Recent progress on epitaxial growth of Fe-based superconducting thin films

Since the discovery of Fe-based superconductors, a lot of effort has been devoted to growing single crystals and epitaxial thin films of them for fundamental studies and applied research of superconductivity. As a result, epitaxial thin films of the most of Fe-based superconductors have been realized. However, some of the materials, namely pristine and transition-metal-doped (Li,Fe)OHFeSe, hydrogen-doped LnFeAsO (Ln = Nd and Sm), Co-doped SmFeAsO, and K-doped BaFe2As2 have been available only in the form of single crystals due to, e.g. the difficulty in doping hydrogen, obtaining high-quality sintered bulks for the target used for pulsed laser deposition, and controlling volatile elements. By solving those issues, the aforementioned compounds have been successfully fabricated as epitaxial thin films in recent years. Unlike single crystals, transport critical current measurements are relatively easy on thin films, which can help evaluate the application potential. In this article, we give an overview over the growth methods for epitaxial thin films of those compounds, followed by their physical properties, especially focusing on electrical transport.


Introduction
Whenever new functional materials are discovered, single crystals are immediately tried to be fabricated to understand their physical properties.Grain boundaries and impurities always mask the intrinsic physical properties.Therefore, such extrinsic factors should be eliminated as much as possible.To minimize the amount of impurities, a self-flux method (e.g.FeAs) has been commonly employed rather than low-melting solvents such as Sn for the growth of Fe-based superconductors.
However, single crystals are not always available, and even if the growth is possible, the available size is often extremely small and insufficient for bulk measurements.Epitaxial thin films sometimes offer the solution for such problems.Hydrogen-doped LnFeAsO (Ln = Nd and Sm), reviewed in this article, is a good example.In other cases, some of the materials have not been realized in the form of epitaxial thin films although single crystals have already been fabricated (K-doped BaFe 2 As 2 and (Li,Fe)OHFeSe, both will be reviewed in this article).Hence, epitaxial thin films are complemental materials to single crystals for fundamental studies.Table 1 summarizes the chemical formula of the epitaxial thin films reviewed in this paper together with some references for films and single crystals.
Thin films are the preferable platform for certain investigations: optical measurements, particularly transmission, and the strain effect using the lattice and thermal expansion mismatch between films and substrates.Additionally, superlattices and monolayers that do not exist in nature can be fabricated, which opens a new opportunity to explore new functionalities.
In terms of applications, thin films are even necessary platforms.High-quality thin films are prerequisite for microelectronic devices.Additionally, it is possible to evaluate the application potential especially for power applications by investigating the transport critical current properties.
In this review article, we focus on the Fe-based superconducting thin films that have appeared since 2017, namely (Li,Fe)OHFeSe, hydrogen-doped LnFeAsO (Ln = Nd and Sm), SmFe 1−x Co x AsO and K-doped BaFe 2 As 2 in chronological order.A brief introduction of each compound will be presented, followed by the thin film growth and physical properties.

Short introduction
Soft-chemical intercalation [26,27] is a powerful tool for tailoring crystal symmetry and lattice parameters of functional materials.For FeSe, the nearly stoichiometric and most simple Fe-based superconductor, several intercalates have been investigated and found superconducting [28], such as alkali or earth-alkali elements (leading to deficient 122 type crystal structures), additional ammonia groups (NH 3 ) y or (NH 2 ) y (NH 3 ) 1−y [29], organic molecules (e.g.ethylenediamine) [30], tetrabutyl ammonium [31], cetyltrimethyl ammonium [32], and trimethylamine [33]), and LiOH [34] (for a review see, e.g.[6]).The latter leads to (Li,Fe)OHFeSe with superconducting transition temperature T c of around 42 K and a crystal structure closely related to the LnFeAsO structures of the pnictide Fe-based superconductors if the hydroxy group is regarded as single entity.It is so far the only intercalated Fe-based superconductor that has been successfully prepared in the form of thin films.Related compounds are (Li,Fe)OHFeS with lower T c up to 8 K [35], hydrogen-free LiFeO 2 Fe 2 Se 2 (43 K) [36], and nonsuperconducting (Na,Fe)OHFeCh (Ch = Se, S) [35].
The intercalation of the Fe-chalcogenide layers by ions or molecules leads to a stretching of the crystallographic c-axis, accompanied by an increase in T c , where 42 or 43 K seems to be the maximum achievable in this system.These T c values are also achievable on FeSe by applying pressure [37], or by direct charge carrier injection in electric double layer transistor experiments [38].
(Li,Fe)OHFeSe can be regarded as link between FeSe single crystals with T c of 8 K and the FeSe unit cell films with T c of 60 K, also regarding their two-dimensional (2D) nature and corresponding large crystallographic and electrical anisotropy.Like the unit cell films (and A x Fe 2−y Se 2 , A = K, Rb; the 245 phase), its Fermi surface does not contain hole-pockets at the Γ point [5].This is important because it shows that the missing hole-like-pockets are not due to interface effects, and that the existence of them is not necessarily a prerequisite for bulk superconductivity in Fe-based superconductors.(Li,Fe)OHFeSe shows different kinds of magnetic ordering, sometimes in coexistence with the superconducting phase [39,40], re-emergent superconductivity at elevated pressures [41]; and even Majorana modes were recently detected [42].It is therefore a very interesting platform for studying the mechanisms of superconductivity as well as the vortex matter in Febased materials.(Li,Fe)OHFeSe shares similarities with the highly anisotropic cuprates, foremost Bi 2 Sr 2 Ca n−1 Cu n O 2n+4 (n = 2 or 3, BSCCO) the material of 1st generation high-T c superconducting wires and tapes: it shows strong 2D behavior, is relatively soft, and easily cleavable, and shows strong superconducting fluctuations and a large vortex liquid region.Compared to FeSe and other intercalated iron selenides, it is a rather clean system without problems of phase separation, structural transitions, and interface effects.Its higher chemical stability in air compared to the monolayer FeSe renders it extremely useful for intrinsic-property measurements of the FeSe system.

Growth method
The growth of epitaxial, superconducting (Li,Fe)OHFeSe films was realized by Huang et al [1] and is based on the matrix-assisted hydrothermal growth (MHE) of (Li,Fe)OHFeSe single crystals [3].A large K 0.8 Fe 1.6 Se 2 single crystal attached to a single crystal LaAlO 3 substrate is used as a seed or matrix for the crystalline film to grow in between.This is in contrast to other methods such as hydrothermal growth from commercial agents or hydrothermal intercalation of FeSe, which only produces polycrystalline samples.Degree of disorder as well as c-axis lattice constant and T c are controllable by the growth parameters, such as temperature and time.Recently, transition-metal (TM)-doped films [43] and a sample series regarding the structural disorder [44] have been realized by the same group.

Physical properties
Huang et al showed in their first publications about (Li,Fe)OHFeSe films that T c is correlated with c-axis lattice parameter (just as found for single crystals) as well as to the minimum in Hall resistance, i.e. the relative strength of the bands contributing to superconductivity [1].The single crystalline films of extremely sharp texture showed high values of critical current density J c (e.g.0.5 MA cm −2 at ∼24 K (0.55T c ) in zero field) despite their clean microstructure [45].These films were studied in more detail shortly after [2] regarding the anisotropy of their electrical transport properties (similar unpublished data in figure 1).It was shown that (Li,Fe)OHFeSe films of optimal T c are highly anisotropic (ratio of the upper critical fields for H ∥ c and ∥ ab, γ Hc2 = 11 for temperatures sufficiently below T c ), nevertheless showing high pinning force densities F p (∼100 GN m −3 at 4 K H ∥ c) and high self-field J c values (extrapolated to 16 MA cm −2 at zero temperature).From this self-field J c the penetration depth of (Li,Fe)OHFeSe was calculated to λ ∼ 160-200 nm with the model of [46].By analyzing the field orientation angle dependence of the exponent n of the V(I) curves, intrinsic pinning at the layered crystal structure could be shown in nearly the complete temperature range.
Li et al were recently able to extend this research to TMdoped (Li,Fe)OHFeSe films [43].Cu, Ni, Co, and Mn were tested as substitutes for Fe.They are homogeneously distributed and, according to neutron diffraction on Mn-doped deuterated single crystals [47], predominantly exchange the Fe in the (Li,Fe)OH layers.For all these substitutes, a T c reduction of 0.5 K % −1 was found, figure 2(a).This is in contrast to TM-doping of FeSe, where the maximum achievable T c depends on the atomic radius of the TM element, and T c is initially increased (except for Co, Cu, and Ni, which leads to immediate T c reduction of ∼3 K % −1 ) [48].The same trends were found for Te-Se substitution: whereas T c increases for FeSe 1−x Te x to a maximum of ∼15 K in bulk samples, it decreases with ∼1 K % −1 in (Li,Fe)OHFeSe 1−x Te x [49].This is probably simply due to the near optimum T c of 42-43 K of (Li,Fe)OHFeSe within the FeSe system.Especially Mn doping has been shown to be extremely beneficial for pinning and J c , figure 2(b).In these films, pinning forces of ∼100 GN m −3 have been measured at 5 K and 30 T, which is an increase by roughly a factor 10 compared to the pristine films [50] at this field or a shift of the F p maximum of similar height from 4 T [2] to ∼35 T. The predominant pinning mechanism for both types of films was determined as normal surface pinning, where the (Li,Fe)OH interlayers were assumed to play a dominant role.The additional point-like disorder due to Mn ions within these sheets seems not to play a dominant role.Whether some kind of magnetic interaction may contribute as well is still to be determined.
Clean samples of (Li,Fe)OHFeSe films, i.e. with high residual resistivity ratio (RRR) and near-optimum T c values, show a distinct feature in their resistive transition for H ∥ c, see figure 1 (arrows) and [2,44,45], i.e. an extra hump near the irreversibility temperature.This feature is not due to inhomogeneities or grain boundary effects, since it develops with magnetic field and disappears for increased disorder by modified growth conditions [44] or TM doping [43].In fact, it is the manifestation of a novel vortex phase within the vortex liquid, somehow related to but not equal to the vortex slush phase observed in YBa 2 Cu 3 O 7−δ (YBCO) films.The relationship to vortex phases in more 2D cuprates, such as BSCCO, is focus of recent investigations regarding transport anisotropy.Indeed, in a recent publication [51], Li et al showed that (Li,Fe)OHFeSe is equally anisotropic as BSCCO with H c2 anisotropies around 150 close to T c with 2D-like angular dependence of H c2 , which allowed completing and explaining the vortex phase diagram within the vortex glass region.With the help of relaxation measurements and J c maxima (determined via magnetization), the transition between a 3D vortex solid and quasi-2D pancake vortices was determined.This transition may easily explain the distinct features in J c (B) and U 0 (B) in [2] although at slightly higher fields for that particular sample.These results also indicate huge differences in the anisotropies of H c2 , ξ, and λ; a distinct difference to the cuprates.
High-quality (Li,Fe)OHFeSe films facilitate the spectroscopy studies on the heavily electron-doped iron selenides.For example, the collective modes within superconducting gaps are identified from Raman spectra [52], emphasizing the Cooper pairing instabilities in the multi-band superconductors.

Short introduction
LnFeAsO electron-doped by a partial substitution of oxygen with fluorine/hydrogen shows the highest superconducting transition temperatures T c among the Fe-based superconductors except for monolayers of FeSe.Hence, a lot of effort has been devoted to the growth of single crystals, however, the available size of those single crystals is typically around a few hundred µm 2 only.Recently, Kappenberger et al reported a new method to grow mm-sized single crystals of LaFeAsO [53] and LaFe 1−x Co x AsO [18,19], which allows conducting bulk measurements (i.e.specific heat).However, such large crystals have not yet been reported for fluorine and hydrogen doped LnFeAsO (see e.g.[14]).
On the other hand, the thin film growth of LnFeAsO has also been started immediately in 2008 [54].Unlike single crystals, epitaxial thin films of LaFeAs(O,F) [55] and NdFeAs(O,F) [56] have already been reported in 2010, followed by SmFeAs(O,F) [57] in 2011.The first superconducting F-doped LaFeAsO film was fabricated by a 'solidphase epitaxy' method [58].An amorphous precursor film was deposited at room temperature by pulsed laser deposition (PLD), followed by vacuum-sealing in a quartz tube together with a sintered LaFeAs(O,F) pellet.The whole arrangement was annealed at 960 • C for 7 h.Microstructural analysis on the fully optimized LaFeAs(O,F) film revealed that a syntaxially grown La(O,F) layer was present between LaFeAs(O,F) and the LaAlO 3 substrate [59].Besides, the LaFeAs(O,F) layer was covered with polycrystalline La(O,F), which is an insulator and, therefore, should be removed for transport measurements.
To date, the parent compounds LnFeAsO (Ln = Nd and Sm) have been readily fabricated by molecular beam epitaxy (MBE) and PLD [60,61].Additionally, epitaxial SmFe 1−x Co x AsO has been grown by PLD [15,16].For F doping, two methods, namely one-step and two-step growth, have been reported.For the former method [62,63], however, the reproducibility is not good.One of the reasons is the fluorine source such as FeF 3 , which is highly hygroscopic.As a result, HF rather than F gas was supplied during the growth.Nevertheless, a high T c of 55 K was achieved for SmFeAs(O,F) [64].
On the other hand, the latter method for F-doping has shown high reproducibility.After growth of parent LnFeAsO, a LnF over-layer was deposited.During deposition, F diffused into LnFeAsO, resulting in superconducting LnFeAs(O,F).The structural characterization by x-ray diffraction revealed that LnF turned into insulating Ln(O,F).

Interestingly, Ln(O,F) grows epitaxially on LnFeAs(O,F) with (001)[110]Ln(O,F)∥(001)[100]LnFeAs(O,F). Fortunately, the LnFeAs(O,F) film is not fully covered with insulating Ln(O,F), which makes transport measurements even without removal of Ln(O,F) possible.
Unlike fluorine doping, hydrogen-doped LnFeAsO was obtained only by a post-growth process.The distinct difference between F and H is their solubility limit.The upper limit of the former for SmFeAsO is around 20% [65], whereas of the latter is up to 80% [66].Hence, it is possible to explore the physical properties of heavily electron-doped LnFeAsO.Another feature is that no over-layers had to be formed on LnFeAs(O,H), which is highly beneficial especially for fabricating bi-layer structures.

Pulsed laser deposition, PLD.
For PLD, a secondharmonic Nd:YAG laser (wave length of 532 nm) has been selected rather than an excimer laser, since the in-situ phase formation has been realized only by Nd:YAG laser so far.The deposition process was conducted under a base pressure of 1 × 10 −6 Pa.The phase-pure PLD target was ablated with a reputation rate of 10 Hz.Importantly, impurity phases from the target should be eliminated as much as possible, especially Ln 2 O 3 and Ln(O,F) [54].Both LaFeAsO [54] and SmFeAsO [61] were epitaxially grown on MgO (001) and (LaAlO 3 ) 0.7 (Sr 2 TaAlO 6 ) 0.7 (001) [LSAT (001)].Similarly, SmFe 1−x Co x AsO epitaxial thin films were realized on various substrates using almost the same deposition setup [15,16].For phase purity and epitaxy, the optimum deposition temperature and substrate were 860 • C and MgO, although a small amount of Sm 2 O 3 was present.However, the films grown on MgO have not shown superconductivity, in contrast to the films on LaAlO 3 and MgAl 2 O 4 , which showed onset of superconductivity, yet more foreign phases.It was concluded, that strain effects on MgO suppressed superconductivity.Only the film grown on CaF 2 (001) showed zero resistance at 8.2 K [15].In this case, cobalt and fluorine co-doping may occur.Later, growth on MgO buffered with Co-doped BaFe 2 As 2 yielded a T c of 13-18 K for SmFe 1−x Co x AsO [16].Unfortunately, J c measurements have not been reported so far.

Molecular beam epitaxy, MBE.
As stated above, parent compound NdFeAsO epitaxial thin films have been readily fabricated [60], although small tuning is always necessary due to slight change in the growth chamber condition over time (e.g.pressure of the deposition chamber).Nevertheless, the deposition method is briefly described.Solid sources of NdF 3 , Fe, As, Fe 2 O 3 , and Ga were charged in Knudsen cells.Oxygen was provided via thermal decomposition of Fe 2 O 3 .Ga has been used to remove excess fluorine during deposition.Although fine tuning is necessary, parent compound NdFeAsO has been fabricated on a large variety of oxide and fluorine substrates [67], as well as technical substrates [68,69].Typical growth temperatures are around 800 • C. The growth rate is approximately 0.8-1 nm min −1 .Most of these films were grown for 30 min, resulting in 24-30 nm thickness.

Topotactic reaction using AeH 2 (Ae = Mg, Ca, Sr
and Ba).Initial attempts for hydrogen doping of epitaxial films have been made by flowing H 2 or H-radical gases during deposition [54].However, none of them were successful.In 2019, the topotactic chemical reaction using CaH 2 for SmFeAs(O,H) was reported [8], followed by NdFeAs(O,H) [11].The reagent powder CaH 2 is in physical contact with the films, which is the key to promote the reaction with homogeneous distribution of H. Any AeH 2 (Ae = Mg, Ca, Sr and Ba) can be used as hydrogen source [9].Although the desorption temperature of AeH 2 is Ae-dependent, the optimized temperature for the topotactic reaction is around 500 • C except for Ae = Mg, which requires only 380 • C.
To obtain reliable results, storing and handling of the CaH 2 powder should be conducted in a controlled Ar-glove box, since CaH 2 easily absorbs moisture and turns into Ca(OH) 2 and H 2 gas.This leads to a change in the amount of CaH 2 consumed during the topotactic reaction.A schematic illustration of the procedure is shown in figure 3. The process temperature should be less than 520 • C, otherwise, the quartz tube will rupture by increased inner pressure during heat treatment.
Quantitative analysis of H content has already been conducted using secondary ion mass spectroscopy (SIMS) with a SmFeAsO 0.4 H 0.6 bulk polycrystalline sample as [8].The depth profile by SIMS for the SmFeAs(O,H) thin film showed inhomogeneous doping of H.The H content with respect to oxygen decreased from 0.34 at the surface to 0.1 at the film/substrate interface.An effective method to avoid such inhomogeneous H doping is decreasing the film thickness, which was proved by the microstructural analysis by transmission electron microanalysis (TEM), shown in figure 4 [12].The 24 nm thick NdFeAs(O,H) film is microstructurally clean (figure 4(a)).The averaged c-axis length determined by the image intensity profile for the H-doped NdFeAsO near the film/substrate interface was almost the same as near the film surface and smaller than that for the parent NdFeAsO.As the c-axis length is decreased with H-doping compared with the parent compound [8], hydrogen was concluded to be partially and homogeneously substituted for oxygen in NdFeAsO.
The effective carrier number per O (x film ) is estimated as 1/e|R H | × V/2, where e is the charge of the carrier, R H is the Hall coefficient measured at 50 K, and V is the unit cell volume evaluated by x-ray diffraction.The carrier density was estimated with the single-carrier model.The Hall coefficient was negative for all samples, and thus the dominant carriers are electrons.Figure 5 shows the x film dependence of T c for various NdFeAs(O,H) films.For comparison, the data of NdFeAs(O,F) are also shown in the same graph.The maximum x film for the F-doped films was around 0.15, whereas the corresponding value for H-doping was 0.5.Hence, the maximum electron concentration for NdFeAs(O,H) is higher than that for NdFeAs(O,F).T c is constant for a wide range of x film , which is similar to bulk polycrystalline samples.This gives a good opportunity to investigate how heavy electron doping affects the superconducting properties, which will be discussed in the following sub-section.

Physical properties of SmFeAs(O,H
). SmFeAsO 1−x H x with x ∼ 0.35 showed an onset T c of around 48 K [8].CaH 2 was used for the topotactic chemical reaction.The anisotropy value estimated from the ratio of the upper critical fields for H ∥ ab and ∥ c near T c was 2.4.To date, no transport J c has been reported, but magnetic J c was measured for SmFeAs(O,H) fabricated by different hydrogen sources, AeH 2 (Ae = Mg, Ca, Sr and Ba).Among them, MgH 2 showed the lowest desorption temperature (<400 • C), and hence the optimum processing temperature for the topotactic transformation was the lowest (∼380 • C).This may explain   A self-field J c of 2 MA cm −2 was recorded at 2 K, which is almost the same as for F-doped SmFeAsO [57].
Recently, the upper critical fields H c2 of SmFeAs(O,H) have been experimentally determined in pulsed fields up to 130 T [10].An H c2 of 120 T was measured at 2.2 K for H ∥ ab.For H ∥ c, H c2 was estimated to be around 80 T at zero kelvin using a dirty-limit two-band model.Angular dependence of H c2 at 37.5 K revealed that the anisotropy was around 2.

Physical properties of NdFeAs(O,H).
Relatively homogeneous H-doping was achieved for NdFeAs(O,H) by reducing the film thickness as stated above.Figure 6(a) compares the temperature dependence of resistivity for NdFeAs(O,H) with a NdFeAs(O,F) film on the same type of MgO substrates.H-doping was conducted using CaH 2 at 520 • C for 36 h.The calculated x film was around 0.22.Although T c around 45 K was almost the same for both F-and H-doped NdFeAsO, the normal state resistivity for NdFeAs(O,H) was lower than that for NdFeAs(O,F).This is mainly due to the larger amount of electron doping for NdFeAs(O,H).As in [11], the anisotropy γ of the upper critical field H c2 of NdFeAs(O,H) was lower than that of NdFeAs(O,F) (γ = 4.5 versus 5.1).A low anisotropy was observed not only in the superconducting state but also in the normal state for NdFeAs(O,H) [13].According to the band calculation for CaFeAsH and CaFeAsF (both have the same crystal structure of ZrCuSiAs type) by Muraba et al, the former showed a more three-dimensional character of the Fermi surface compared to the latter [70].Similar to CaFeAsH, the lower anisotropy of NdFeAs(O,H) may be due to the more three-dimensional character of the Fermi surface.
The irreversibility field H irr for H ∥ c is related to H c2 by the following formula: H irr ∝ γ −2 H c2 [72].Hence the smaller anisotropy, typically the bigger H irr at a given (reduced) temperature for a certain system.In fact, H irr for NdFeAs(O,H) is larger than that for NdFeAs(O,F) (figure 6

(b)), whereas H c2 of NdFeAs(O,H) is comparable to that of NdFeAs(O,F).
Heavy electron doping benefits not only low anisotropy but also high critical current density.Figure 6(c) shows the field dependence of transport J c at 4 K. Magnetic field was applied parallel to the crystallographic c-axis.As can be seen, selffield J c reached over 17 MA cm −2 at 4 K.This value is more than twice the best-performing NdFeAs(O,F) film having an onset T c of 45 K [71].Since the film is microstructurally clean (figure 4(a)), J c decreased rather quickly with field.As discussed in [12], the high J c may be due to the short penetration depth λ by heavy electron doping, although the direct evidence is still missing.Recently, considerable improvement of J c by over-doping has been reported for YBa 2 Cu 3 O y [73].Stangl et al concluded that the condensation energy was increased by over-doping.Furthermore, by combining a thermodynamic approach with microstructural modification by BaHfO 3 nano particles, Miura et al reported on a record pinning force density F p of 3.17 TNm −3 at 4.2 K and 18 T (H ∥ c) for (Y,Gd)Ba 2 Cu 3 O 7−δ grown on technical substrate [74].As shown in figure 5, T c is almost constant in a wide range of doping for NdFeAs(O,H), which is the most suitable system for the improvement of J c by heavy carrier doping.

Short introduction
Unlike electron and isovalently doped BaFe 2 As 2 (Ba122), the epitaxial growth of hole doped Ba122, in particular Ba 1−x K x Fe 2 As 2 thin films, was challenging due to the difficulty in controlling volatile K.In the early stage of research on Fe-based superconductors, K-doped Ba122 was fabricated by solid-phase epitaxy [75].Although the film showed a T c of around 40 K, the films were only c-axis fiber textured.Almost at the same time, such films with different K contents were also grown by MBE [76], and the phase diagram (i.e.superconducting dome) was constructed.However, in-plane alignment was not reported, and hence grain boundary effects potentially masked intrinsic and pinning-related properties.
In 2014, the end member KFe 2 As 2 (K122) was fabricated via solid-phase epitaxy [20].The film grown on LSAT was weakly textured.Later, the growth conditions were optimized, resulting in epitaxial K122 thin films [21].Briefly, a K-rich K122 polycrystalline bulk was ablated by a KrF laser (248 nm) at room temperature.The amorphous precursor film was covered by MgO substrate, and placed on an Al 2 O 3 boat, which was filled with K122 powder.The whole arrangement was coved with an Al 2 O 3 lid and sealed in an Ar-filled stainless tube.Finally, the sample was heat-treated at 1000 • C for 30 min.Although the film grew epitaxially on MgO with a small full width at half maximum of 0.06 • for the rocking curve (the out-of-plane, 002 reflection), the film was extremely sensitive against ambient air.Hence, such films have to be protected against air during characterization.
Finally, epitaxial K-doped Ba122 thin films were realized by MBE in 2021 [22].The key to success was to employ a lowtemperature growth and fluoride substrates.The film showed a surprisingly high J c of over 14 MA cm −2 at 5 K [23].Additionally, the pinning force density of the film was higher than that of the pinning-enhanced K-doped single crystal.In the following sub-section, we review the growth of epitaxial K-doped Ba122 together with recent activities.

Growth methods
As stated above, a low deposition temperature of around 400 • C and using fluoride substrates are important for the epitaxial growth of K-doped Ba122 [22].Ba was charged in a W-basket, whereas Fe was placed on an Al-coated W-basket due to the high reactivity between W and Fe.In-K alloy was used as K source for safety issue as well as good controllability.Both In-K and As were charged in homemade-effusion cells.An AeF 2 (Ae: Ca, Sr and Ba) substrate cleaned by acetone was transferred into a custom-designed MBE chamber (base pressure ∼1.3×10 −7 Pa) equipped with atomic absorption spectroscopy (AAS) and electron impact emission spectroscopy (EIES).The signals obtained by AAS and EIES were fed back to a personal computer that controls resistive heaters of each element (K, Ba, and Fe).The substrate temperature was increased to around 600 • C for thermal cleaning.Then the substrate was cooled to around 400 • C and held at this temperature for deposition of K-doped Ba122.A 10 min growth time results in an approximate 100 nm layer thickness.K-doped Ba122 thin films were grown epitaxially and phase-pure on AeF 2 regardless of Ae [22], although the lattice mismatch of 10.8% between Ba 0.6 K 0.4 Fe 2 As 2 and BaF 2 is relatively large compared with CaF 2 (−1.2%) and SrF 2 (4.6%).
Figure 7(a) shows the 2θ χ /ϕ-scans in the vicinity of the 400 reflections of K-doped Ba122 grown on AeF 2 .Since the inplane lattice parameter of K-doped Ba122 is close to the lattice constant of CaF 2 divided by √ 2 (i.e. a CaF2 / √ 2 = 3.854 Å), the 400 diffraction peak of K-doped Ba122 overlaps with the 440 peak of CaF 2 .Hence the a-axis length was determined from the 103 diffraction angle and the lattice constant c.For the film grown on SrF 2 , the lattice constant a was determined from the Nelson-Riley function using the 200, 400, 220 and 440 reflections.For the film grown on BaF 2 , the peak was quite broad due to the two peaks (figure 7(b)), arising from different strain states or different doping levels.The relationship between the a-and c-axis length for K-doped Ba122 grown on CaF 2 and SrF 2 is shown in figure 7(c).For comparison, the data of bulk samples are also superimposed [77].The slope of the films shifts upward from the bulk one, which may indicate that both films are strained.
Microstructural analysis shown in figure 8 revealed that the film grown on CaF 2 consisted of columnar grains having a width of d ∼ 30-60 nm, corresponding to a matching field of ∼2 T [23].Additionally, the average rotation angle of the grains around the a-or b-axis is 1.5 • and 1 • around the c-axis.As a result, low-angle grain boundaries and their networks were present in these K-doped Ba122 films, which work as strong vortex pinning centers especially for the field direction of the substrate normal.as fluoride bicrystal substrates have not been commercially available to their brittle it is to explore grain boundary properties using bicrystal experiments.To conduct bicrystal experiments, K-doped Ba122 thin films should be realized on oxide substrates for which bicrystals are commercially available such as SrTiO 3 , LSAT and MgO.Among them, MgO and SrTiO 3 have been recognized as common bicrystal substrates.For SrTiO 3 , oxygen is released under ultra high vacuum conditions and, therefore, the only choice is MgO.Initially, the growth of K-doped Ba122 was attempted without buffer layer.After optimization, however, only c-axis oriented films were obtained (figure 9(a)).The 103 ϕ-scan showed that some domains were rotated around the c-axis by 30 • (figure 9(b)).The reason is not clear.So far, the epitaxial growth of K-doped Ba122 has not been realized on bare MgO.
Since the growth temperature cannot be increased above 500 • C due to the volatility of K, a buffer layer with good lattice matching and chemical compatibility to K-doped Ba122 is required for promoting epitaxial growth even at low temperatures.The parent Ba122 fulfills the above requirements.Additionally, undoped Ba122 has been grown epitaxially on MgO by both MBE [78] and PLD [79].In fact, either doped or undoped Ba122 has been implemented as a buffer layer for epitaxial growth of Fe(Se,Te) [80] and SmFeAsO [81], respectively.
A 20-30 nm thick parent Ba122 buffer was grown on MgO at 720 • C by MBE.Then the 100 nm thick K-doped Ba122 thin film was grown on Ba122-buffered MgO.The K content was around 40%, confirmed by TEM-EDX.The structural characterization by x-ray diffraction is summarized in figure 10.The peak splitting of the 00l reflections is getting obvious with higher 2θ value.The former peak corresponds to the parent (or slightly K-doped) Ba122 buffer and the latter to the actual K-doped Ba122 film.Although two phases are clearly visible in the out-of-plane scans, they are hard to recognize in inplane scans due to the small difference in the lattice parameter a (figures 10(c) and (d)).The 103 ϕ-scan confirmed that Kdoped Ba122 grew epitaxially on Ba122-buffered MgO [24].

Physical properties of Ba 1−x KxFe 2 As 2 grown on AeF 2
As demonstrated in [22], all K-doped Ba122 films on AeF 2 had almost the same T c of 36±1 K.All films were deposited at the same growth run.Hence, the K content of all these films  is expected to be the same.Figure 11 shows the upper critical field H c2 and the irreversibility field H irr as a function of reduced temperature t = T/T c,90 .For both directions, H c2 (t) of the film grown on BaF 2 was slightly lower.This may be due to some sample degradation.In fact, H irr for the film on BaF 2 was not determined.For the films on CaF 2 and SrF 2 , H c2 (t) was almost identical, while H irr of the film on CaF 2 was slightly higher at low fields.A clear kink in H irr (t) at around 2 T was recognized, which is ascribed to the matching field effect [23].
The critical current density J c was determined by I-V measurements using an electrical field criterion of 1 µVcm −1 .The I-V characteristics can be described by V ∼ I n in the vicinity of J c , if the measured samples are free from weak-links.Here, the exponent n contains information on the pinning potential, if the measured sample is sufficiently homogenous.In fact, the field dependence of n behaves similar to that of J c (i.e.n scales with J c ) for K-doped Ba122.This relation was reported for many superconductors, e.g.YBCO [82], LnFeAs(O,F) [83,84], Fe(Se,Te) [85] and MgB 2 [86].The following relation n − 1 ∼ J α c for K-doped Ba122 was observed (figure 12(a)) with α = 0.57.Here, we plot n − 1 versus J c rather than n versus J c , since the inverse of n − 1 corresponds to the flux creep rate S.Although the physical meaning of α is not fully clear, it may be related to the shape of the I-V curves near the glass-liquid transition.The data above n > 50 start to deviate from the trendline, which may be due to heating of the contact pads/wires.Another distinct feature compared with other Febased superconductors are relatively high n values, indicative of a low flux creep rate S. For instance, n > 20 for entire magnetic fields (up to 16 T) even at 15 K was recorded.This value is comparable to NdFeAs(O,F) with T c = 47.1 K measured at 4.2 K [84].
J c for H ∥ c is getting larger than that for H ∥ ab at T ⩽ 25 K for fields sufficiently smaller than H irr , which is the opposite expected from the H c2 anisotropy (figures 12(b) and (c)).To understand the origin of this behavior, angular dependence of J c was shown in figures 13(a) and (b).As can be seen in figure 13(a), J c for H ∥ c was larger than that for H ∥ ab below 25 K, which is due to the presence of strong pinning along the c-axis.This is clearly seen in the normalized data (figure 13(b)).These results indicate that the pinning along the c-axis begins to be active between 30 and 25 K.The microstructure analyses revealed that grain boundaries between columnar grains of K-doped Ba122 created the c-axis correlated pinning [23].
The I-V measurements were limited at low temperatures and fields due to heating at the contact pads/wires.Therefore, the field dependence of J c for H ∥ c was evaluated from magnetization measurements too (figures 14(a) and (b)).A large self-field J c of 14.4 MA cm −2 was recorded at 4 K. Selffield J c scales with [1−(T/T c ) 2 ] m with m = 1.93, as shown in figure 14(c).Theoretically, m = 7/6 and 5/2 represent the δT c -pinning and δl-pinning, respectively [88].The intermediate value obtained for this film indicates mixed pinning, despite insufficient data close to T c . Figure 14(d) shows the field dependence of the pinning force density F p for the K-doped Ba122 thin film on CaF 2 obtained from J c in figure 14(b).As can be seen, F p of the K-doped Ba122 thin film is higher than that of a Pb-ion irradiated single crystal up to 4 T [87].These results suggest that low angle grain boundaries and their networks act as strong pinning centers, comparable to the pinning enhancement achieved by ion-irradiation.

Physical properties of Ba 1−x KxFe 2 As 2 grown on MgO
The temperature dependence of the resistivity of K-doped Ba122 on bare MgO shown in figure 9(a) exhibited a low T c,90 of 33.2 K (figure 15(a)).Due to the presence of high angle grain boundaries, a large transition width of T c,90 − T c,0 = 3.2 K was observed.The broadening of the superconducting transition was more obvious with fields (figure 15(b)).Once the high angle grain boundaries are eliminated, such broadening is absent: figures 15(c) and (d) show the temperature dependence of the resistance for the K-doped Ba122 epitaxial film grown on Ba122-buffered MgO.The film  showed a high T c,90 of 39.2 K with a small transition width of 1.7 K.The high T c value is ascribed to the strain effect [24].The presence of high angle grain boundaries also reduces J c significantly (figure 16(c)).Here, J c was obtained from the M-H measurements using the Bean model.As can be seen, the self-field J c of the film grown on bare MgO is two orders of magnitude lower than on Ba122-buffered MgO.Additionally, J c decreased quickly with H for the film on bare MgO.

Discussion and summary
Table 2 summarizes the deposition methods, substrates, the maximum T c and the maximum self-field J c for the various Fe-based superconductors reviewed in this article.Selffield J c of (Li,Fe)OHFeSe was estimated by an extrapolation to 4 K. Except for SmFe 1−x Co x AsO with significantly lower T c , self-field J c of (Li,Fe)OHFeSe, NdFeAs(O,H).and Ba 1−x K x Fe 2 As 2 is more than 10 MA cm −2 at low temperatures (i.e.below 5 K).Although self-field J c of Mn-doped (Li,Fe)OHFeSe has not been reported, in-field J c is relatively high (i.e.0.32 MA cm −2 at 33 T and 5 K for H ∥ c, figure 17) due to the pinning induced by Mn.J c of SmFeAs(O,H) is one order of magnitude lower than that of NdFeAs(O,H).The reason for the low J c is not clear yet.The highest selffield J c was obtained for NdFeAs(O,H), followed by pristine (Li,Fe)OHFeSe.
Figure 17(a) summarizes the in-field J c for various Febased superconductors shown in table 2. For comparison, the data of other Fe-based superconductors grown on single crystalline substrates are superimposed.Because of the clean film of (Li,Fe)OHFeSe, J c decreased very quickly with fields.But the pinning-enhanced Mn-doped (Li,Fe)OHFeSe was superior to other Fe-based superconductors, especially at high fields.This is also clearly seen in the field dependence of pinning force density F p (figure 17(b)).Decrease of J c in lowfield regime was significant for the microstructurally clean NdFeAs(O,H), NdFeAs(O,F) and P-doped Ba122.films.A high F p of over 200 GNm −3 was recorded for K-doped Ba122 due to the highly c-axis-correlated grain-boundaries.This value is almost the same as for a Pb-ion irradiated K-doped Ba122 single crystal [87].
Although the main crystal classes and many of the different Fe-based superconductors have been fabricated in the form of epitaxial thin films, several compounds such as Ca 1−x La x FeAs 2 (112) [92] and CaAFe 4 As 4 (A = K, Rb, Cs) (1144) [93] as well as structures with large blocking layers have not yet been realized as thin films.Fabricating such compounds is challenging due to the presence of volatile elements; and so far, no reports on the attempt on the growth of those films have been published.This should be a focus of future studies.
Hydrogen-doped LnFeAsO is a good model system for increasing the depairing current density J d by a heavy doping method.Unlike cuprates, the superconducting transition temperature of LnFeAs(O,H) stays constant around 50 K over a wide range of doping.If the condensation energy is increased by over-doping, J d and, hence, J c can be increased.Systematic investigation is necessary to prove this scenario.
As stated above, realizing epitaxial thin films gives an opportunity for studying the nature of grain boundaries.In fact, we have studied the grain boundary characteristics of K-doped Ba122 [94,95], which will be published in near future.
Table 2.The list of Fe-based superconductors reviewed in this article.Growth method, substrates, and their physical parameters are summarized.Self-field Jc for SmFeAsO 1−x Hx at 5 K and Ba 1−x KxFe 2 As 2 at 4 K was evaluated by a magnetization method.For NdFeAsO 1−x Hx transport measurements were employed for self-field Jc at 4 K.

Figure 1 .
Figure 1.Resistive transition for fields H ∥ c in linear (a) and logarithmic (b) presentation of a high-quality (Li,Fe)OHFeSe film (residual resistivity ratio, RRR = 64, sample A of [2]) together with the two logarithmic derivatives (c), (d) used for determining the characteristic temperatures glass-liquid transition Tg, critical region T * , and exotic vortex phase transition T ′ (marked with arrows for the highest fields in (a), (c), (d)).The mean values of the activation energy U 0 determined from simple Arrhenius plots are marked by dashes in (d).(e) H − T phase diagram.

Figure 2 .
Figure 2. Effect of transition metal doping of (Li,Fe)OHFeSe thin films on (a) critical temperature Tc, and (b) critical current density Jc at 9 T and 10 K for H ∥ c.Reproduced from [43].© IOP Publishing Ltd.All rights reserved.

Figure 4 .
Figure 4. Microstructural analysis by TEM.(a) TEM cross-sectional view of the NdFeAs(O,H) epitaxial thin film revealed almost no apparent defects.Additionally, no reaction layer between the film and the MgO substrate was observed.(b) The magnified ADF images of NdFeAsO and (c) NdFeAs(O,H).(d) Image intensity profiles along the c-axis direction extracted from (b) and (c), averaged in the a-axis direction.The c-axis lattice parameters averaged over 10 layers are 8.64 Å and 8.50 Å, respectively.The distances from the 1st to the 11th layer and from the 18th to the 28th layer are the same in the NdFeAs(O,H) film.Reproduced from [12].CC BY 4.0.

Figure 5 .
Figure 5.The superconducting transition temperature (Tc) as a function of the effective carrier number per O (x film ) for NdFeAs(O,F) and NdFeAs(O,H) films.The carrier density at 50 K was estimated with the single-carrier model.

Figure 6 .
Figure 6.Comparison of the physical properties between NdFeAs(O,H) and NdFeAs(O,F).(a) Temperature dependence of the resistivity.(b) The upper critical field H c2 and the irreversibility field H irr for H ∥ c as a function of reduced temperature.(c) Low-temperature field dependence of Jc for H ∥ c.The data were re-produced from[11,17].

Figure 7 .
Figure 7. (a) The 2θχ/ϕ-scans around the 400 reflections for K-doped Ba122 grown on AeF 2 (Ae = Ca, Sr, and Ba).(b) Enlarged view of the 2θχ/ϕ-scans around the 400 reflection for K-doped Ba122 grown on BaF 2 .The deconvoluted spectrum is shown.(c) The relationship between the a-and c-axis length for K-doped Ba122 thin films grown on AeF 2 substrates.The data of bulk samples (Ba 1−x KxFe 2 As 2 )together with the nominal K content are also superimposed[77].

Figure 10 .
Figure 10.(a) 2θ/ω-scan and (b) enlarged view around the 008 reflection as well as (c) 2θχ/ϕ-scan of the h00 reflections and (d) enlarged view around the 400 reflection for a K-doped Ba122 film grown on Ba122-buffered MgO.

Figure 11 .
Figure 11.The upper critical field H c2 and the irreversibility field H irr of K-doped Ba122 for (a) H ∥ c and (b) H ∥ ab.(c) Comparison of H irr between the films grown on CaF 2 and SrF 2 for both major crystallographic directions.

Figure 12 .
Figure 12.(a) The exponent n − 1 as a function of Jc for H ∥ c.(b) The field dependence of Jc for K-doped Ba122 grown on CaF 2 measured at various temperatures for H ∥ c and (c) H ∥ ab.Panels (b) and (c) reproduced from [23].CC BY 4.0.

Figure 13 .
Figure 13.Angle dependence of Jc measured at 4 T and several temperatures.The respective angles θ = 90 • and 180 • are for H ∥ c and ∥ ab.(a)Absolute values and (b) normalized to the Jc values at H ∥ ab (J ab c ). Reproduced from [23].CC BY 4.0.

Figure 14 .
Figure 14.(a) Field dependence of magnetization M measured at various temperatures.The applied magnetic field was H ∥ c.(b) Field dependence of Jc extracted from the M-H measurement shown in (a).(c) Self-field Jc as a function of 1−(T/Tc) 2 .(d) Field dependence of pinning force density Fp for H ∥ c at 4 K.For comparison, the data of Pb-ion-irradiated K-doped Ba122 single crystal measured at 5 K are also shown [87].Panels (a), (b) and (d) reproduced from [23].CC BY 4.0.

Figure 15 .
Figure 15.Comparison of the resistive transition in zero field and for H ∥ c between K-doped Ba122 film on bare MgO (a), (b) and on Ba122-buffered MgO (c), (d).

Figure 16 .
Figure 16.(a) Magnetic phase diagram for K-doped Ba122 grown on bare MgO (black) and Ba122-buffered MgO (red) for H ∥ c.The solid and open symbols represent the upper critical field H c2 and the irreversibility field H irr , respectively.(b) The phase diagram shown in (a) is re-plotted as a function of reduced temperature.(c) Field dependence of Jc for K-doped Ba122 grown on Ba122-buffered MgO (circle) and bare MgO (square).Applied magnetic field was parallel to the c-axis.

Table 1 .
The list of Fe-based superconductors reviewed in this article.