Realization of epitaxial thin films of the superconductor K-doped BaFe$_\text{2}$As$_\text{2}$

The iron-based superconductor Ba$_{1-x}$K$_x$Fe$_\text{2}$As$_\text{2}$ is emerging as a key material for high magnetic field applications owing to the recent developments in superconducting wires and bulk permanent magnets. Epitaxial thin films play important roles in investigating and artificially tuning physical properties; nevertheless, the synthesis of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ epitaxial thin films remained challenging because of the high volatility of K. Herein, we report the successful growth of epitaxial Ba$_{1-x}$K$_x$Fe$_\text{2}$As$_\text{2}$ thin films by molecular-beam epitaxy with employing a combination of fluoride substrates (CaF$_\text{2}$, SrF$_\text{2}$, and BaF$_\text{2}$) and a low growth temperature (350$-$420$^\circ$C). Our epitaxial thin film grown on CaF$_\text{2}$ showed sharp superconducting transition at an onset critical temperature of 36 K, slightly lower than bulk crystals by ~2 K due presumably to the strain effect arising from the lattice and thermal expansion mismatch. Critical current density ($J$$_\text{c}$) determined by the magnetization hysteresis loop is as high as 2.2 MA/cm$^\text{2}$ at 4 K under self-field. In-field $J$$_\text{c}$ characteristics of the film are superior to the bulk crystals. The realization of epitaxial thin films opens opportunities for tuning superconducting properties by epitaxial strain and revealing intrinsic grain boundary transport of Ba$_{1-x}$K$_x$Fe$_\text{2}$As$_\text{2}$.


I. INTRODUCTION
Iron-based superconductors (IBSCs) have been regarded as new candidate materials for superconducting applications [1]. There are several families including: LnFeAsO (Ln-1111, Ln = lanthanoid elements) with the highest superconducting transition temperature (Tc) of 55 K [2], AeFe2As2 (Ae-122, Ae = alkaline-earth elements) with the highest Tc of 38 K [3], and FeCh (FeCh-11, Ch = chalcogens) with Tc ~ 15 K [4] but reaching above 40 K in thin films [5−9]. Among these materials, Ba-122 is one of the most promising materials for high magnetic field applications because of its high upper critical field (Hc2) with small anisotropy [10−12], large critical current density (Jc) [13−16], and large critical grain-boundary angle [17−19]. In fact, powder-in-tube processed K-doped Ae-122 wires and tapes [20,21], and K-doped Ba-122 bulk magnets [22] have been fabricated as proof-of-principle studies for high-field applications, although the information on the Jc transparency across the grain boundary for K-doped Ae-122 is not clear yet. This is a sharp contrast to other IBSCs, where high-quality films have been grown on a variety of single-and bicrystalline, and technical substrates and, hence, fundamental and application-related research has been developed [23−25].
The difficulty of growing epitaxial Ae1−xKxFe2As2 thin films is mainly due to the volatility of K. To overcome this problem, several attempts have been reported to date. Lee et al. reported a postannealing technique [26,27], where precursor thin films of BaFe2As2 were postannealed in a quartz tube with K metal. The resultant films are c-axis oriented and show a superconducting transition with Tc on − Tc end = 40.0-37.5 K; however, they were not epitaxially grown. More recently, Hatakeyama et al. and Hiramatsu et al. have developed a solid-phase epitaxy technique to prepare epitaxial thin films of the end member, KFe 2 As 2 [28,29]. To produce KFe 2 As 2 films, it is essential to suppress revaporization of K at high annealing temperatures, e.g., as high as 1000°C.
Previously we have reported the importance of the low-temperature growth for incorporating volatile K into Sr1−xKxFe2As2 and Ba1−xKxFe2As2 films [30−33]. Films grown on bare oxide substrates were polycrystalline and c-axis oriented films were realized only with (K,As)-buffered substrates. These c-axis oriented films were not in-plane aligned but the highest Tc of 38.3 K was attained. Hence, a proper substrate should be explored for realizing the epitaxial growth of K-doped Ba-122. Fluoride substrates (CaF2, SrF2, and BaF2) are typically superior to oxide substrates for thin-film growth of IBSCs [34−38]. Additionally, even for a wide range of the growth temperature (280−500ºC), epitaxially grown Fe(Se,Te) thin films are realized [34,39]. Here we employ the combination of a low-temperature growth, up to 420ºC, and fluoride substrates that yield truly epitaxial films of Ba1−xKxFe2As2 with a high superconducting transition (Tc on ~ 36 K), a sharp transition width of 1.5 K, and a high self-field Jc of 2.2 MA/cm 2 at 4 K.

II. EXPERIMENT
The Ba1−xKxFe2As2 thin films were grown in a customdesigned molecular-beam epitaxy (MBE) chamber (base pressure of ~1 × 10 -9 Torr). The details of our film growth approach have been presented in our previous report [23]. Briefly, all elements (Ba, Fe, and As) except for K were supplied from pure metal sources by resistive heating. Elemental K was supplied from an In-K alloy (In8K5). We used electron impact emission spectrometry (EIES) [23] and atomic absorption spectrometry (AAS) [23] for the real-time rate monitoring of various elements: EIES for Ba and Fe, and AAS for K. The K-doping level in Ba1−xKxFe2As2 films was aimed at x = 0.4. The amount of supplied K flux was substantially (2-3 times) higher than the nominally required amount to compensate for K reevaporation. The As flux was optimized by adjusting the cell temperature. The growth rate was ~1.5 Å/s and the deposition time of 10 min yielded Ba1−xKxFe2As2 thin films ~1000Å thick. The optimum growth temperatures were 700-720°C for parent BaFe2As2 and 350-420°C for Ba1−xKxFe2As2. Fluoride substrates, CaF2(001), SrF2(001), and BaF2(001), were used in this study. MgO(001) substrate was used as a reference. K-containing films, especially grown on oxide substrates, quickly degraded in air; therefore, we coated films with a polystyrene resin (commercially called "Q-dope") diluted by toluene as a capping layer immediately after removing the films from the MBE chamber.
The films were characterized by in situ reflection highenergy electron diffraction (RHEED), x-ray diffraction (XRD) using both two-circle ( 2) and four-circle (   ) diffractometers with Cu-K radiation, transmission electron microscopy (TEM), and resistivity (ρ-T) measurements. Magnetic measurements were performed using a superconducting quantum interference device magnetometer to determine Tc and Jc. Jc values were determined by the Bean critical state model.

III. RESULTS AND DISCUSSION
A. Crystal structure Figure 1 shows the XRD patterns and RHEED images of Ba1−xKxFe2As2 films. In Fig. 1(a), the XRD patterns of Ba1−xKxFe2As2 films grown on CaF2 and MgO are compared. The film grown on MgO(001) does not show any appreciable diffraction peaks outside the (002) MgO peak, which indicates that the film is polycrystalline. On the other hand, the film grown on CaF2 is essentially single phased and c-axis oriented with minor iron arsenide impurity peaks. Compared to Ba1−xKxFe2As2 films, pristine BaFe2As2 films (single phased and c-axis oriented) were easily grown on either MgO or CaF2. Figure 1(b) shows the result of x-ray in-plane measurements, i.e., the  scan of the (103) reflection peak of the Ba0.6K0.4Fe2As2 film on CaF2. The fourfold symmetry observed in the  scan with a small full width at half maximum value  ~ 1.39 confirms that the film is in-plane aligned and single crystalline. Similar results were obtained in the films grown on SrF2 and BaF2, suggesting that the use of fluoride substrates is critical for obtaining single-crystalline Ba1−xKxFe2As2 films (see Supplemental Material, Fig. S1 [40]) . The lattice parameters of the film on CaF2 are af ~ 3.889Å and cf ~ 13.380Å. The literature [16,40] shows that the lattice parameters of bulk samples follow ab = 3.96 -0.12x (Å) and cb = 13.00 + 0.84x (Å). Estimating on the basis of these bulk data, Ba1−xKxFe2As2 films with x = 0.40 should have a = 3.91Å and c = 13.33Å. The actual film has shorter af and longer cf compared to this estimation. The difference arises from the thermal expansion mismatch and/or the inplane lattice mismatch between the Ca-Ca distance (3.863Å) of CaF2 and the in-plane lattice constant (3.91Å) of Ba0.6K0.4Fe2As2. The in-plane compressive strain leads to the out-of-plane tensile strain, which leads to a stretch in cf arising from the Poisson effect.
As seen in Figs. 1(c) and 1(d), the RHEED patterns of pristine BaFe2As2 and Ba1−xKxFe2As2 grown on CaF2 demonstrate that both films are single crystalline, which agrees with the XRD results. There is a small difference between the two samples. Pristine BaFe2As2 shows streaks whereas Ba1−xKxFe2As2 shows streaky spots, which indicates that transmission diffraction is partly involved. Specifically, the surface of Ba1−xKxFe2As2 is less smooth than that of pristine BaFe2As2. However, immediately after starting the growth of Ba1−xKxFe2As2, the diffraction pattern in the RHEED image starts with streaks. This observation suggests smooth initial growth of Ba1−xKxFe2As2 on CaF2, which indicates a good physical and chemical matching between the films and the substrate. The image contrast slightly varies in the Ba0.6K0.4Fe2As2 layer mainly in the in-plane direction, which indicates that the formation of columnar grains occurs perpendicular to the substrate surface. This is more clearly seen in a magnified image shown in Fig. 2(b), where several boundaries lie approximately perpendicular to the substrate surface at a several tens of nanometers interval. The columnar growth observed in TEM agrees with the RHEED image in Fig. 1(d). Of note, a lattice fringe is recognized in the entire area of the Ba0.6K0.4Fe2As2 layer in Fig. 2(b), which corresponds to the (001) interplanar spacing of Ba 0.6 K 0.4 Fe 2 As 2 . This means that the Ba 0.6 K 0.4 Fe 2 As 2 film has strong (001) texture and almost no defects such as stacking fault or crack. Figure 2(c) shows a selected area electron diffraction (SAED) obtained from an area of 100-nm size over the Ba0.6K0.4Fe2As2/CaF2 interface, which indicates a clear epitaxial relationship, i.e., the (001) planes of Ba0.6K0.4Fe2As2 are parallel to the (001) planes of CaF2 and the [100] direction of Ba0.6K0.4Fe2As2 is parallel to the [110] direction of CaF2. An atomic-resolution image is shown in Fig. 2(d), where each atomic column in the [100] direction can be recognized [42,43]. This column arrangement is blurred at grain boundaries owing to misorientation as shown in Fig. 2(e). However, a similar atomic-column arrangement is still recognized, meaning that the misorientation is not so large. This small misorientation is consistent with the XRD results shown in Fig. 1(b). Energy-dispersive x-ray spectroscopy (EDX) mapping at the ADF-STEM field of view revealed that the distribution of K in the Ba1−xKxFe2As2 film is nearly homogeneous with x ~ 0.40   (see Supplemental Material, Fig. S2 [40]). Figure 3(a) demonstrates the superconducting transition observed by in-plane resistivity measurements for a Ba0.6K0.4Fe2As2 film on CaF2, which shows a sharp transition with Tc on of 36.4 K. Here Tc on is defined as the temperature at which the resistivity becomes 90% of the normal state. The Tc on values of Ba1−xKxFe2As2 films on fluoride substrates are slightly (~2 K) lower than bulk Tc of 38 K [3]. The slightly lower Tc can be considered as a result of the in-plane compressive strain. The in-plane lattice mismatch between CaF2 and Ba1−xKxFe2As2 increases by decreasing temperature from the growth temperature (673 K) to the measurement temperatures (i.e., 4 ≤ T ≤ 40 K). The in-plane strain is estimated to be around 2.4% at 40 K (see Supplemental Material, Fig. S3 [40]). It is reported that the in-plane compressive strain gives a negative impact on Tc for Ba1−xKxFe2As2 (x ≥ 0.28) [44], which also supports our results of slightly lower Tc on CaF2 substrate. The inset of Fig. 3(a) compares the temperature dependences of resistivity for the epitaxial film on CaF2 and the polycrystalline film on MgO. The residual resistance ratio (RRR) is fairly high (~7) for the epitaxial film of Ba0.6K0.4Fe2As2 on CaF2. This trend was also confirmed for the films on other fluoride substrates (see Supplemental Material, Fig. S1 [40]). However, the polycrystalline film on MgO shows a lower RRR value (2.7) with a broad superconducting transition, although a Tc on of is 34.5 K reasonably high. Figure 3(b) shows the temperature dependence of magnetic susceptibility (χ-T), for the zero-field-cooled (ZFC) and fieldcooled (FC) Ba0.6K0.4Fe2As2 film on CaF2. The data were normalized to their absolute value at 4 K. The film shows a clear diamagnetic signal below 33.5 K, which approximately agrees with the temperature (T c zero ), at which the resistivity becomes zero in transport measurements. Although the χ-T curve for ZFC of this film shows a broad transition, most of our films grown by the similar condition exhibited a Tc of 33 K with a sharp transition (see Supplemental Material, Fig. S4 [40]). Hence, the lower Tc of our films than that of single crystals is not associated with the extrinsic factors such as chemical homogeneity and crystalline imperfection but rather the strain effect discussed above. Figure 4 shows the magnetic field dependence of Jc for the Ba0.6K0.4Fe2As2 film on CaF2. The self-field Jc at 4 K is as high as 2.2 MA/cm 2 and decreases monotonously with the increase in temperature. However, the value is still above 10 5 A/cm 2 even at 28 K. Of note, the level of Jc for our thin films is superior to that of a single crystal [16]. The Jc shows a rather weak dependence on the magnetic field, indicating that the c-axis correlated pinning centers are present in the film. As stated above, grain boundaries lie approximately perpendicular to the substrate surface at a several tens of nanometers interval, which may work as pinning centers. The Jc values from the preliminary transport measurements were confirmed to be comparable to those from the magnetization measurements, indicating that supercurrent flows macroscopically in the film without being interrupted by dislocations or high-angle grain boundaries, which also supports that the sample is an epitaxial film. The detailed transport Jc measurements of Ba1-xKxFe2As2 thin films would be the direction of our next study.

C. Superconducting properties
Our results expand the possibilities for wide-reaching researches. Firstly, the uniaxial pressure dependence of Ba1-xKxFe2As2 can be investigated, since in-plane strain can be induced by using the lattice or thermal expansion mismatch between films and fluoride substrates, e.g., Refs. [45,46]. Secondly and most importantly, single-crystalline-like Ba1-xKxFe2As2 thin films are realized for a wide range of substrates on which fluoride is epitaxially grown. This opens up avenues to grow Ba1-xKxFe2As2 on fluoride-buffered technical and bicrystalline substrates.

IV. CONCLUSION
To conclude, we demonstrate the epitaxial growth of Ba1-xKxFe2As2 films on fluoride substrates such as CaF2, SrF2, and BaF2. Both of the XRD and TEM analyses indicate that the films are highly textured and single-crystalline-like: the films consist of columnar nanograins showing small misorientation angles in the a-b plane of Ba1-xKxFe2As2 at nanograin interfaces. The superconducting transition is as sharp as 1.5 K, although the Tc on of 36.4 K of Ba0.6K0.4Fe2As2 on CaF2 is slightly (~2 K) lower than the bulk Tc. This Tc suppression is due

H//c
presumably to the strain effect. The self-field Jc at 4 K is as high as 2.2 MA/cm 2 and decreases monotonously with an increase in temperature. It should be noted that the level of Jc for our thin films is superior to that of a single crystal. J c shows a rather weak dependence on magnetic fields. The successful realization of epitaxial thin films opens the opportunities to investigate the transport properties for evaluating the application potentials.
In this Supplemental Material, we include x-ray diffraction and temperature dependence of resistance data for Ba1−xKxFe2As2 films grown on various fluoride (CaF2, SrF2, and BaF2) substrates, chemical composition analysis by TEM-EDX, temperature dependence of the in-plane lattice parameter and in-plane strain, and superconducting transition temperature of several Ba1−xKxFe2As2 thin films on CaF2 substrates.
I. X-ray diffraction and resistivity data for Ba1−xKxFe2As2 films grown on various fluoride (CaF2, SrF2, and BaF2) substrates All the Ba1−xKxFe2As2 films were grown simultaneously on CaF2, SrF2, and BaF2 substrates with a slightly higher content of K compared to that of the film on CaF2 substrate in Fig. 3 of the manuscript. Films are single crystalline, which is shown in Figs. S1 (a) and (b). All films are c-axis oriented in the − scan (a) and in-plane aligned in the  scan (b). Temperature dependence of resistance measurements were also conducted for these three films and the data for the films on CaF2 and SrF2 are presented in Fig. S1 (c). Unfortunately, however, the film on BaF2 was deteriorated before the R-T measurements, so the data is not presented.

II. Chemical composition analysis by TEM-EDX
Chemical compositions in the grown film on the CaF 2 substrate were evaluated by energy-dispersive x-ray spectroscopy (EDX) performed in a transmission electron microscope (TEM). Elemental maps (characteristic x-ray intensity distributions) of Ba, K, Fe, As, and other related elements like Ca and F (substrate) are shown in Fig. S2 (a). The data were obtained from a crosssectional slab sample extracted by a focused ion beam (FIB). After the FIB process, the cross-sectional slab sample was exposed in the air during sample transportation to the TEM, resulting in the detection of O atoms due to inevitable oxidation. The sample has a uniform thickness as understood from the flat contrast in the annular dark-field (ADF) image (top left). K atoms seem to distribute almost uniformly in the film, as shown in the elemental map, except for the vicinity of the substrate. The obtained EDX spectra were converted to chemical compositions by a conventional method using Cliff-Lorimer factors. Chemical composition variations along the normal to the substrate surface are plotted in Figs. S2 (b) and (c), where the compositions are averaged in the in-plane direction. In Fig. S2 (b), all the 8 elements are included in the composition calculation. Note that the x-ray absorption in the sample is not considered here, so the light elements, O and F, are severely underestimated. As shown, Ba, K, Fe, and As profiles are recognized to show a constant composition in a large part of the film, suggesting the formation of the stoichiometric film. A thin (~5 nm) layer of K-depleted BaFe2As2 is found at the interface between the film and the substrate, as denoted with a broken line and an arrowhead in Fig. S2 (c). This fact suggests that the substrate affects the film composition in the early stage of the film growth although the substrate effect can be negligible after 5 nm growth of the film.  ).
Using CaF 2 (300 K) = 5.463 Å and the thermal expansion coefficient [1], CaF 2 (40 K) is calculated to be 5.445 Å. The ( ) above 300 K for Ba1−xKxFe2As2 is not available, therefore we estimated the in-plane strain by using that of BaFe1.84Co0.16As2 [2]. The in-plane strain at 40 K is calculated to be  Figure S4 shows the normalized  for Ba1−xKxFe2As2 thin films on CaF2 substrates as a function of temperature. The data is normalized to the value at 4 K. The growth condition was similar to the one presented in the manuscript. As can be seen, both films show a Tc of 33 K with a sharp transition. Hence, the lower Tc of our films than that of single crystals is not associated with the extrinsic factors such as chemical homogeneity and crystalline imperfection but rather the strain effect.

IV. Superconducting transition temperature of Ba1−xKxFe2As2 thin films on CaF2 substrates
FIG. S4. Temperature dependence of the magnetic susceptibility for Ba1−xKxFe2As2 thin films grown on CaF2. The growth condition is almost the same as presented in the manuscript. The growth temperature Ts was (a) 383ºC and (b) 416ºC, respectively.