Introduction

Superconducting magnets have been widely used in diverse fields, such as advanced medical applications and transportation infrastructure1,2,3,4,5. Their fundamental performance is determined by the transition temperature of superconductivity (Tc), critical current density (Jc), and irreversibility field (Hirr). A higher Tc is primarily important for reducing cooling costs, and larger Jc and Hirr are inevitably required to realize compact and strong magnets. The only solution to address the excellent properties of Tc, Jc, and Hirr is the utilization of high-temperature superconductors (HTSs), i.e., cuprates and iron-based superconductors (IBSs)6,7. HTS-based magnets have significantly broadened potential application fields in the form of not only wire but also bulk8,9,10.

Considering fabrication costs, superconducting magnets made of polycrystalline wires are preferable. However, the grain boundaries (GBs) with larger misorientation angles in HTSs act as weak links, leading to a fatal reduction in Jc11,12. In the case of cuprates, a large Jc realized in single-crystal samples decreases by several orders of magnitude in polycrystalline samples13,14,15. This problem has been extensively studied using artificial grain boundaries (AGBs) formed in films grown epitaxially on bicrystal substrates. The results showed that Jc across AGBs (intergrain Jc) decreases with increasing misorientation angle (θGB)16,17,18. In fact, the exponential decay of the intergrain Jc for YBa2Cu3O7−δ starts at approximately θGB = 3–5°18. This characteristic angle is defined as the critical angle (θc). To avoid weak links in HTSs, crystallographic axes (a, b, and c-axes) of adjoining grains should be aligned within θc. As a result, several innovative techniques involving biaxially textured substrates have been developed19,20,21. However, the full-scale industrial application of HTSs is still limited due to the high cost of their fabrication.

On the other hand, the IBSs are another candidate for which the properties of GBs have also been investigated. To date, [001]-tilt AGBs have been examined, where the ab plane rotates around the c-axis with various values of θGB22,23,24,25,26. These experiments revealed that the influence of GBs on the Jc properties in IBSs is very subtle; the reported θc for IBSs is ~9° for all investigated materials. Furthermore, the exponential decay of intergrain Jc over θc is much slower than that of cuprates12. Based on these findings, IBSs are considered highly promising materials for superconducting magnets. Among the variety of IBSs, AeFe2As2 (Ae122, Ae = alkaline earth elements) is one of the most extensively studied systems because of its wide material diversity, relatively high Tc, and general ease of specimen growth9. In particular, potassium-doped BaFe2As2 (Ba122:K) exhibited the highest Tc of up to 38 K27 in the AeFe2As2 system. In addition, recent advancements in synthesis technologies have confirmed that the preparation of high-quality Ba122:K is possible in various sample configurations, including powder-in-tube processed wires28,29,30 and bulk polycrystals28,31,32. Indeed, the bulk polycrystals exhibit a self-field Jc of 0.1 MA/cm2 at 4 K, which remains ~1/10 of that of single crystals32. These values indicate that excellent properties are still present, even in the form of polycrystals. To further improve the performance of Ba122:K, Cheng et al. investigated the effect of doping level on the Jc transparency across GBs30. Although the intragrain Jc showed a maximum at x = 0.287 in Ba1−xKxFe2As2, the maximum intergrain Jc was obtained at x ~ 0.46 due to the stronger proximity effect. However, detailed information on the characteristics of GBs, which are the most fundamental components for understanding the macroscopic Jc of polycrystalline materials, has not been reported.

To address this issue, we report the preparation of Ba122:K AGBs and their excellent transport properties. We used the recently established growth technique of Ba122:K epitaxial thin films33,34,35 to grow Ba122:K on [001]-tilt-type bicrystal substrates. The temperature and magnetic field dependence of their transport properties across the AGBs were measured as a function of θGB. The results indicate that even at θGB = 24°, the self-field Jc at 12 K across the AGB still exceeds 1 MA/cm2 and remains at 0.1 MA/cm2 even at 28 K, further exceeding the boiling temperature of liquid hydrogen (i.e., 20 K). In addition, θc is unaltered even in an applied magnetic field of 5 T, which differs from other IBSs. This class of unprecedentedly large Jcs at high-angle GBs, along with its tolerance against magnetic fields, is remarkably superior to other IBSs, demonstrating the great potential of Ba122:K as a candidate material for next-generation superconducting magnets.

Results

Structural characteristics of the Ba122:K thin films

To investigate the Jc characteristics of Ba122:K at AGBs, films were epitaxially grown on symmetric [001]-tilt-type bicrystal MgO substrates with various θGB by molecular beam epitaxy (MBE). We employed the parent compound BaFe2As2 (Ba122) as a buffer layer, which enabled us to realize highly crystalline films on MgO34. Figure 1a shows the out-of-plane 2θ−ω X-ray diffraction (XRD) pattern for the Ba122:K thin film grown on a Ba122-buffered MgO bicrystal substrate with θGB = 6°. The 00 l peaks of Ba122:K together with Ba122 were observed, indicating that a 00l-oriented thin film was obtained. Since the c-axis length of Ba122:K increases with increasing K substitution36, the Ba122:K- and Ba122-related peaks can be clearly distinguished. The estimated c-axis length of Ba122:K was 13.247 Å, which is almost identical to that of the Ba122:K (36%) film (13.22 Å)34. The estimated c-axis lengths of the films grown on the bicrystal MgO substrates with θGB = 13° and 24° are 13.251 Å and 13.275 Å, respectively, which are slightly longer than those of the film with θGB = 6°. This suggests that the films grown on θGB = 13° and 24° substrates may be slightly overdoped. Figure 1b–d shows the 103 ϕ-scan spectra of the Ba122:K films grown on [001]-tilt MgO bicrystal substrates with θGB = 6°, 13°, and 24°. For each film, fourfold symmetric peaks were observed, reflecting its tetragonal structure. All the peaks exhibited a bipeak separated by θGB for each film, indicating that the texture of the bicrystal substrates was transferred to Ba122:K via the Ba122 buffer layers. For the film with θGB = 6°, weak peaks corresponding to 45°-rotated grains were found in the middle of the fourfold bipeaks. A small number of grains rotated at 45° also seem to be present in the films with θGB = 13° and 24°.

Fig. 1: Structural analysis of the (Ba,K)Fe2As2 (Ba122:K) thin films grown on BaFe2As2-buffered [001]-tilt bicrystal substrates.
figure 1

a Out-of-plane X-ray diffraction spectrum of the Ba122:K/Ba122 film grown on a [001]-tilt MgO bicrystal substrate with θGB = 6°. The 00 l peaks from Ba122:K together with the Ba122 buffer layer were observed. b–d In-plane ϕ-scan spectra for the 103 peaks of Ba122:K grown on the bicrystal substrates with grain boundary angles θGB of 6°, 13°, and 24°. e Low-magnification cross-sectional view of the film grown on [001]-tilt MgO bicrystal substrates with θGB = 24° observed by atomic resolution annular dark-field (ADF) scanning transmission electron microscopy (STEM). f, g Magnified ADF-STEM images taken at the blue and red square regions displayed in e.

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To directly determine the AGB of Ba122:K, cross-sectional observation using scanning transmission electron microscopy (STEM) was performed on the film with θGB = 24°. Figure 1e shows a low-magnification view obtained by annular dark-field STEM (ADF-STEM). GB was clearly observed in the MgO bicrystal. Figure 1f shows an enlarged view of the Ba122:K/Ba122 interface enclosed by the blue frame in Fig. 1e. In the image, the layered structure was observed as bright arrays of Ba (or Ba/K) sites and zig-zag spot pairs of Fe-As layers. Additionally, the Ba122:K/Ba122 interface along the [100] zone axis is found due to the difference in the Z contrast between the Ba/K layers in Ba122:K and Ba layers in Ba122. The thickness of the film was estimated from the cross sectional images from e.g. Fig. 1e; the Ba122 buffer and Ba122:K layer thicknesses are 20 nm and 80–100 nm, respectively. Figure 1g shows an enlarged view of the Ba122:K GB enclosed by the red frame in Fig. 1e. Since the image was taken along the [010] direction of the right field of Fig. 1g, clear elemental stacking is observed only on this side, whereas the left side appears defocused. This indicates that the [001]-tilt-type AGB of Ba122:K was successfully realized. As shown in Fig. 1g, however, the ~2-nm-wide AGB seems to have formed with meandering within an ~5-nm-wide region, accompanied by a blurred arrangement of elemental columns in its vicinity. Hence, slight structural deformations and/or distortions are spontaneously introduced around the AGB.

Device fabrication and transport properties of Ba122:K grain boundaries

The films were fabricated into sub-μm bridge structures for transport measurements. To avoid serious degradation of Ba122:K, an all-dry fabrication process was employed. A thin film with θGB = 6° was processed into a bridge structure approximately 40 μm wide and 1 mm long using an Ar-ion milling system. On the other hand, thin films with θGB = 13° and 24° were cut into bridges approximately 80–100 μm wide and 1 mm long by a laser marking system. Figure 2a shows an optical micrograph of Ba122:K grown on the [001]-tilt bicrystal substrate with θGB = 24°. As depicted in the schematic illustration in the lower part of Fig. 2a, the bicrystal substrate (the schematic is shown in Fig. 2b) is separated by a grain boundary (red line) existing at the center of the substrate, and each domain rotates around the c-axis (perpendicular to the surface of the paper) by θGB/2. Therefore, a bridge fabricated to cross the grain boundary contains the AGB, which is referred to as an inter-GB bridge. In addition, bridges prepared in the same domain, referred to as intra-GB bridges, were also fabricated.

Fig. 2: Bridge configuration on the Ba122:K thin films and superconducting transitions measured by a 4-probe method.
figure 2

a Optical micrograph of the Ba122:K thin film grown on a [001]-tilt-type bicrystal substrate of MgO with θGB = 24°. The intra- and inter-GB bridges were prepared on the same film. A schematic of the fabricated bridge structures is also shown. Al wires for a four-terminal measurement are fixed using silver paste. b Schematic image of the [001]-tilt bicrystal substrate. The temperature dependence of the resistivity under an external magnetic field H for inter-GB bridges fabricated on Ba122:K thin films grown on [001]-tilt-type substrates with θGB = c 6°, e 13°, and g 24° measured in the range of μ0H = 0 to 9 T with an increment of 1 T. The applied field was parallel to the c-axis. The corresponding data for the intra-GB bridges with θGB = d 6°, f 13°, and h 24° are also displayed. The temperature dependence of the upper critical field (Hc2) is plotted for the inter- and intra-GB bridges with θGB = i 6°, j 13°, and k 24°.

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Figure 2c, d displays the temperature dependence of the resistivity under various external magnetic fields H for the inter- and intra-GB bridges with θGB = 6°, respectively. Both bridges show a clear superconducting transition with an onset Tc of 38.6 K for inter-GB bridges and 38.4 K for intra-GB bridges, indicating no apparent difference between the inter-GB and intra-GB bridges. In addition, these values are comparable to those of the optimally doped Ba122:K single crystals, which is consistent with the c-axis length determined from the XRD measurements, as mentioned above. Clear superconducting transitions were also observed in Ba122:K thin films with θGB = 13° and 24° (Fig. 2e–h). For the thin film grown on the θGB = 13° substrate, the onset Tc values were 36.1 K (intra-GB bridge) and 35.9 K (inter-GB bridge). The respective intra- and intergrain Tc values for θGB = 24° were 35.9 K and 35.4 K, respectively. No appreciable difference in Tc, irrespective of the presence of GBs, was detected. However, the observed Tc is approximately 3 K lower than that of the film with θGB = 6°. Considering the estimation of the c-axis lengths for the films, the decrease in Tc in the films with θGB = 13° and 24° may be ascribed to the slight overdoping of K. We also estimated the Hc2, which was defined by 90% of the normal-state resistivity, as plotted in Fig. 2(i–k). For each film, the inter- and intra-GB temperature dependencies appear to be identical. The slope dHc2/dT of each bridge, determined using data at μ0H > 2 T, also shows similar values: –8.1 T/K (θGB = 6°), –7.9 T/K (θGB = 13°), and −8.8 T/K (θGB = 24°), indicating minimal variation in superconducting properties across all bridges. For the magnetoresistance, none of the bridges shows an apparent field dependence on the resistivity, which agrees with the bulk reports of single-crystalline Ba122:K37. We finally mentioned the trial of film growth on the [010]-tilt (roof type) bicrystal substrate, although the optimization of the growth conditions was not completed. The detailed results are provided in the supplementary material.

Critical current density evaluated from the E−J characteristic measurements

To determine how Jc is affected by the presence of GBs, the voltage V − current I characteristics of the intra- and inter-GB bridges with θGB = 6°, 13° and 24° were measured. The temperatures were varied from 12 K to 30 K. The magnetic field applied parallel to the c-axis was varied from μ0H = 0 to 9 T. For the estimation of Jc, the V−I data were converted to the electric field E − current density J by the geometrical parameters. Note that the measurements at temperatures lower than 12 K could not be conducted for every bridge due to the fatal thermal damage caused by large feeding currents.

Figure 3a shows the magnetic field dependence of the E−J characteristic at 12 K for the intra-GB bridges with θGB = 6°. First, a power-law behavior described as E ~ Jn was observed for the intra-GB bridge in self-field (μ0H = 0 T) measurements, which represents flux creep effects. By adopting a standard criterion of Ec = 1 μV/cm shown in Fig. 4(a, b) as dashed line, the self-field Jc was estimated to be 2.1 MA/cm2. The reported self-field Jc of Ba122:K bulk single crystals measured by a magnetization method is ~0.5 MA/cm2 at 10 K36, which is approximately 25% of that of the thin film. Since the deposition conditions of this study are almost identical to those of ref. 35, strong pinning centers caused by low-angle grain boundaries and their networks are present in the films, leading to an improved Jc value. Under magnetic fields, Jc exhibits a systematic decrease with increasing magnetic field, yet Jc = 0.5 MA/cm2 is still maintained even at 9 T. Such robust behavior of Jc against magnetic fields has also been reported in bulk studies31,37.

Fig. 3: Electric field E – current density J characteristics and the temperature and magnetic field dependence of the critical current density Jc for inter- and intra-GB bridges.
figure 3

a, b E–J curves of the intra- and inter-GB bridges measured at 12 K and various magnetic fields for θGB = 6°. The curves taken at μ0H = 0, 0.2, 0.6, 1, 3, 5, 7, and 9 T are plotted. c–e Temperature dependence of self-field (μ0H = 0 T) Jcs of intra- (gray circles) and inter-GBs (black circles) for θGB = 6°, 13°, and 24°. f–h Field dependence of Jc at various temperatures for f θGB = 6°, g θGB = 13°, and h θGB = 24°. The open circles show the intra-GB data, and the closed circles show the inter-GB data.

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Fig. 4: The grain boundary angle dependence of Jc for Ba122:K and other iron-based superconductors.
figure 4

Comparison of the Jc−θGB characteristics of Ba122:K for a self-field and c μ0H = 1 and 5 T. b, d Jc ratio of the inter-GB bridge to the intra-GB bridge (inter-Jc/intra-Jc) as a function of θGB. For comparison, the data for Ba122:Co, Fe(Se,Te), and NdFeAs(O,F) are also plotted22,23,25.

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We next observe the Jc characteristics of the inter-GB bridge with θGB = 6° (Fig. 3b). The bridge also shows a steep increase in E with J, reaching a self-field Jc of 2.7 MA/cm2 at 12 K, which slightly exceeds the performance of the intra-GB bridge (Fig. 3a). This behavior is found at all temperatures we measured, as displayed in the temperature dependence of the self-field Jc (Fig. 3c). One possible explanation is that AGB acts as a pinning center. In this case, the pinned flux is easily moved by the application of a small magnetic field, and a flux-flow state should be observed. Indeed, as shown in Fig. 3b, a non-ohmic linear differential (NOLD) behavior (i.e., E starts to change linearly with J, indicative of the flux flow along the AGBs) is observed38 at E > 10 μV/cm. In addition, the self-field Jc of the inter-GB deteriorated by approximately 22% by applying only a weak field of μ0H = 0.2 T, which seems to indicate a steeper decay than that occurring in the intra-GB bridge (9%), suggesting the presence of flux flow along the AGBs. On the other hand, under magnetic fields larger than 0.2 T, there is no clear difference in Jc between inter- and intra-GB; they trace almost identical curves, as plotted in the black and gray circles in Fig. 3(f), which indicates that Jc is limited by the intragrain depinning of fluxoids of at least 9 T. Sequential comparisons of the magnetic field dependence of Jc at different temperatures for the inter-GB and the counterpart of the intra-GB are depicted in Fig. 3f. The open circles indicate the intra-GB bridge, and the closed circles indicate the inter-GB bridge. Surprisingly, even at 30 K, the intra- and inter-GB behaviors are almost identical. Hence, it is concluded that there is no clear decay in the Jc characteristics of Ba122:K, at least for θGB = 6°.

At larger θGB values of 13° and 24°, the evaluation of E−J properties and the determination of Jcs were conducted both for the intra- and inter-GB bridges. At 12 K, the inter-GB bridge with θGB = 13° has a self-field Jc = 1.7 MA/cm2, which corresponds to ~40% degradation compared to that of the intra-GB bridge (2.8 MA/cm2). The results at higher temperatures also show similar behavior, as shown by the black and gray circles in Fig. 3d. As the magnetic field increases, Jc of the inter-GB with θGB = 13° remains approximately half that of the intra-GB up to 24 K [Fig. 3g], resulting in 10 kA/cm2 at 24 K under 8 T. However, at 28 K, the decay of Jc due to the magnetic field becomes prominent, inferring the presence of weak links in superconductivity at AGBs. With a much larger θGB of 24°, a significant reduction in Jc was observed. Under the self-field, Jc of the inter-GB bridge at 12 K was reduced by approximately 80% compared to that of the intra-GB bridge (Fig. 3e). Moreover, the application of a weak field of only 0.2 T triggered a nearly 90% decrease in Jc, suggesting that the aforementioned flux pinning at the AGB was significantly weak. Since the intra-GB bridges prepared on the bicrystal substrate with θGB = 24° were broken during measurement, comparative studies between the inter- and intra-GB bridges at magnetic fields higher than 1 T are impossible. However, as shown in Fig. 3h, the inter-GB bridge still maintains Jc above 10 kA/cm2 even at 20 K under a magnetic field of up to 8 T.

Discussion

Comparison of the critical current densities between Ba122:K and other iron-based superconductors

By comparing the intergrain Jc of Ba122:K with that of other IBSs, we demonstrate the excellence of the GB characteristics of Ba122:K. The contrasting feature of IBSs compared with cuprates is the metallic nature of GBs, which is considered one of the reasons for the larger θcs of IBSs. Indeed, the reported linear resistance products RNA (where RN is the normal-state resistance and A is the cross-sectional area of the GB) of Ba122:Co, NdFeAs(O,F), and Fe(Se,Te) are smaller than those of YBCO39. Here, the RNA of Ba122:Co has an exceptionally small value of 5 × 10−11 Ωcm2 for θGB = 4° at 12 K22. We estimated the RNA for θGB = 6° at 12 K in the NOLD region to be 8.8 × 10−11 Ωcm2, meaning that the metallicity of the AGB of Ba122:K is almost comparable to that of Ba122:Co22.

Figure 4a summarizes the θGB dependence of self-field Jc for various IBSs. NdFeAs(O,F) (green inverted triangle) exhibited the highest Tc among the IBSs, but its Jc showed a large decrease with increasing θGB. This is due to some damage to the GB area caused by preferential F diffusion26. However, for Ba122:Co (red square), for which the Tc is almost half as low as that of NdFeAs(O,F), the Jcs of Ba122:Co at 12 K (0.5Tc) were twice as high as that of NdFeAs(O,F) at 4 K (0.09Tc). Thus, the best Jc−θGB performance of IBSs reported to date is Ba122:Co. However, the Jc−θGB performance of Ba122:K (red circle) measured at 12 K exceeds one order of magnitude for every θGB. Indeed, Jc remains greater than 1 MA/cm2 even at θGB = 24°, meaning that the decay of Jc at higher angles is more gradual than that of Ba122:Co. Even according to a fair comparison using the same reduced temperature t = T/Tc of 0.5, the Jc of Ba122:K is still five times greater than that of Ba122:Co in the range of 0°\(\le\)θGB\(\le\)24°. Furthermore, the Jc−θGB performance at 28 K (t = 0.72) is still comparable to that of Ba122:Co at 12 K (t = 0.5). The systematic θGB dependence of Jc in Fe(Se,Te) and NdFeAs(O,F) has only been studied at 4 K, yet it is obvious that both cases are far behind Ba122:K, indicating that Ba122:K has the best GB performance among the IBSs so far reported.

To estimate the critical misorientation angle θc of Ba122:K, the inter-GB Jc was normalized to the intra-GB Jc [Fig. 4b]. As clearly shown in Fig. 4b, no degradation of Jc was observed at θGB = 6°. On the other hand, a significant reduction in Jc was found at 13°, followed by a one order of magnitude decrease at 24°. This indicates that the θc of Ba122:K lies between 6° and 13°, indicating similarity to that of other IBSs. Hence, the θc of IBSs seems to be universally ~9°. Further discussion on this point will be provided later.

The Jc properties of Ba122:K under magnetic fields show more characteristic tolerability against the misorientation angles. Figure 4c displays the θGB dependence of Jc measured at 12 K (t = 0.33) under 1 T and 5 T. Jc at 5 T remains above 10 kA/cm2 at θGB = 24°, which exceeds the value of Ba122:Co measured at 4 K (t = 0.17). A more striking feature is that θc does not decrease when magnetic fields are applied. Indeed, as shown in Fig. 4d, the Jc ratio for Ba122:Co under magnetic fields at 4 K shows a clear exponential decay from the smaller θGB values, inferring that θc is reduced below 5°. In contrast, no clear change in θc was observed, even at the 5 T application in Ba122:K.

Next, we discuss the possible origin of the especially high Jc performance of Ba122:K, even exceeding that of Ba122:Co. As displayed in Fig. 1(g), the obtained film has structural perturbations such as structural distortion and/or twisting near the AGBs. This class of misorientation domains could plausibly act as flux pinning centers, as discussed in ref. 31. The difference in the doping level among the specimens, which we discussed in the Results section, should also be considered since the Jc ratio (inter-Jc/intra-Jc) of Ba122:K changes according to ref. 30. Assuming that our film is fully relaxed, the estimated K content of each film based on the c-axis length is 0.303 (θGB = 6°), 0.307 (13°) and 0.336 (24°) (see supplementary materials). The K doping levels of θGB = 6° and θGB = 13° are almost identical, whereas the film with θGB = 24° is possibly overdoped by ~4% relative to the film with θGB = 6°. Correspondingly, based on ref. 30, the Jc ratios of both films are estimated to be ~0.052 (θGB = 6°) and ~0.065 (θGB = 24°), indicating that the Jc ratio of the 24° specimen with the same doping level as that of the 6° specimen may decrease by approximately 20%. This may lead to a slight overestimation of the θGB dependence of the Jc ratio at 24°.

Additionally, spontaneous connectivity modification at the AGB may play an important role. Figure 5a displays the cross-sectional crystalline orientation mapping by scanning precession electron diffraction (SPED) at the AGB with θGB = 6°. The color map of the rotation angle in Fig. 5a was prepared to magnify the small angle rotation around the [001] axis. As clearly shown in Fig. 5a, a steep GB was found in the bicrystal MgO. According to the line profiles taken at the MgO substrate (L3 in Fig. 5a), the angle difference at the boundary was 6°, which corresponds to θGB (Fig. 5d). The AGB of Ba122:K was formed on the GB of bicrystal MgO, yet its location was slightly slipped. According to the line profiles of the misorientation angles in the Ba122:K layer represented as L1 and L2 in Fig. 5(a), the misorientation gradually changes with a width of approximately 20 nm and finally reaches an ~6° difference against the other side of the crystalline orientation (Fig. 5b, c). This class of the accumulation of small-angle rotations of [001]-tilting at AGB would assist the intergrain supercurrent even under magnetic fields, which causes the high tolerance of θc against magnetic fields, as mentioned above. The recent remarkable improvement in the superconducting performance of Ba122:K bulk materials is possibly ascribed to such an effect28,29,30,31,32. A detailed microstructural analysis of natural GBs existing in bulk materials should be performed. At the same time, we should be careful about the determination of θc of Ba122:K: although the θGB values determined from the XRD analysis correspond well to the boundary angles of the bicrystal substrates, they may not strictly reflect the actual θGB, which consists of small-angle grain boundaries. To address this issue, further efforts are required to establish well-defined AGBs of Ba122:K.

Fig. 5: Nanoscale crystal orientation map determined by scanning precession electron diffraction for the film grown on [001]-tilt MgO bicrystal substrates with θGB = 6°.
figure 5

a Color map of the misorientation angle in the cross-sectional direction. To highlight small angle rotations and distinguish the substrate/Ba122 boundary, the color coordination for the Ba122:K/Ba122 part and the MgO part is set as the triangular color codes placed at the right of the figure. b–d Line profiles of the misorientation angle at L1-L3 in a. Note that L1 and L2 are for the Ba122:K layer, and L3 is for the MgO substrate.

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Conclusion

Herein, using the epitaxial film growth technique, we prepared [001]-tilt-type Ba122:K AGBs on bicrystal substrates with different θGB values. Systematic transport measurements of AGBs at various temperatures and magnetic fields revealed that the Jc properties of Ba122:K exhibit unprecedentedly high grain boundary performance. Indeed, practical levels of Jc (> 0.1 MA/cm2) were achieved even for the AGB with θGB = 24° at 28 K (self-field), which surpasses other IBSs reported to date. On the other hand, the θc of Ba122:K in the self-field seems to be between 6° and 13°, supporting the empirical tendency where the θc of IBSs is universally ~9°. Although θc shows an apparent reduction after applying only 1 T in the reported IBSs, Ba122:K maintains an identical θc to at least 5 T.

Methods

Thin film preparation and structural analysis

Ba122:K thin films were grown on bicrystal substrates using a custom-made MBE system following the method described in refs. 33,34,35. Bicrystal substrates with various tilting angles have been commercially available for only a few oxide substrates, such as MgO and SrTiO3. Previous results have shown the challenges in growing Ba122:K directly on oxide substrates33. Thus, we employed the recently established self-buffer method, where the parent Ba122 was grown first as a buffer layer, followed by Ba122:K34. The deposition was carried out with a base pressure of 1 × 10−7 Pa. Ba, Fe and As were supplied individually from pure metal sources by resistive heating, while K was supplied as an In-K alloy in Knudsen cells. The supplied fluxes of Ba and Fe during deposition were monitored by electron impact emission spectrometry, and that of K was monitored by atomic absorption spectrometry. The growth mode of the film was monitored by reflection high-energy electron diffraction. The typical substrate temperatures were 700 °C for Ba122 and 400 °C for Ba122:K. The films did not show apparent degradation of crystallinity or superconducting performance, even after several hours of exposure to air. In some cases, the film surfaces were coated in situ with CaF2 for surface protection to enhance the film stability. The deposition of CaF2 was performed after the film cooled to room temperature. The crystallinity of the thin films was then evaluated using both an out-of-plane XRD spectrometer (RINT2100, RIGAKU, Japan) and an in-plane XRD spectrometer (ULTIMA-IV, RIGAKU, Japan). After the measurements, microstructural analyses were conducted on some of the samples. Cross-sectional specimens were picked from the films using focused ion beam (FIB) milling. Atomic-resolution structural observation was conducted using aberration-corrected STEM (Titan Cubed G2, Thermo Fisher Scientific, USA) at an acceleration voltage of 300 kV. The annular dark-field (ADF) detection angle range was set from 68 to 200 mrad. Crystal orientation mapping by SPED with better than 10 nm spatial resolution was conducted using a transmission electron microscope (ARM-200F, JEOL Ltd., Japan) equipped with a crystal orientation mapping system (ASTAR, NanoMEGAS, Belgium) at an acceleration voltage of 200 kV40.

Bridge fabrication

Since the critical currents of HTSs are very high, microfabrication of the specimen is required to evaluate Jc by electrical transport measurements. Such fabrication is usually carried out using photolithographic patterning, followed by etching, but Ba122:K degrades in wet processes such as H2O immersion. For this reason, we employed an all-dry process. The Ba122:K films with AGBs with θGB = 6° were processed into bridge shapes using a custom-built Ar-ion dry etching system. A 50-μm-diameter Ag wire and an Al foil were placed on the films as a protective cover, followed by irradiation with Ar ions. To suppress thermal damage during the milling process, the sample stage was cooled by liquid nitrogen. The fabricated bridge was approximately 40 μm wide and 1 mm long. On the other hand, Ba122:K thin films with θGB = 13° and 24° were patterned by a nanosecond pulsed laser irradiation system (Kokyo, Japan). Due to the limitation of the laser spot size, the line width of the bridges was 80 μm ~ 100 μm. For every bridge, electrode pads (~1 mm2) were prepared to make four-terminal electrical connections possible.

Transport characteristic measurements

In total 20 μmϕ Al wires were wired to the bridges obtained as described above, followed by silver paste for further reinforcement. Several wires were bonded to the current feed lines and reinforced with indium to alleviate the current limitation. A liquid He cryogenic system (PPMS, Quantum Design, USA) was used to evaluate the transport characteristics. For the V−I characteristics, the current was applied using a source measurement unit, and the voltage difference between the bridges was measured using a nanovoltmeter (B2902A, 34420 A, Keysight Technologies USA). The current application and voltage measurements were conducted with increasing temperature and magnetic field. Note that at each current condition, the measurement with the inverse current was also performed to compensate for the thermoelectric components in the V−I characteristics.