High critical temperature superconductors have zero power consumption and could be used to produce ideal electric power lines. The principal obstacle in fabricating superconducting wires and tapes is grain boundaries—the misalignment of crystalline orientations at grain boundaries, which is unavoidable for polycrystals, largely deteriorates critical current density. Here we report that high critical temperature iron pnictide superconductors have advantages over cuprates with respect to these grain boundary issues. The transport properties through well-defined bicrystal grain boundary junctions with various misorientation angles (θGB) were systematically investigated for cobalt-doped BaFe2As2 (BaFe2As2:Co) epitaxial films fabricated on bicrystal substrates. The critical current density through bicrystal grain boundary (JcBGB) remained high (>1 MA cm−2) and nearly constant up to a critical angle θc of ∼9°, which is substantially larger than the θc of ∼5° for YBa2Cu3O7–δ. Even at θGB>θc, the decay of JcBGB was much slower than that of YBa2Cu3O7–δ.
Grain boundary (GB) engineering of high critical temperature (Tc) cuprate superconductors has been a critical issue in developing practical superconducting wires and tapes1, because their superconducting properties heavily depend on the misorientation angle (θGB) at GBs; therefore, grains in cuprate superconductors must be highly textured to minimize deterioration of the critical current density (Jc) across misoriented GBs. In a representative cuprate superconductor, YBa2Cu3O7–δ (YBCO), a fundamental study of intergrain Jc in bicrystal GBs (JcBGB) has been performed using several types of bicrystal substrates2. Significantly misaligned adjacent grains cause JcBGB to decay exponentially as a function of θGB from 3° to 40° (ref. 3). Therefore, to produce YBCO superconducting tapes with a high Jc, it is necessary to insert well-aligned buffer layers with a small distribution of in-plane misalignment Δφ<5° on polycrystalline metal substrates using the ion-beam-assisted deposition technique4 or rolling-assisted biaxially textured substrates (RABiTS)5. Although recent progress in buffer-layer technology has established Δφ<5°, which provides a self-field Jc of several MA cm−2 at 77 K (ref. 6), fabricating such a buffer layer is time consuming and expensive. The development of new high-Tc and high upper critical magnetic field (Bc2) superconducting materials with a more gradual JcBGB(θGB) dependence allows for a simple and low-cost fabrication process and provides wider flexibility in superconductor power lines and their applications.
Iron pnictide superconductors7,8 have received increasing interest as a new family of high-Tc superconductors because they have attractive properties such as a high Tc up to 56 K (ref. 9) and high Bc2(0) well over 100 T (refs 10, 11). The iron pnictide family shares several characteristics with the cuprates, such as a layered crystal structure, superconductivity induced by carrier doping and the presence of competing orders. However, there are some noteworthy differences, such as the metallic nature of normal states of the iron pnictides instead of the antiferromagnetic Mott insulators of the cuprates, smaller anisotropy in superconducting properties, which is primarily due to the multi-pocket structures of their Fermi surfaces, and a highly symmetric order parameter based on s-wave instead of a d-wave pairing one12. Therefore, we expect that these characteristics of iron pnictides would make them more favourable than cuprates with respect to the supercurrent conduction mechanism in misoriented GBs.
We have studied epitaxial films of the AEFe2As2 (AE=Sr and Ba) system13,14,15,16,17,18, because they have considerably small anisotropy in superconducting properties, high Bc2(0) >50 T and weak thermal fluctuations with a Ginzburg number Gi of 1.7×10−4 among iron pnictide materials19,20. In particular, cobalt-doped BaFe2As2 (BaFe2As2:Co) appears to have great potential for device applications15,16,17,21,22,23,24, because it is rather easy to grow films by pulsed laser deposition (PLD) and chemically stable in an ambient atmosphere15. It was previously reported that in-field transport properties across bicrystal GBs (BGBs) with 4 different θGB=3°–24° formed in BaFe2As2:Co epitaxial films grown on -tilt SrTiO3 bicrystal substrates suggested that even low-angle BGB with θGB=6° obstructs supercurrent, and the weak-linked BGBs exhibit a similar behaviour to YBCO BGBs22.
In this article, we report comprehensive results on transport properties of BaFe2As2:Co BGB junctions grown directly on insulating bicrystal substrates in the full range of θGB from 3° to 45°. Among the results, it is particularly noteworthy that the critical angle θc of ∼9° for BaFe2As2:Co is much larger than the previously reported value, and the decay slope is much smaller than that of cuprates. The large θc allows a simpler and lower-cost fabrication process of superconducting tapes. This advantageous GB nature is demonstrated by the high Jc>1 MA cm−2 of a BaFe2As2:Co superconducting tape fabricated on a polycrystalline flexible metal substrate25.
BaFe2As2:Co bicrystal grain boundary (BGB) junctions
BaFe2As2:Co epitaxial films with the optimal Co concentration of 8% were fabricated on -tilt bicrystal substrates of MgO with θGB=3°–45° and (La, Sr)(Al, Ta)O3 (LSAT) with θGB=5°–45° by PLD with a Nd:YAG laser (λ=532 nm) at a substrate temperature of 850 °C (ref. 16). To date, different techniques that employ conductive buffer layers of SrTiO3, BaTiO3 (ref. 23) or Fe (ref. 26) have been proposed to enhance high-quality epitaxial growth. However, we have reported that it is possible to grow high-quality BaFe2As2:Co epitaxial films with high self-field Jc>1 MA cm−2 directly on insulating MgO and LSAT single-crystalline substrates without any buffer layer, which has been achieved by optimizing the growth conditions16. The directly grown BaFe2As2:Co films exhibited an onset Tc of 20.7 K for MgO bicrystal substrates and 21.6 K for LSAT bicrystal substrates with sharp transition widths (ΔTc) of 1.1 K (ref. 17).
Figure 1a illustrates the device structure fabricated on -tilt bicrystal substrates. To perform transport measurements of JcBGB, the BaFe2As2:Co epitaxial films were patterned into 300-μm-long, 8-μm-wide micro-bridge structures. To compare the intergrain Jc (JcBGB) and intragrain Jc (JcGrain), two types of micro-bridges were fabricated: one was a 'BGB junction' that contained a BGB each, and the other was a 'Grain bridge' that did not contain a BGB. The electrical contacts were formed with In metal pads and Au wires. The current–voltage (I–V) characteristics of BGB junctions and Grain bridges were measured by the four-probe method.
High critical angle of strong-link—weak-link transition
The correlation between the transport JcBGB and the θGB is the most important index in characterizing the GB properties of superconductors. Figure 1b summarizes the self-field JcBGB(θGB) measured at 4 and 12 K, and Figure 1c shows the JcBGB/JcGrain ratio at 4 K. For comparison, the generally accepted average JcBGB(θGB) properties of YBCO BGB junctions measured at 4 and 77 K (ref. 2) are also plotted. The JcGrain for all of the BaFe2As2:Co Grain bridges are greater than 1 MA cm−2 at 4 K and 1.0–0.5 MA cm−2 at 12 K. For the BGB junctions with low θGB≤∼9°, the JcBGB/JcGrain ratio remained almost at unity, indicating that the low-angle BGB junctions do not behave like a weak link. However, with the increase in θGB from 9° to 45°, JcBGB decreases to ∼5%, which indicates that the transition from the strong link to the weak link occurs at θc of ∼9°. In the YBCO system, the JcBGB values at 4 K for θGB<5° were slightly less than the JcGrain values, and the JcBGB values for θGB>5° showed a clear weak-link behaviour2,27. Although the reported data are somewhat scattered2, the typical values of θc=3–5° are almost half the magnitude of those obtained for the BaFe2As2:Co BGB junctions.
Gentle JcBGB decay in weak-link regime
It is well known that the BGB junctions of the cuprates exhibit nearly exponential decay in their JcBGB(θGB) curves in the weak-link regime with an empirical equation of Jc0exp(−θGB/θ0), where θ0 denotes the characteristic angle. The JcBGB(θGB) curves are expressed by 3.0×107exp(−θGB/4.3°) at 4 K and 7.0×106exp(−θGB/4.2°) at 77 K. The present BaFe2As2:Co BGB junctions also show an exponential decay, approximated as 2.8×106exp(−θGB/9.0°) at 4 K (the red line in Fig. 1b) and 1.5×106exp(–θGB/8.5°) at 12 K (the blue line in Fig. 1b). It should be noted that the θ0 values for the BaFe2As2:Co BGB junctions are twice as large as those for the YBCO BGB junctions, which indicates that the JcBGB(θGB) of the BaFe2As2:Co BGB junctions shows a more gradual decrease than that of the YBCO BGB junctions. Consequently, the JcBGB of the BaFe2As2:Co BGB junction exceeds that of the YBCO BGB junctions at θGB≥20° at 4 K.
BGB junction characteristics
Figure 2a shows the I–V characteristics measured at 12 K for 8-μm-wide BGB junctions with θGB=4°, 16° and 45°. The BGB junction with θGB=4° only exhibits a sharp resistivity jump at a large Ic of 50 mA because of the normal state transition. Similar I–V characteristics were observed for all of the BGB junctions with θGB ≤ 9°. On the other hand, the I–V curves of BGB junctions with θGB=16° and 45° show nonlinear characteristics without hysteresis in the low-voltage region. In general, the shapes of the I–V curves of BGB junctions depend on the fractions of the Josephson current exhibiting resistively shunted junction (RSJ) behaviour (WRSJ) and a supercurrent showing flux flow (FF) behaviour (WFF). A phenomenological model to explain their fractions in I–V curves was previously proposed as follows28: I–V curves are expressed by the combination of the RSJ and the FF behaviours, where the RSJ current follows and the FF current follows IFF=IS−A exp(−V/V0) (RN is the normal-state resistance of the barrier, and IS, A and V0 are constants). The fitting results based on this model drawn by the blue lines reproduce the experimental I–V curves well. The fractions of the RSJ current WRSJ are approximately 0, 70 and 100% for the BGB junctions with θGB=4°, 24° and 45°, respectively. The 100% RSJ current is further confirmed by good agreement with the commonly used Ambegaokar–Halperin (AH) model29 drawn by the red line for the BGB junctions with θGB=45°. The RSJ behaviour in the I–V curves of the BGB junctions with θGB=45° was observed in the whole temperature range below Tc. The junction resistance RNA, where A is the cross-sectional area of the junction, provides information on the nature of the barrier in BGB junctions. The RNA products were estimated by fitting the above-mentioned model to the experimental I–V curves28. The RNA of the BaFe2As2:Co BGB junctions are 5×10−11 Ωcm2 for θGB=16° and 5×10−10 Ωcm2 for θGB=45°, which are one or two orders of magnitude smaller than those of the YBCO BGB junctions (6×10−9–8×10−8 Ωcm2 for θGB=16°–45°, respectively). These results suggest that the BaFe2As2:Co BGB junctions work as superconductor–normal metal–superconductor junctions. On the other hand, the YBCO BGB junctions generally show hysteretic I–V curves at low temperatures well below Tc, indicating relatively large junction capacitances and resistances due to the insulating nature of their junction barriers. In the case of the BaFe2As2:Co BGB junctions, the nonhysteretic curves, even at low temperatures, suggest the metallic nature of the junction barriers.
Figure 2b,c show the Josephson junction properties of 3-μm-wide BGB junctions with a small θGB=16° and a large θGB=45°, respectively. The left figures show the magnetic field B dependencies of Ic (Ic−B) under B applied perpendicular to the film surfaces, and the right figures show the I–V curves of the BGB junctions irradiated with microwaves at a frequency of 1.39 GHz for θGB=16° and 2.0 GHz for θGB=45° measured at 16 K. The Ic−B pattern of the BGB junction with θGB=45° is distinct from the ideal Fraunhofer pattern, probably due to the inhomogeneous current distribution along the BGB; however, the junctions exhibit an Ic modulation of almost 100%, which corresponds to the fact that the BGB junction with θGB=45° exhibits the 100% RSJ current. The BGB junction with θGB=16° exhibits an Ic modulation of only 35% due to the excess current attributable to the FF current. Furthermore, both devices clearly show Shapiro steps with periodic current steps. The measured step voltage heights of 2.9 μV for θGB=16° and 4.1 μV for θGB=45° are consistent with the Josephson relation VRF=nhfRF/2e, where fRF is the frequency of the applied microwaves.
Atomic structures of BGBs
Here we examined the microstructure and the local chemical composition deviation of the BGBs to check the effect of an impurity phase on the weak-link junction behaviours. Figure 3a–c show plan-view high-resolution transmission electron microscope (HR-TEM) images of the BaFe2As2:Co BGB junctions with θGB=4°, 24° and 45°, respectively. The -axes of BaFe2As2:Co are indicated by the arrows. Symmetrically tilted junctions were formed in almost the entire region of the BGBs for all of the junctions. In the BGB junctions with θGB=4° and 24°, periodic misfit dislocations at intervals of ∼5.0 nm for θGB=4° and 1.2 nm for θGB=24° are clearly observed along the BGBs. On the other hand, the BGB with θGB=45° has blurred lattice fringes across the entire region. Using a geometric tilted boundary model, the grain boundary dislocation spacing D is given by D=(|b|/2)/sin(θGB/2), where |b| is the norm of the corresponding Burgers vector3. With the lattice constant a=0.396 nm of BaFe2As2 (ref. 30), D is estimated to be 5.7 and 1.0 nm for θGB=4° and 24°, respectively. The estimated D values are very similar to the D values observed above. For θGB=45°, the D value is estimated to be 0.5 nm. This value is almost the same as the lattice parameter; therefore, we cannot observe periodic misfit dislocations in the BGB with θGB=45° in Figure 3c. Energy dispersive spectroscopy line spectra across the BGBs and parallel to the BGBs confirmed that the chemical compositions of the BGBs and the film region are homogeneous, and no secondary phase was observed in the BGB regions.
Next, we discuss the relationship between θc and the BGB dislocation spacing D observed by TEM. For the BaFe2As2:Co BGB junctions, the observed critical angles θc are ∼9°, which correspond to a D value of approximately 2.8 nm. This is comparable with or slightly larger than the coherence length ξab(T) of 2.6 nm at 4 K estimated from the reported ξab(0 K)=2.4 nm for BaFe2As2:Co (ref. 19). The above relationship supports the notion that strong current channels still remain between the dislocations when θGB is below θc, whereas coherent superconducting current cannot pass through the BGBs at θGB>θc and behaves like a weak link.
Note that there would be other factors that affect the GB transport properties. For instance, the dislocation cores formed along BGBs can produce residual strains, which have been considered to have one of the major roles in current blocking at BGBs of cuprates31,32. This possibility would help us to obtain a more informative insight into the weak-link behaviour in iron pnictide superconductors; however, further microstructure and strain analyses are necessary to evaluate the strain field and discuss their effects.
In-field characteristics of BGB junctions
To investigate the weak-link behaviour in a B, JcBGB(B) values for the BGB junctions withθGB=3°–45° were measured at B up to 9 T applied parallel to the c-axis. Figure 4a shows the JcBGB(B) curves measured at 4 K, and the inset figure shows a magnified view in the low B region up to 0.2 T. The JcGrain measured for the Grain bridge on the 3° MgO bicrystal substrate is also plotted by the black squares. For the BGB junctions with θGB=3° and 4°, the JcBGB(B) values are almost indistinguishable from those of the JcGrain(B) curves, and a reduction in JcBGB is not observed. The other BGB junctions with larger θGB show more rapid decreases than those of the JcGrain(B), even in a low magnetic field. The JcBGB(B) of the BGB junctions with large θGB=24° and 45° decrease sharply to 2 and 0.8% of the JcGrain(B) on the application of 0.1 T. For the BGB junctions with θGB=8° and 11°, the JcBGB(B) curves show an intermediate behaviour between the strongly linked and weakly linked states, where the rapid decrease in JcBGB(B) at < 1 T can be attributed to the weak pinning force of the flux trapped at the dislocation cores despite the existence of strong channels with almost the same width as the coherence length ξab(T).
Metallic nature of high-angle BGB junctions
The temperature dependence of JcBGB (JcBGB(T)) provides more information about the nature of the barriers formed in BGBs. In general, Jc of a superconductor–normal metal–superconductor junction follows a quadratic temperature dependence. On the other hand, a superconductor–insulator– superconductor junction shows a linear dependence on T. Figure 4b shows the JcBGB(T) from Tc down to 4 K for BGB junctions with high θGB=16°–45°. All of the JcBGB(T) curves of the BaFe2As2:Co BGB junctions show a quadratic temperature dependence as described by Ic=I0(1−T/Tc)2 κd/sinh(κd), which is the de Gennes' theory based on a conventional proximity effect in the dirty limit33. This relation is indicated by the orange lines in the figure, where d is the barrier thickness and κ−1 is the decay length for normal metal. In particular, the BGB junctions with θGB=30° and 45° have this quadratic relationship with temperature, which is more clearly confirmed in the Jc−(1−T/Tc)2 plots in the inset figure. For the BGB junctions with θGB=16° and 24°, JcBGB(T) deviates downward from the quadratic dependence and assumes a linear relation at temperatures lower than 10 and 8 K, respectively. This result can be explained by the long-junction limit with w/λJ>4 because the critical currents become so large that the Josephson penetration depth λJ becomes smaller than the junction width w. The dependencies of the JcBGB(T) curves of the BaFe2As2:Co BGB junctions are distinctly different from those reported for the YBCO BGB junctions because the latter closely follow the linear relation α(1−T/Tc) over a wide temperature range below Tc (ref. 34).
The doubly larger θc and the much gentler slope decay than those of YBCO BGB junctions make it easier to produce high Jc BaFe2As2:Co superconducting tapes because the formation of a buffer layer with Δφ≤9° is much easier than those used for the cuprates, which require much smaller Δφ of <5°, but such buffer layers have been achieved only by a few groups using an extra MgO or CeO2 buffer layers35,36. Therefore, the large θc allows us to use a simpler and lower cost production process of superconducting tapes, and the iron pnictide superconducting tapes would find practical applications under a higher magnetic field, if further improvement in Jc will be achieved.
The powder-in-tube technique has been rather progressing as an alternative technology for superconducting wires also in iron pnictides37; however, their Jc values still remains at ∼104 A/cm2 (ref. 38) due probably to existence of large angle GBs with θGB much greater than θc=9°. The grain boundary issue in iron pnicides will be largely relaxed by the present finding. Actually, we recently succeeded in obtaining high transport Jc=3.5 MA cm−2 with a BaFe2As2:Co-biaxially textured thin film on a polycrystalline Hastelloy tape with an ion-beam-assisted deposition-MgO-textured buffer layer25.
In conclusion, we fabricated high-quality BaFe2As2:Co films with large JcGrain on bicrystal substrates with the entire range of θGB=3–45° and comprehensively examined the grain boundary nature of the iron pnictide. The primary point clarified by the present study is that the BaFe2As2:Co BGB junctions exhibit a large θc of ∼9°. The low-angle BGBs with θGB≤9° consist of long-period dislocation cores and, therefore, JcBGB is similar to JcGrain; whereas the high-angle BGBs show a weak-link behaviour with a gradual decay of JcBGB(θGB) expressed by the exponential equation of 2.8×106exp(−θGB/9.0°). Such grain boundary natures together with the high Bc2(0) make the iron pnictides to be more promising materials for application to high Jc superconducting tapes.
BaFe2As2:Co epitaxial films on bicrystal substrates
BaFe2As2:Co epitaxial films were fabricated by PLD on -tilt bicrystal substrates of MgO with θGB=3°–45° and also of LSAT with θGB=5°–45°. A Nd:YAG laser (wavelength: 532 nm, INDI-40, Spectra-Physics) typically used for epitaxial growth of iron pnictide films13,39 with a repetition rate of 10 Hz on the PLD target of a high-purity BaFe1.84Co0.16As2 polycrystalline disk was used as the excitation source16. Films with 250–350 nm in thickness were grown at a temperature of 850 °C and the thickness of each film was measured precisely with a surface profiler. The base pressure in our PLD chamber was ≤1×10−6 Pa, and film deposition was carried out in a vacuum at approximately 10−5 Pa. The BaFe2As2:Co epitaxial films grown under these conditions showed high Jc values of 1–4 MA cm−2 at 4 K, which were confirmed by I–V characteristic measurements with a 1-μV cm−1 criterion17.
Transport properties through BGB
The BaFe2As2:Co films were patterned using photolithography and Ar-ion milling into 300-μm-long and 8-μm-wide micro-bridge structures (Fig. 1a) to perform 4-terminal I–V measurements of the JcBGB across the BGB and of the JcGrain not across the BGB and under magnetic fields perpendicular to the film surface. The critical current (Ic) and the asymptotic junction resistance (RNA) were estimated from the I–V characteristics28.
Microstructure and chemical composition analysis of BGB
The microstructures around the BGBs were examined by plan-view HR-TEM. The TEM samples were prepared by a focused-ion-beam micro-sampling technique in which the area near the BGBs was mechanically cutout, and that area was only thinned by focused-ion-beam technique. All of the operations were performed in a high-vacuum chamber. The chemical composition of the bulk film and the BGBs was analysed by energy dispersive X-ray spectroscopy with a spatial resolution of approximately 1 nm.
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This work was supported by the Japan Society for the Promotion of Science, Japan, through the 'Funding Program for World-Leading Innovative R&D on Science and Technology Program'.
The authors declare no competing financial interests.
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Katase, T., Ishimaru, Y., Tsukamoto, A. et al. Advantageous grain boundaries in iron pnictide superconductors. Nat Commun 2, 409 (2011). https://doi.org/10.1038/ncomms1419
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