [79], Ba1−xKxBi1−yNayO3 [79], BaPd1−xBixO3 [80], and La2CuO4+y [81].Recently, the hydrothermal growth of (Li1−xFex)OHFeSe single crystals has been reported [53].The crystal precursors were prepared by cleaving the OFZ-grown single crystals of AxFe2−ySe2 (A = K, Rb, and Cs) [63].C(NH2)2Se (99.95%),Fe powder (99.995%),LiOH (99.95%), and 9 mL H2O with a mol ratio of Se:Fe:Li = 1:4.38:51.47-154.41 were used for preparing the mixtures.Both the crystal precursors and the mixtures were tightly sealed in a Teflon-lined steel autoclave (30 mL) prior to being heated in a box furnace from room temperature to 120-180 °C at a rate of 60 °C/h.The crystal precursors and mixtures were held at the temperature for up to 4 d, before cooling down naturally to room temperature.The large as-grown (Li1−xFex)OHFeSe single crystals were separated and washed several times with methanol solution to obtain clean surfaces.Figure 4a,b show the Teflonlined hydrothermal synthesis autoclave reactor and the growth procedure, respectively.Similar hydrothermal growth methods have been used to prepare (Li1−xFex)OHFeSe materials, but, the precursor chosen has significant effects on the final products.Using tetragonal FeSe as the precursor, small (~10 × 10 × 1 μm) crystals were grown [82].Without using any precursor, polycrystalline samples were obtained [52].

Crystal Characterization Techniques
The (Li1−xFex)OHFeSe and AxFe2−ySe2 (A = K, Rb, and Cs) single crystals have been characterized by different kinds of techniques [2,52,53,63].The actual composition of the crystals is determined by energy-dispersive X-ray (EDX) spectroscopy or more precise inductively coupled plasma atomicemission spectroscopy (ICP-AES) analysis.The crystal structures are characterized by X-ray diffraction (XRD) and neutron powder diffraction (NPD).Electrical resistivity is measured by a standard four-probe technique to exclude the resistance of the leads using a physical properties measuring system (PPMS, Quantum Design).The contact resistance is smaller than 100 μΩ.Measurements of the magnetic susceptibility are investigated by a superconducting quantum interface device (SQUID) magnetometer (Quantum Design MPMS).

Crystal Structure
The final shape and size of the obtained (Li1−xFex)OHFeSe single crystals depends on the precursor crystals used.Thus, the large OFZ-grown AxFe2−ySe2 (A = K, Rb, and Cs) crystal precursors used in the hydrothermal growth allows the preparation of large, high-quality (Li1−xFex)OHFeSe single crystals ~1 cm in diameter, as shown in Figure 5a.Due to the hydrothermal reaction, a thin layer made from [(Li1−xFex)OH](Fe1−yLiy)Se is usually deposited on the surface of the as-grown crystals, which shows Tc ~ 30-40 K with a broad transition [83], as shown in Figure 5b.When the

Crystal Characterization Techniques
The (Li 1−x Fe x )OHFeSe and A x Fe 2−y Se 2 (A = K, Rb, and Cs) single crystals have been characterized by different kinds of techniques [2,52,53,63].The actual composition of the crystals is determined by energy-dispersive X-ray (EDX) spectroscopy or more precise inductively coupled plasma atomic-emission spectroscopy (ICP-AES) analysis.The crystal structures are characterized by X-ray diffraction (XRD) and neutron powder diffraction (NPD).Electrical resistivity is measured by a standard four-probe technique to exclude the resistance of the leads using a physical properties measuring system (PPMS, Quantum Design).The contact resistance is smaller than 100 µΩ.Measurements of the magnetic susceptibility are investigated by a superconducting quantum interface device (SQUID) magnetometer (Quantum Design MPMS).

Crystal Structure
The final shape and size of the obtained (Li 1−x Fe x )OHFeSe single crystals depends on the precursor crystals used.Thus, the large OFZ-grown A x Fe 2−y Se 2 (A = K, Rb, and Cs) crystal precursors used in the hydrothermal growth allows the preparation of large, high-quality (Li 1−x Fe x )OHFeSe single crystals ~1 cm in diameter, as shown in Figure 5a.Due to the hydrothermal reaction, a thin layer made from [(Li 1−x Fe x )OH](Fe 1−y Li y )Se is usually deposited on the surface of the as-grown crystals, which shows T c ~30-40 K with a broad transition [83], as shown in Figure 5b.When the deposited materials are carefully removed with Q-cotton in methanol, the black and plate-like crystal surface appears, as shown in Figure 5a.The as-grown crystals can be easily cleaved along the (001) direction, as shown in Figure 5c.This because that the c-axis is increased by 31%, since the adjacent edge-sharing FeSe 4 tetrahedra are linked to the intercalated (Li 1−x Fe x )OH layer via a much weaker hydrogen bonding interaction [52,53,65], however, the (001) plane, i.e., the surface of the crystal, is robust during the hydrothermal growth, as shown in Figure 5d.The as-grown crystals of (Li 1−x Fe x )OHFeSe are easily decomposed at room temperature, however, they are stable and can be stored in low-temperature environments like [(Li 1−x Fe x )OH](Fe 1−y Li y )Se [83].7a-c show the XRD patterns of the A0.80Fe1.81Se2(A = K, Rb, and Cs) crystal precursors.In the three figures, the (00l) reflections demonstrating a tetragonal structure with space group I4/m are related to the 245 insulating phase.The ordered and disordered iron vacancies along the c-axis in the AxFe2−ySe2 crystals are characterized by slightly different lattice constants.It can be seen that there are three weak shoulders beside the (008), (0010), and (0012) reflections, as marked with the asterisks.The second set of the (00l) reflections with lower intensity is attributed to phase separation in the crystals [60].The stronger reflections come from the superstructure, indicating that they are related to the iron vacancy-ordered insulating phase.Thus, the second phase marked with asterisks must come from the minor metallic phase which is free of iron vacancy ordering, indicating that the crystal precursor only has a small volume (10%) of the SC phase [84].However, only one set    008), (0010), and (0012) reflections, as marked with the asterisks.The second set of the (00l) reflections with lower intensity is attributed to phase separation in the crystals [60].The stronger reflections come from the superstructure, indicating that they are related to the iron vacancy-ordered insulating phase.Thus, the second phase marked with asterisks must come from the minor metallic phase which is free of iron vacancy ordering, indicating that the crystal precursor only has a small volume (10%) of the SC phase [84].However, only one set of the 00l (l = 2n) peaks is measured in (Li 1−x Fe x )OHFeSe single crystals, indicating all of them are in a pure phase, as shown in Figure 7a-c.Hydrothermal growth parameters greatly influence the structure and properties of the (Li 1−x Fe x )OHFeSe single crystals.In order to find the optimum synthesis conditions, it is necessary to study the effects of the important growth parameters such as growth time (t), growth temperature (T g ), and the molar ratio of lithium ions (c m ) on c.  8) Å respectively, such that the range of variation in c due to changes in T g spans the ranges of variation in c due to changes in t and c m .Therefore, compared with t and c m , T g is more preferable for investigating the structural changes of the crystals, because by varying T g both the highest values and the broadest distribution of c can be achieved at the same time.In addition, it is reported that reductive lithiation of the hydrothermally synthesized samples using lithium/ammonia solution can increase the c lattice parameter to obtain the SC phase [82].Hydrothermal growth parameters greatly influence the structure and properties of the (Li1−xFex)OHFeSe single crystals.In order to find the optimum synthesis conditions, it is necessary to study the effects of the important growth parameters such as growth time (t), growth temperature (Tg), and the molar ratio of lithium ions (cm) on c.Therefore, compared with t and cm, Tg is more preferable for investigating the structural changes of the crystals, because by varying Tg both the highest values and the broadest distribution of c can be achieved at the same time.In addition, it is reported that reductive lithiation of the hydrothermally synthesized samples using lithium/ammonia solution can increase the c lattice parameter to obtain the SC phase [82].

Superconductivity, Spin Density Wave, Antiferromagnetism and Ferromagnetism
Surprisingly, although the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors have very different properties, all the synthesized (Li 1−x Fe x )OHFeSe crystals show enhanced SC properties, indicating that the intercalating layers play important roles in the high-T c superconductivity mechanism [53].
Figure 9a-f show the electrical and magnetic properties of the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors and the (Li 1−x Fe x )OHFeSe crystals.It can be clearly seen that the properties of the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors are different despite their similar structures.
The K 0.80 Fe 1.81 Se 2 precursor is a good superconductor, with a T c of 31.76 (29.31)K derived from magnetic (electrical) measurements.After the hydrothermal ion-exchange process, its T c is increased by 6.08 (13.38)K. Its zero field cooled (ZFC) susceptibility is nearly temperature independent before the onset of superconductivity, indicating that the normal state is Pauli paramagnetic, which can be found in the SC samples of (Li 1−x Fe x )OHFeSe, A x Fe 2−y Se 2 (A = K, Rb, and Cs), and FeSe [3,7,56,62,87,88].The hump peak of the normalized resistance versus temperature (R ab /R p -T) curve shifts from 220.79 K to 266.06 K and the resistivity of the hump peak is decreased from 560 mΩcm to 0.13 mΩcm due to the hydrothermal reaction.The peak-shift effect indicates that the SC/metallic property is improved.The SC transition width is defined as ∆T = T c (onset) − T c (0), where T c (onset) is the temperature where the resistivity starts to deviate from the normal-state resistivity, and T c (0) is the temperature where zero resistivity state is achieved.For the K 0.80 Fe 1.81 Se 2 crystal precursor ∆T is 4.19 K, which is smaller than those for all the (Li 1−x Fe x )OHFeSe crystals, indicating that some inhomogeneous structures resulting from the intercalating layers broaden the transition width.

Superconductivity, Spin Density Wave, Antiferromagnetism and Ferromagnetism
Surprisingly, although the A0.80Fe1.81Se2(A = K, Rb, and Cs) precursors have very different properties, all the synthesized (Li1−xFex)OHFeSe crystals show enhanced SC properties, indicating that the intercalating layers play important roles in the high-Tc superconductivity mechanism [53].
Figure 9a-f show the electrical and magnetic properties of the A0.80Fe1.81Se2(A = K, Rb, and Cs) precursors and the (Li1−xFex)OHFeSe crystals.It can be clearly seen that the properties of the A0.80Fe1.81Se2(A = K, Rb, and Cs) precursors are different despite their similar structures.
The K0.80Fe1.81Se2precursor is a good superconductor, with a Tc of 31.76 (29.31)K derived from magnetic (electrical) measurements.After the hydrothermal ion-exchange process, its Tc is increased by 6.08 (13.38)K. Its zero field cooled (ZFC) susceptibility is nearly temperature independent before the onset of superconductivity, indicating that the normal state is Pauli paramagnetic, which can be found in the SC samples of (Li1−xFex)OHFeSe, AxFe2−ySe2 (A = K, Rb, and Cs), and FeSe [3,7,56,62,87,88].The hump peak of the normalized resistance versus temperature (Rab/Rp-T) curve shifts from 220.79 K to 266.06 K and the resistivity of the hump peak is decreased from 560 mΩcm to 0.13 mΩcm due to the hydrothermal reaction.The peak-shift effect indicates that the SC/metallic property is improved.The SC transition width is defined as ΔT = Tc(onset) − Tc(0), where Tc(onset) is the temperature where the resistivity starts to deviate from the normal-state resistivity, and Tc(0) is the temperature where zero resistivity state is achieved.For the K0.80Fe1.81Se2crystal precursor ΔT is 4.19 K, which is smaller than those for all the (Li1−xFex)OHFeSe crystals, indicating that some inhomogeneous structures resulting from the intercalating layers broaden the transition width.The Rb0.80Fe1.81Se2precursor is non-conductive.As the temperature increases its resistance decreases monotonically and sharply, indicating that it acts as an electrical insulator.
The Cs0.80Fe1.81Se2precursor (Tc = 28.67K) exhibits poor superconducting properties.Its resistance does not reach zero even at T = 2.53 K, but its Rab/Rp is as high as 7.80%.Its electrical transport properties are complex.It can be seen that its Rab/Rp-T curve shows two hump peaks, P1(61.31K, 0.991) and P2(31.46K, 1.000), dividing the curve into three regions: high-, medium-, and lowtemperature regions, which are denoted as 'I', 'II', and 'III', respectively.In region 'I', it shows The Rb 0.80 Fe 1.81 Se 2 precursor is non-conductive.As the temperature increases its resistance decreases monotonically and sharply, indicating that it acts as an electrical insulator.
The Cs 0.80 Fe 1.81 Se 2 precursor (T c = 28.67K) exhibits poor superconducting properties.Its resistance does not reach zero even at T = 2.53 K, but its R ab /R p is as high as 7.80%.Its electrical transport properties are complex.It can be seen that its R ab /R p -T curve shows two hump peaks, P 1 (61.31K, 0.991) and P 2 (31.46 K, 1.000), dividing the curve into three regions: high-, medium-, and low-temperature regions, which are denoted as 'I', 'II', and 'III', respectively.In region 'I', it shows semiconducting behavior.Additionally, the first peak P 1 is reached at T = 61.31K, which is much smaller than those for the K 0.80 Fe 1.81 Se 2 crystal precursor and all the (Li 1−x Fe x )OHFeSe crystals, indicating that an insulating/semiconducting phase is dominant in the high-temperature region.In region 'II', R ab /R p decreases with temperature because the metallic phase starts to play a role, and at the valley point 'V' (T = 47.32 K) the balance between the competitive conductive and non-conductive phases happens.After the 'V' point an unbalance occurs and thus the resistance increases again before the second hump peak 'P 2 ' is reached, where the SC state arises.In region 'III', the SC phase plays a leading role, and a sharp drop in resistance occurs after 'P 2 ' under the co-effects of the SC and metallic phases.
Despite the significant variation in the properties of the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors, high-quality (Li 1−x Fe x )OHFeSe crystals with high T c were obtained from all of them.The susceptibility measurements show that all the (Li 1−x Fe x )OHFeSe crystals have high-temperature SC transitions, with T c = 37.84 K, 38.69 K, and 39.03 K measured from samples produced from the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors, respectively.The superconductive shielding fraction estimated from the zero-field-cooling magnetization at T = 3 K is 97%, 100%, and 100% respectively, indicating the bulk superconductivity nature and high quality of the crystals.The electrical measurements show onset T c = 42.69K, 43.87 K, and 44.66 K respectively, confirming the SC transitions.Zero resistance of the (Li 1−x Fe x )OHFeSe crystals grown using the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors is measured below 35.12, 32.79, and 38.18 K respectively, giving associated transition widths ∆T of 7.57 K, 11.08 K, and 6.48 K.In addition, it is found that the ionic radius of A + (R A +) influences greatly the structures and properties of the (Li 1−x Fe x )OHFeSe crystals.Both T c and c increase with R A +, suggesting that T c depends on c.Among the (Li 1−x Fe x )OHFeSe crystals, the crystal using the Cs 0.80 Fe 1.81 Se 2 precursor shows the best superconductivity: the highest T c , the highest T c (0), and the narrowest ∆T.In addition, the R ab /R p -T curves of all the obtained crystals show a hump peak near room temperature, which is attributed to the doping effect of the (Li 1−x Fe x )OH layers [82].For the crystals made from the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors, the hump temperature T h = 266.06,276.18, and 281.34K respectively.It shows that as R A + (or c) increases, T h shifts toward high temperatures, indicating that the SC/metallic property is enhanced obviously in the crystals with the largest c-axis length, but the non-conductive property is weakened.Therefore, T c increases due to the enhanced doping.
The (Li 1−x Fe x )OHFeSe and the A x Fe 2−y Se 2 (A = K, Rb and Cs) crystals demonstrate complex electrical transport properties, which could be attributed to the doping effects of the (Li 1−x Fe x )OH layer or A ions or the vacant sites in the FeSe layer [60,82,89].However, using the same hydrothermal synthesis route, all (Li 1−x Fe x )OHFeSe crystals have been synthesized with high superconductive shielding fraction and high T c , despite the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors having significantly different properties that vary from being a good superconductor, to an insulator, and finally to a poor superconductor.
It is interesting to point out that SC and non-SC (Li 1−x Fe x )OHFeSe single crystals can be selectively grown by controlling the growing parameters.SC crystals with large c-axis length can be prepared by a low-temperature hydrothermal reaction (e.g., 120 • C) or a high-temperature hydrothermal reaction for a short time (e.g., 160 • C for 40 h).In contrast, non-SC crystals with small c-axis length can be grown at high hydrothermal reaction temperatures for a long time (e.g., 180 • C and 72 h).Non-SC single crystals exhibit AFM spin density wave (SDW) transitions.Figure 10 shows the XRD patterns for a non-SC crystal prepared using a Cs 0.80 Fe 1.81 Se 2 crystal precursor.The inset shows that the AFM SDW transition temperature T s = 125.41K [53].For polycrystalline (Li 1−x Fe x )OHFeSe, the SC sample with T c = 40 K was grown at 120 • C for 96 h, while the non-SC sample with T s = 125 (127) K was grown at 160 (180) • C for 72 h [90].
In addition, the (Li 1−x Fe x )OHFeSe provides a new platform to study the interplay between superconductivity and magnetism.It was reported that in polycrystalline (Li 0.8 Fe 0.2 )OHFeSe superconductivity coexists with a field-induced ferromagnetism under external magnetic field and antiferromagnetism at zero field [52,91].In [(Li 1−x Fe x )OH](Fe 1−y Li y )Se, superconductivity below T c = 43 K coexists with ferromagnetism below 10 K [83].The study of SC and non-SC (Li 1−x Fe x )OHFe 1−y Se suggests a glassy magnetic state, probably comprising clusters of iron ions of varying cluster sizes distributed within the lithium hydroxide layer [92].

Phase Diagram
The phase diagram of the (Li1−xFex)OHFeSe single crystals using the A0.80Fe1.81Se2(A = K, Rb, and Cs) crystal precursors is established based on c dependence of Ts and Tc, as shown in Figure 11.It can be seen that the crystals show AFM SDW and SC transitions in low and high c regions, respectively.As T > Ts (Tc), Curie-Weiss (Pauli paramagnetic) phase forms.The phase diagram shows a step behavior of the AFM SDW and SC transitions between 9.254(3) and 9.255(1) Å, which is similar to that for polycrystalline samples of LaO1−xFxFeAs [93], but different from those for cuprate SCs [94] and other FeSCs [95], such as CeFeAsO1-xFx, (K,Tl)FexSe2 [96], NaFe1-xCoxAs [97] In addition, as c increases the Tc-c relationship experiences three regions successively: region 'I', region 'II', and region 'III'.In region 'I' ('II'), Tc gradually decreases (increases) stably as c increases.However, in region 'III', the Tc-c relationship is not stable, indicating that a large c-axis weakens the hydrogen bonding interaction between the layers which makes the structure and property unstable.The Tc-c relationship has a V-shape, which is in sharp contrast to the inverse Vshaped one in cuprate SCs [94] and other FeSCs [93,[95][96][97][98].The complex SC phase diagram can be attributed to the doping effect of the (Li1−xFex)OH layer (the Fe/Li ratio, the migration of Fe and the charge transfer from the intercalated layer to the FeSe layer) as well as the complex competing effects between the several different states related to phase separation [18,52,82,89,[99][100][101].Comparison of this phase diagram to that for (Li1−xFex)OHFeSe polycrystals shows some similarities [90].They both have AFM SDW and SC phases, which lie in the low and high c regions, respectively.However, for the single crystals, the AFM SDW phase exists in the region where c ≤ 9.254(3) Å, whereas for the polycrystals, the SC phase forms for c ≥ 9.2152(8) Å [90].Therefore, in the region where 9.2152(8) Å ≤ c ≤ 9.254(3) Å, the phase of the single crystal system differs from that of the polycrystalline system, even if both systems have the same c value.During the hydrothermal growth of (Li1−xFex)OHFeSe, the chemical reactions are different for synthesizing these two different kinds of samples: For the

Phase Diagram
The phase diagram of the (Li 1−x Fe x )OHFeSe single crystals using the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) crystal precursors is established based on c dependence of T s and T c , as shown in Figure 11.It can be seen that the crystals show AFM SDW and SC transitions in low and high c regions, respectively.As T > T s (T c ), Curie-Weiss (Pauli paramagnetic) phase forms.The phase diagram shows a step behavior of the AFM SDW and SC transitions between 9.254(3) and 9.255(1) Å, which is similar to that for polycrystalline samples of LaO 1−x F x FeAs [93], but different from those for cuprate SCs [94] and other FeSCs [95], such as CeFeAsO 1−x F x , (K,Tl)Fe x Se 2 [96], NaFe 1−x Co x As [97], Ba(Fe In addition, as c increases the T c -c relationship experiences three regions successively: region 'I', region 'II', and region 'III'.In region 'I' ('II'), T c gradually decreases (increases) stably as c increases.However, in region 'III', the T c -c relationship is not stable, indicating that a large c-axis weakens the hydrogen bonding interaction between the layers which makes the structure and property unstable.The T c -c relationship has a V-shape, which is in sharp contrast to the inverse V-shaped one in cuprate SCs [94] and other FeSCs [93,[95][96][97][98].The complex SC phase diagram can be attributed to the doping effect of the (Li 1−x Fe x )OH layer (the Fe/Li ratio, the migration of Fe and the charge transfer from the intercalated layer to the FeSe layer) as well as the complex competing effects between the several different states related to phase separation [18,52,82,89,[99][100][101].Comparison of this phase diagram to that for (Li 1−x Fe x )OHFeSe polycrystals shows some similarities [90].They both have AFM SDW and SC phases, which lie in the low and high c regions, respectively.However, for the single crystals, the AFM SDW phase exists in the region where c ≤ 9.254(3) Å, whereas for the polycrystals, the SC phase forms for c ≥ 9.2152(8) Å [90].Therefore, in the region where 9.2152(8) Å ≤ c ≤ 9.254(3) Å, the phase of the single crystal system differs from that of the polycrystalline system, even if both systems have the same c value.During the hydrothermal growth of (Li 1−x Fe x )OHFeSe, the chemical reactions are different for synthesizing these two different kinds of samples: For the polycrystals it is a three-dimensional (3D)-diffusion-3D-growth process, but for growing the single crystals, it is a 2D-diffusion-1D-growth process, as shown in Figure 4.These different growth mechanisms, along with the size effect, are likely to lead to the significant differences in the characteristics observed between the two types of samples.polycrystals it is a three-dimensional (3D)-diffusion-3D-growth process, but for growing the single crystals, it is a 2D-diffusion-1D-growth process, as shown in Figure 4.These different growth mechanisms, along with the size effect, are likely to lead to the significant differences in the characteristics observed between the two types of samples.

Anisotropic Behavior
The anisotropic properties of a high-quality (Li1−xFex)OHFeSe single crystal have been systematically investigated by performing electrical and magnetic measurements [102].
Figure 12 shows the temperature dependence of the Hall coefficient RH.It can be seen that RH is negative in the whole temperature range from 2-300 K, indicating that electron-like charge carriers dominate in the crystal.RH decreases as T decreases from room temperature, and reaches a minimum value at T* ≈ 150 K, below which it demonstrates a remarkable upturn.The strong temperature dependence of RH may suggest a strong multiband-effect in the crystal: the electron scattering rate of each band varies with temperature differently, and thus a combined contribution of multiple bands may result in a strongly temperature dependent RH.Another possible reason can be due to the magnetic skew scattering mechanism: scattering of conduction electrons from local moments is not symmetric because of spin-orbital coupling [103].However, it is hard to distinguish between the different contributions from different mechanisms.A rough estimation based on the simple relation RH = −1/ne indicates that the carrier density n is low, i.e., n is estimated to be 3.0 × 10 21 cm −3 at 225 K, which is similar to other anisotropic SCs, such as NdFeAsO0.82F0.18,polycrystalline LaFeAsO0.9F0.1−δ, and cuprate SCs [103,104].
Figure 13 shows ρab-T curves measured near Tc, where ρab is the ab-plane resistivity.The onset Tc = 43 K and the residual resistance ratio RRR = ρab(300 K)/ρab(43 K) = 4.95.For both H || ab and H || c, Tc(0) decreases faster than Tc(onset) as μ0H increases, resulting in a broadening effect of ΔT. Figure 13c shows that both ΔT(H || ab) and ΔT(H || c) increase monotonically with μ0H.A quantitative fit gives ΔT ∝ H α , where α is a constant.For H || ab, α is 0.177 in the range of 0-9 T. For H || c, α is 0.076, 0.155, and 0.195 in region "I" (≤1 T), region "II" (1-3 T), and region "III" (3-9 T), respectively.The broad SC transition at 0 T can be attributed to minority impurities, which are not observable in XRD measurements but may influence ΔT.Such minorities could be a normal state

Anisotropic Behavior
The anisotropic properties of a high-quality (Li 1−x Fe x )OHFeSe single crystal have been systematically investigated by performing electrical and magnetic measurements [102].
Figure 12 shows the temperature dependence of the Hall coefficient R H .It can be seen that R H is negative in the whole temperature range from 2-300 K, indicating that electron-like charge carriers dominate in the crystal.R H decreases as T decreases from room temperature, and reaches a minimum value at T* ≈ 150 K, below which it demonstrates a remarkable upturn.The strong temperature dependence of R H may suggest a strong multiband-effect in the crystal: the electron scattering rate of each band varies with temperature differently, and thus a combined contribution of multiple bands may result in a strongly temperature dependent R H . Another possible reason can be due to the magnetic skew scattering mechanism: scattering of conduction electrons from local moments is not symmetric because of spin-orbital coupling [103].However, it is hard to distinguish between the different contributions from different mechanisms.A rough estimation based on the simple relation R H = −1/ne indicates that the carrier density n is low, i.e., n is estimated to be 3.0 × 10 21 cm −3 at 225 K, which is similar to other anisotropic SCs, such as NdFeAsO 0.82 F 0.18 , polycrystalline LaFeAsO 0.9 F 0.1−δ , and cuprate SCs [103,104].
Figure 13 shows ρ ab -T curves measured near T c , where ρ ab is the ab-plane resistivity.The onset T c = 43 K and the residual resistance ratio RRR = ρ ab (300 K)/ρ ab (43 K) = 4.95.For both H || ab and H || c, T c (0) decreases faster than T c (onset) as µ 0 H increases, resulting in a broadening effect of ∆T. Figure 13c shows that both || ab) and ∆T(H || c) increase monotonically with µ 0 H.A quantitative fit gives ∆T ∝ H α , where α is a constant.For H || ab, α is 0.177 in the range of 0-9 T. For H || c, α is 0.076, 0.155, and 0.195 in region "I" (≤1 T), region "II" (1-3 T), and region "III" (3-9 T), respectively.The broad SC transition at 0 T can be attributed to minority impurities, which are not observable in XRD measurements but may influence ∆T.Such minorities could be a normal state and/or SC phase.Furthermore, it can be seen that ∆T(H || c) is always larger than ∆T(H || ab), indicating that the broadening effect is anisotropic.The anisotropy ratio of ∆T is defined as η = ∆T(H || c)/∆T(H || ab). Figure 13c shows that in region "I", η increases rapidly with µ 0 H.In region "II", the increase of η is very slow, and the maximum value η max = 1.67 is obtained at 3 T.In region "III", η decreases steadily as µ 0 H increases, and η = 1.64 is reached at 9 T, showing that high fields can suppress the anisotropy ratio.The tunability of η as a function of µ 0 H shows great potential toward practical applications like magnetic sensors and switching devices.13c shows that in region "I", η increases rapidly with μ0H.In region "II", the increase of η is very slow, and the maximum value ηmax = 1.67 is obtained at 3 T.In region "III", η decreases steadily as μ0H increases, and η = 1.64 is reached at 9 T, showing that high fields can suppress the anisotropy ratio.The tunability of η as a function of μ0H shows great potential toward practical applications like magnetic sensors and switching devices.The broadening behavior of ΔT can be analyzed based on the thermally activated flux flow (TAFF) model, and the TA resistivity ρ(T,H) = ρ0exp(-U/T), where ρ0 is a constant and U is the activation energy [105].Assuming U = U0(1 − t), where t = T/Tc is the reduced temperature and U0 is apparent activation energy, the Arrhenius relation can be derived as lnρ(T, H) = lnρ0 + U0/Tc − U0/T. Figure 14a,b show that the experimental data can be fitted very well using the Arrhenius relation (solid lines).Figure 14c shows the μ0H dependence of U0.Inset of Figure 14c displays the same data on a double-logarithmic scale.It is seen that U0 for H || ab is much higher than for H || c, indicating a much stronger flux pinning for H || ab.In addition, for both configurations, it is found that U0 decreases with increasing μ0H according to the power law of U0 ∝ (1/H) α , where α is a constant.In region "I" (≤1 T) and region "II" (1-9 T), α = 0.364 (0.615) and 0.645 (0.436) for H || ab (H || c), respectively.For H || ab, the weak power-law decrease of U0 in region "I" suggests that single-vortex pinning is dominant in low-field, while a more rapidly decrease of U0 in region "II" can be related to the crossover to a collective pinning regime in high-field.However, it is reversed for H || c, suggesting that in region "I" ("II") collective (single-vortex) pinning is dominant.Furthermore, it can be seen that the anisotropy ratio σ = U0(H || ab)/U0(H || c) also shows a crossover at 1 T. In region "I", σ increases rapidly with μ0H, from σ = 3.91 at 0.25 T to the maximum value σmax = 5.53 at 1 T.However, in region "II", σ decreases slowly as μ0H increases, to a minimum value σmin = 3.52 at 9 T, indicating that high field weakens the anisotropy.In addition, σ is higher than that for a Bi2.2Sr2Ca0.8Cu2O8+δsingle crystal, which typically lies in the range of 1.5-3 [105].Since σ can be tuned by the applied field, it shows great potential for device applications, such as in the development of magnetic field and temperature sensors.The broadening behavior of ∆T can be analyzed based on the thermally activated flux flow (TAFF) model, and the TA resistivity ρ(T,H) = ρ 0 exp(-U/T), where ρ 0 is a constant and U is the activation energy [105].Assuming U = U 0 (1 − t), where t = T/T c is the reduced temperature and U 0 is apparent activation energy, the Arrhenius relation can be derived as lnρ(T, H) = lnρ 0 + U 0 /T c − U 0 /T. Figure 14a,b show that the experimental data can be fitted very well using the Arrhenius relation (solid lines).Figure 14c shows the µ 0 H dependence of U 0 .Inset of Figure 14c displays the same data on a double-logarithmic scale.It is seen that U 0 for H || ab is much higher than for H || c, indicating a much stronger flux pinning for H || ab.In addition, for both configurations, it is found that U 0 decreases with increasing µ 0 H according to the power law of U 0 ∝ (1/H) α , where α is a constant.In region "I" (≤1 T) and region "II" (1-9 T), α = 0.364 (0.615) and 0.645 (0.436) for H || ab (H || c), respectively.For H || ab, the weak power-law decrease of U 0 in region "I" suggests that single-vortex pinning is dominant in low-field, while a more rapidly decrease of U 0 in region "II" can be related to the crossover to a collective pinning regime in high-field.However, it is reversed for H || c, suggesting that in region "I" ("II") collective (single-vortex) pinning is dominant.Furthermore, it can be seen that the anisotropy ratio σ = U 0 (H || ab)/U 0 (H || c) also shows a crossover at 1 T. In region "I", σ increases rapidly with µ 0 H, from σ = 3.91 at 0.25 T to the maximum value σ max = 5.53 at 1 T.However, in region "II", σ decreases slowly as µ 0 H increases, to a minimum value σ min = 3.52 at 9 T, indicating that high field weakens the anisotropy.In addition, σ is higher than that for a Bi 2.2 Sr 2 Ca 0.8 Cu 2 O 8+δ single crystal, which typically lies in the range of 1.5-3 [105].Since σ be tuned by the applied field, it shows great potential for device applications, such as in the development of magnetic field and temperature sensors.Figure 15a shows temperature dependence of μ0Hc2, where μ0Hc2 is determined from the 10% and 50% criteria of the normal resistivity at the onset temperature.For both configurations, the curves show an upward curvature and the values of d(μ0 ‖ )/dT and d(μ0 ‖ )/dT are calculated to be −12.30(−4.01) and −1.61 (−1.27)T/K under the 50% (10%) criterion, respectively.For both criteria, the more positive curvature leads to much higher μ0Hc2 for H || ab than for H || c.It is observed that in some FeSCs, μ0Hc2 depends linearly on T due to the orbital limiting effect [106].Based on this, using linear extrapolation (LE), under the 50% (10%) criterion, the zero-temperature μ0Hc2, μ0Hc2(0), is estimated Figure 15a shows temperature dependence of µ 0 H c2 , where µ 0 H c2 is determined from the 10% and 50% criteria of the normal resistivity at the onset temperature.For both configurations, the curves show an upward curvature and the values of d(µ 0 H ab c2 )/dT and d(µ 0 H c c2 )/dT are calculated to be −12.30(−4.01) and −1.61 (−1.27)T/K under the 50% (10%) criterion, respectively.For both criteria, the more positive curvature leads to much higher µ 0 H c2 for H || ab than for H || c.It is observed that in some FeSCs, µ 0 H c2 depends linearly on T due to the orbital limiting effect [106].Based on this, using linear extrapolation (LE), under the 50% (10%) criterion, the zero-temperature µ 0 H c2 , µ 0 H c2 (0), is estimated to be 457.66(144.74)T and 57.55 (39.17)T for H || ab and H || c, respectively, as shown in Figure 15b.The anisotropic ratio γ = H ab c2 (0)/H c c2 (0) = 7.95 (3.70) is obtained for the 50% (10%) criterion.In addition, µ 0 H c2 (0) can also be estimated using the Werthamer-Helfand-Hohenberg (WHH) equation [107].For the 50% (10%) criterion, µ 0 H c2 (0) = 324.28(102.84)T and 42.45 (32.77)T are obtained from the WHH equation for H || ab and H || c, respectively, and thus γ = 7.64 (3.14) is obtained for the 50% (10%) criterion.The values of µ 0 H c2 (0) and γ obtained by the WHH model are all smaller than by the LE method.Based on the WHH theory and using the parameter values under the 50% criterion, the zero-temperature coherence lengths ξ ab (0) and ξ c (0) are estimated to be 2.7858 nm and 0.3647 nm, respectively, from Ginzburg-Landau theory.Furthermore, using γ = (m c /m ab ) 1/2 , a value of m c /m ab = 2.76 is obtained, where m c and m ab are the effective mass tensors when the electrons are moving perpendicular and parallel to the FeSe layers, respectively.
The magnetization hysteresis loops of the crystal indicated anisotropic behavior and type-II superconductivity, as shown in Figure 16.The critical current density J ab c (J c c ) for H || c (H || ab) can be calculated using the extended Bean model [108].Figure 17a,b show that for a given T (µ 0 H), as µ 0 H (T) increases both J ab c and J c c decrease.When T ≤ 5 K, J ab c (J c c ) exceeds 1.44 × 10 4 (8.29 × 10 3 ) A/cm 2 in high fields up to 4 T. Figure 17c shows the temperature dependence of zero-field J c , whose values are extracted by extrapolation to 0 T. J ab c is higher than J c c for a given T. The anisotropic ratio δ = J ab c /J c c increases from 2.90 to the maximum value of 3.48 as T increases from 2-7 K, but decreases as T increases further, and reaches its lowest value of 2.62 at 30 K.These results show that δ can be adjusted by varying temperature, providing a new basis for designing power-control or power-switching devices.
In order to study the vortex pinning mechanism, the authors plot the normalized pinning force f p = F p /F max p as a function of the reduced field h = H/H irr , where the pinning force density F p = µ 0 HJ c and the irreversibility field µ 0 H irr is obtained by extrapolating the J c 1/2 (µ 0 H)  18 shows that the formula f p ∝ h p (1 − h) q fits the experimental data well for each configuration at 15 K. Flux-pinning parameters of p = 0.686 (0.365) and q = 3.242 (2.452) are obtained for H || ab (H || c) by fitting.The position of the maximum of F p /F max p is h max ≈ p/(p + q).For H || ab (H || c), the fitting value h fit max = 0.175 (0.130) is consistent with the peak position h exp max = 0.174 (0.129) of the experimental curve.These values are close to h max = 0.2 responsible for normal surface pinning (NSP) [110], indicating that the NSP mechanism is dominant in the crystal for each configuration.The ratio 0.175/0.130= 1.35 shows a small anisotropy between the two orientations.However, for the quenched K x Fe 2−y Se 2 single crystals h max = 0.32 or 0.34, indicating that the normal point pinning (NPP) is dominant [111,112].For the Mn doped K x Fe 2−y Se 2 single crystal h max = 0.27 is smaller than for the K x Fe 2−y Se 2 quenched crystals, implying that the NPP may coexist with NSP [112].In the Mn doped K x Fe 2−y Se 2 single crystals, Mn atoms can form non-SC K-Fe-Mn inclusion phases, and such large normal inclusions may serve as the NSP centers in the crystals [112].In comparison with the quenched and the Mn doped K x Fe 2−y Se 2 single crystals, h max for the (Li 1−x Fe x )OHFeSe single crystal is much smaller, indicating that the hydrothermal ion-exchange process is more effective for obtaining NSP centers and changing the pinning mechanism.

Superconducting Mechanism
Density functional theory (DFT) calculations were used to investigate the dominant roles of the (Li0.8Fe0.2)OHlayers in the high-Tc superconductivity of (Li0.8Fe0.2)OHFeSe,and it was found that substitution of Li by Fe can enhance the structural stability both in the ab plane and along the c axis.The Fe0.2 atoms can be the origin of significant electron injection into FeSe.The (Li0.8Fe0.2)OHlayers can be either AFM or FM depending on the spatial distribution of Fe0.2 atoms.The stable structure with large electron injection leads to high-Tc superconductivity [113].In addition, low temperature scanning tunneling microscopy (STM) suggests that the (Li1−xFex)OHFeSe is a plain s-wave superconductor with strong coupling mechanism [114,115].

Conclusions
FeSCs have been attracting a great deal of research interest for the development of new high-Tc SCs.Their diverse structures, complex phases, and exotic SC properties are important for both fundamental studies and technical applications.In general, Tc can be enhanced by chemical and physical methods, such as ion doping and the application of external pressure.In addition, many measures have also been taken to improve other SC properties in FeSC systems.In this paper, a hydrothermal method which can be used for inducing intercalation to increase Tc and improve other SC properties is reviewed, taking the (Li1−xFex)OHFeSe single crystal system as an example.

Superconducting Mechanism
Density functional theory (DFT) calculations were used to investigate the dominant roles of the (Li 0.8 Fe 0.2 )OH layers in the high-T c superconductivity of (Li 0.8 Fe 0.2 )OHFeSe, and it was found that substitution of Li by Fe can enhance the structural stability both in the ab plane and along the c axis.The Fe0.2 atoms can be the origin of significant electron injection into FeSe.The (Li 0.8 Fe 0.2 )OH layers can be either AFM or FM depending on the spatial distribution of Fe0.2 atoms.The stable structure with large electron injection leads to high-T c superconductivity [113].In addition, low temperature scanning tunneling microscopy (STM) suggests that the (Li 1−x Fe x )OHFeSe is a plain s-wave superconductor with strong coupling mechanism [114,115].

Conclusions
FeSCs have been attracting a great deal of research interest for the development of new high-T c SCs. Their diverse structures, complex phases, and exotic SC properties are important for both fundamental studies and technical applications.In general, T c can be enhanced by chemical and physical methods, such as ion doping and the application of external pressure.In addition, many measures have also been

Figure 1 .
Figure 1.Schematic illustrations of the (a) self-flux; and (b) Bridgman growth methods.

Figure 1 .
Figure 1.Schematic illustrations of the (a) self-flux; and (b) Bridgman growth methods.

Figure 2 .
Figure 2. Optical floating-zone (OFZ) growth setup (left); and snapshot (right) of the real iron-based superconductor growth process.

Figure 3 .
Figure 3. (a) Schematic drawing illustrates the OFZ growth process of the AxFe2−ySe2 single crystals, which form between the solid-liquid interface temperature (Ti) and the decomposition temperature (Td), below which the crystals undergo a continuous decomposition during the molten zone traveling; (b) a typical as-grown K0.80Fe1.81Se2single-crystal ingot.Inset shows a crystal cleaved along the growing direction; (c,d) single crystals cut off from ingots of Rb0.80Fe1.81Se2and Cs0.80Fe1.81Se2,respectively.

Figure 2 .
Figure 2. Optical floating-zone (OFZ) growth setup (left); and snapshot (right) of the real iron-based superconductor growth process.

Figure 2 .
Figure 2. Optical floating-zone (OFZ) growth setup (left); and snapshot (right) of the real iron-based superconductor growth process.

Figure 3 .
Figure 3. (a) Schematic drawing illustrates the OFZ growth process of the AxFe2−ySe2 single crystals, which form between the solid-liquid interface temperature (Ti) and the decomposition temperature (Td), below which the crystals undergo a continuous decomposition during the molten zone traveling; (b) a typical as-grown K0.80Fe1.81Se2single-crystal ingot.Inset shows a crystal cleaved along the growing direction; (c,d) single crystals cut off from ingots of Rb0.80Fe1.81Se2and Cs0.80Fe1.81Se2,respectively.

Figure 3 .
Figure 3. (a) Schematic drawing illustrates the OFZ growth process of the A x Fe 2−y Se 2 single crystals, which form between the solid-liquid interface temperature (T i ) and the decomposition temperature (T d ), below which the crystals undergo a continuous decomposition during the molten zone traveling; (b) a typical as-grown K 0.80 Fe 1.81 Se 2 single-crystal ingot.Inset shows a crystal cleaved along the growing direction; (c,d) single crystals cut off from ingots of Rb 0.80 Fe 1.81 Se 2 and Cs 0.80 Fe 1.81 Se 2 , respectively.

Figure 4 .
Figure 4. Growth of (Li1−xFex)OHFeSe single crystals via hydrothermal ion exchange.(a) Schematic apparatus of the autoclave used for the crystal growth; (b) illustration of the Li/Fe-O-H ions diffusing in between the FeSe layers and the A ions diffusing out from the AxFe2−ySe2 (A = K, Rb, and Cs) precursors during the hydrothermal growth process [53].Reprinted with permission from IOP.All rights reserved.

Figure 4 .
Figure 4. Growth of (Li 1−x Fe x )OHFeSe single crystals via hydrothermal ion exchange.(a) Schematic apparatus of the autoclave used for the crystal growth; (b) illustration of the Li/Fe-O-H ions diffusing in between the FeSe layers and the A ions diffusing out from the A x Fe 2−y Se 2 (A = K, Rb, and Cs) precursors during the hydrothermal growth process [53].Reprinted with permission from IOP.All rights reserved.
carefully removed with Q-cotton in methanol, the black and plate-like crystal surface appears, as shown in Figure5a.The as-grown crystals can be easily cleaved along the (001) direction, as shown in Figure5c.This because that the c-axis is increased by 31%, since the adjacent edge-sharing FeSe4 tetrahedra are linked to the intercalated (Li1−xFex)OH layer via a much weaker hydrogen bonding interaction[52,53,65], however, the (001) plane, i.e., the surface of the crystal, is robust during the hydrothermal growth, as shown in Figure5d.The as-grown crystals of (Li1−xFex)OHFeSe are easily decomposed at room temperature, however, they are stable and can be stored in low-temperature environments like [(Li1−xFex)OH](Fe1−yLiy)Se[83].

Figure 6
Figure 6 shows the layered structure of the (Li1−xFex)OHFeSe crystal.During the hydrothermal growth, intercalated (Li1−xFex)OH layers are formed due to the ion exchange of A (K, Rb, and Cs).Along the c-axis anti-PbO type layers of (Li1−xFex)OH alternate with anti-PbO type FeSe layers.In the hydroxide crystal, positively polarized hydrogen atoms of the (Li1−xFex)OH layer point towards the negatively polarized selenium of the FeSe layer.The (Li1−xFex)OH layer has a similar structure to LiOH itself, which likewise crystallizes in the anti-PbO-type [52,83].The hydrothermal growth process induces a complete structural change.The obtained (Li1−xFex)OHFeSe single crystals show an intergrowth of the ion-exchanged (Li1−xFex)OH layers and the FeSe layers along the c-axis, which is greatly different from the structure of the AxFe2−ySe2 (A = K, Rb, and Cs) crystals, representing an intergrowth of the iron-vacancy-ordered and -disordered states along the c-axis.Figure7a-cshow the XRD patterns of the A0.80Fe1.81Se2(A = K, Rb, and Cs) crystal precursors.In the three figures, the (00l) reflections demonstrating a tetragonal structure with space group I4/m are related to the 245 insulating phase.The ordered and disordered iron vacancies along the c-axis in the AxFe2−ySe2 crystals are characterized by slightly different lattice constants.It can be seen that there are three weak shoulders beside the (008), (0010), and (0012) reflections, as marked with the asterisks.The second set of the (00l) reflections with lower intensity is attributed to phase separation in the crystals[60].The stronger reflections come from the superstructure, indicating that they are related to the iron vacancy-ordered insulating phase.Thus, the second phase marked with asterisks must come from the minor metallic phase which is free of iron vacancy ordering, indicating that the crystal precursor only has a small volume (10%) of the SC phase[84].However, only one set Figure 6 shows the layered structure of the (Li1−xFex)OHFeSe crystal.During the hydrothermal growth, intercalated (Li1−xFex)OH layers are formed due to the ion exchange of A (K, Rb, and Cs).Along the c-axis anti-PbO type layers of (Li1−xFex)OH alternate with anti-PbO type FeSe layers.In the hydroxide crystal, positively polarized hydrogen atoms of the (Li1−xFex)OH layer point towards the negatively polarized selenium of the FeSe layer.The (Li1−xFex)OH layer has a similar structure to LiOH itself, which likewise crystallizes in the anti-PbO-type [52,83].The hydrothermal growth process induces a complete structural change.The obtained (Li1−xFex)OHFeSe single crystals show an intergrowth of the ion-exchanged (Li1−xFex)OH layers and the FeSe layers along the c-axis, which is greatly different from the structure of the AxFe2−ySe2 (A = K, Rb, and Cs) crystals, representing an intergrowth of the iron-vacancy-ordered and -disordered states along the c-axis.Figure7a-cshow the XRD patterns of the A0.80Fe1.81Se2(A = K, Rb, and Cs) crystal precursors.In the three figures, the (00l) reflections demonstrating a tetragonal structure with space group I4/m are related to the 245 insulating phase.The ordered and disordered iron vacancies along the c-axis in the AxFe2−ySe2 crystals are characterized by slightly different lattice constants.It can be seen that there are three weak shoulders beside the (008), (0010), and (0012) reflections, as marked with the asterisks.The second set of the (00l) reflections with lower intensity is attributed to phase separation in the crystals[60].The stronger reflections come from the superstructure, indicating that they are related to the iron vacancy-ordered insulating phase.Thus, the second phase marked with asterisks must come from the minor metallic phase which is free of iron vacancy ordering, indicating that the crystal precursor only has a small volume (10%) of the SC phase[84].However, only one set

Figure 6
Figure 6 shows the layered structure of the (Li 1−x Fe x )OHFeSe crystal.During the hydrothermal growth, intercalated (Li 1−x Fe x )OH layers are formed due to the ion exchange of A (K, Rb, and Cs).Along the c-axis anti-PbO type layers of (Li 1−x Fe x )OH alternate with anti-PbO type FeSe layers.In the hydroxide crystal, positively polarized hydrogen atoms of the (Li 1−x Fe x )OH layer point towards the negatively polarized selenium of the FeSe layer.The (Li 1−x Fe x )OH layer has a similar structure to LiOH itself, which likewise crystallizes in the anti-PbO-type [52,83].The hydrothermal growth process induces a complete structural change.The obtained (Li 1−x Fe x )OHFeSe single crystals show an intergrowth of the ion-exchanged (Li 1−x Fe x )OH layers and the FeSe layers along the c-axis, which is greatly different from the structure of the A x Fe 2−y Se 2 (A = K, Rb, and Cs) crystals, representing an intergrowth of the iron-vacancy-ordered and -disordered states along the c-axis.Figure 7a-c show the XRD patterns of the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) crystal precursors.In the three figures, the (00l) reflections demonstrating a tetragonal structure with space group I4/m are related to the 245 insulating phase.The ordered and disordered iron vacancies along the c-axis in the A x Fe 2−y Se 2 crystals are characterized by slightly different lattice constants.It can be seen that there are three weak shoulders beside the (008), (0010), and (0012) reflections, as marked with the asterisks.The second set of the (00l) reflections with lower intensity is attributed to phase separation in the crystals[60].The stronger reflections come from the superstructure, indicating that they are related to the iron vacancy-ordered insulating phase.Thus, the second phase marked with Figure 6 shows the layered structure of the (Li 1−x Fe x )OHFeSe crystal.During the hydrothermal growth, intercalated (Li 1−x Fe x )OH layers are formed due to the ion exchange of A (K, Rb, and Cs).Along the c-axis anti-PbO type layers of (Li 1−x Fe x )OH alternate with anti-PbO type FeSe layers.In the hydroxide crystal, positively polarized hydrogen atoms of the (Li 1−x Fe x )OH layer point towards the negatively polarized selenium of the FeSe layer.The (Li 1−x Fe x )OH layer has a similar structure to LiOH itself, which likewise crystallizes in the anti-PbO-type [52,83].The hydrothermal growth process induces a complete structural change.The obtained (Li 1−x Fe x )OHFeSe single crystals show an intergrowth of the ion-exchanged (Li 1−x Fe x )OH layers and the FeSe layers along the c-axis, which is greatly different from the structure of the A x Fe 2−y Se 2 (A = K, Rb, and Cs) crystals, representing an intergrowth of the iron-vacancy-ordered and -disordered states along the c-axis.Figure 7a-c show the XRD patterns of the A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) crystal precursors.In the three figures, the (00l) reflections demonstrating a tetragonal structure with space group I4/m are related to the 245 insulating phase.The ordered and disordered iron vacancies along the c-axis in the A x Fe 2−y Se 2 crystals are characterized by slightly different lattice constants.It can be seen that there are three weak shoulders beside the (008), (0010), and (0012) reflections, as marked with the asterisks.The second set of the (00l) reflections with lower intensity is attributed to phase separation in the crystals[60].The stronger reflections come from the superstructure, indicating that they are related to the iron vacancy-ordered insulating phase.Thus, the second phase marked with Crystals 2017, 7, 167 7 of 26 of the 00l (l = 2n) peaks is measured in (Li1−xFex)OHFeSe single crystals, indicating all of them are in a pure phase, as shown in Figure 7a-c.

Figure 7 .
Figure 7. (a-c) The X-ray diffraction (XRD) patterns of the cleaved parent A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) and the ion-exchanged (Li 1−x Fe x )OHFeSe crystals, respectively [53].Reprinted with permission from IOP.All rights reserved.
Figure 8a-c show t, T g , and c m dependent XRD patterns, respectively [53].The insets of the figures show the parameter dependence of c.In the experiments t, T g , and c m vary in the ranges 20-120 h, 120-200 • C, and 51.47-154.41respectively, and c has the maximum value (c max ) as each parameter varies.For t and T g , c max is obtained in the medium parameter ranges, and c max = 9.278(3) Å and 9.282(0) Å for t = 72 h and T g = 160 • C, respectively.For c m , however, the c max = 9.278(8) Å is obtained at the lowest c m = 51.47.The maximum c max = 9.282(0) Å is obtained as T g = 160 • C. It is noted that as T g , t, and c m are adjusted the c values vary in the ranges 9.246(3)-9.282(0)Å, 9.255(1)-9.278(3)Å, and 9.262(3)-9.278(
Figure 8a-c show t, Tg, and cm dependent XRD patterns, respectively [53].The insets of the figures show the parameter dependence of c.In the experiments t, Tg, and cm vary in the ranges 20-120 h, 120-200 °C, and 51.47-154.41respectively, and c has the maximum value (cmax) as each parameter varies.For t and Tg, cmax is obtained in the medium parameter ranges, and cmax = 9.278(3) Å and 9.282(0) Å for t = 72 h and Tg = 160°C, respectively.For cm, however, the cmax = 9.278(8) Å is obtained at the lowest cm = 51.47.The maximum cmax = 9.282(0) Å is obtained as Tg = 160 °C.It is noted that as Tg, t, and cm are adjusted the c values vary in the ranges 9.246(3)-9.282(0)Å, 9.255(1)-9.278(3)Å, and 9.262(3)-9.278(8)Å respectively, such that the range of variation in c due to changes in Tg spans the ranges of variation in c due to changes in t and cm.

Figure 8 .
Figure 8. Dependence of the XRD patterns of the obtained (Li1−xFex)OHFeSe single crystals using the K0.80Fe1.81Se2precursors on (a) t, (b) Tg, (c) cm.The insets show the effects of these three parameters on c, respectively [53].Reprinted with permission from IOP.All rights reserved.

Figure 8 .
Figure 8. Dependence of the XRD patterns of the obtained (Li 1−x Fe x )OHFeSe single crystals using the K 0.80 Fe 1.81 Se 2 precursors on (a) t, (b) T g , (c) c m .The insets show the effects of these three parameters on c, respectively [53].Reprinted with permission from IOP.All rights reserved.

Figure 9 .
Figure 9. 4πχ-T curves for the (a) K 0.80 Fe 1.81 Se 2 precursor and (Li 1−x Fe x )OHFeSe single crystal; (b) (Li 1−x Fe x )OHFeSe single crystal using the Rb 0.80 Fe 1.81 Se 2 precursor; (c) (Li 1−x Fe x )OHFeSe single crystal using the Cs 0.80 Fe 1.81 Se 2 precursor; R ab /R p -T curves for the (d) K 0.80 Fe 1.81 Se 2 precursor and (Li 1−x Fe x )OHFeSe single crystal; the (e) Rb 0.80 Fe 1.81 Se 2 precursor and (Li 1−x Fe x )OHFeSe single crystal; the (f) Cs 0.80 Fe 1.81 Se 2 precursor and (Li 1−x Fe x )OHFeSe single crystal.R ab is the the ab-plane resistance, and R p is the maximum value of R ab [53].Reprinted with permission from IOP.All rights reserved.

Figure 10 .
Figure 10.XRD patterns for the (Li 1−x Fe x )OHFeSe single crystal which was synthesized at 180 • C for 72 h using the Cs 0.80 Fe 1.81 Se 2 precursor.The inset is the 4πχ-T curve, showing the antiferromagnetic (AFM) spin density wave (SDW) transition occurs at T s = 125.41K [53].Reprinted with permission from IOP.All rights reserved.

Figure 11 .
Figure 11.Phase diagram of (Li 1−x Fe x )OHFeSe single crystals grown using A 0.80 Fe 1.81 Se 2 (A = K, Rb, and Cs) precursors.The values of T s and T c were derived from the 4πχ-T curves [53].Reprinted with permission from IOP.All rights reserved.

Figure 12 .
Figure 12.Temperature-dependent RH of single-crystal (Li1-xFex)OHFeSe.The point-dashed curve is a guide for the eyes.

Figure 12 .
Figure 12.Temperature-dependent R H of single-crystal (Li 1−x Fe x )OHFeSe.The point-dashed curve is a guide for the eyes.

Figure 14 .
Figure 14.Arrhenius plot of ρ ab for (a) H || ab and (b) H || c. (c) µ 0 H dependence of U 0 and σ.Inset of (c) shows the same data on a double-logarithmic scale.

Figure 18 .
Figure 18.F p /F max p as a function of h = H/H irr for (a) H || ab and (b) H || c.The solid curves are fits of the data to the formula F p /F max p ∝ h p (1−h) q .