High-field transport properties of a P-doped BaFe2As2 film on technical substrate

High temperature (high-Tc) superconductors like cuprates have superior critical current properties in magnetic fields over other superconductors. However, superconducting wires for high-field-magnet applications are still dominated by low-Tc Nb3Sn due probably to cost and processing issues. The recent discovery of a second class of high-Tc materials, Fe-based superconductors, may provide another option for high-field-magnet wires. In particular, AEFe2As2 (AE: Alkali earth elements, AE-122) is one of the best candidates for high-field-magnet applications because of its high upper critical field, Hc2, moderate Hc2 anisotropy, and intermediate Tc. Here we report on in-field transport properties of P-doped BaFe2As2 (Ba-122) thin films grown on technical substrates by pulsed laser deposition. The P-doped Ba-122 coated conductor exceeds a transport Jc of 105 A/cm2 at 15 T for main crystallographic directions of the applied field, which is favourable for practical applications. Our P-doped Ba-122 coated conductors show a superior in-field Jc over MgB2 and NbTi, and a comparable level to Nb3Sn above 20 T. By analysing the E − J curves for determining Jc, a non-Ohmic linear differential signature is observed at low field due to flux flow along the grain boundaries. However, grain boundaries work as flux pinning centres as demonstrated by the pinning force analysis.

reported for FBS 6 . Whereas in the former case Fe is incorporated interstitially 14 , in the latter case the Fe may form Fe-containing particles or regions with differing P-content, both acting as pinning centres 6 . Furthermore, the high J c and low anisotropy P-doped Ba-122 thin films can be fabricated by tuning the processing conditions only, without any modification of the target material used in pulsed laser deposition (PLD) 15 .
The aforementioned advantages of P-doped Ba-122 are very suitable for high-field-magnet applications. Indeed, P-doped Ba-122 thin films on technical substrates have been demonstrated as FBS coated conductors 16,17 . To date, two kinds of technical substrates have been employed for FBS coated conductors: The cube-textured metal tapes with buffer layers (i.e., RABiTS) 18 and the Hastelloy tape on which biaxially textured buffer layers are prepared by ion-beam-assisted-deposition (IBAD) 19 .
In contrast to Fe(Se, Te) coated conductors 20,21 , transport properties of P-doped Ba-122 coated conductors in the presence of extremely high magnetic fields have not yet been reported. Here, we report on in-field transport properties of a P-doped Ba-122 thin film grown by PLD on metal substrate with biaxially textured MgO template (IBAD-MgO) in a wide range of temperature and DC magnetic field up to 35 T. We employ IBAD-MgO template with a relatively large in-plane full width at half maximum (FWHM) value (Δ φ MgO = 8°), since it has been demonstrated by x-ray diffraction (XRD) and transmission electron microscope (TEM) characterisations that the texture of MgO is transferred to the overlying P-doped Ba-122 film, generating dislocation networks 17 . Such dislocation networks enhance the vortex pinning in P-doped Ba-122 17 , since θ c is less than 9° 5 . Indeed, in-field J c properties of our P-doped Ba-122 on IBAD-MgO with Δ φ MgO = 8° were superior to those of the film on a template with Δ φ MgO = 4° 17 . A high density of threading dislocations is very effective for improving J c for H||c in a wide range of temperature and magnetic field even close to H irr . Despite the relatively large θ c of 6°-9° for Ba-122, J c of our P-doped Ba-122 coated conductor with sharp FWHM values of both in-plane, Δ φ Ba−122 = 5.7°, and out-of-plane misorientaion, Δ ω Ba−122 = 1.2° (see Supplemental Fig. S1) is limited by the GBs in the low field regime. However, at high field, it exceeds a transport J c of 10 5 A/cm 2 at 15 T for field applied in both main crystallographic directions. Our P-doped Ba-122 coated conductor sample shows superior in-field J c properties over MgB 2 and NbTi, and a comparable level to Nb 3 Sn above 20 T.

Results
Resistivity measurements. The normal-state resistivity ρ n (Fig. 1a) can be approximated by ρ n = ρ 0 + AT n with an exponent n-value of 1.28, ρ 0 = 3.32 × 10 −2 mΩ⋅ cm and A = 8.22 × 10 −5 mΩ⋅ cm/K 1.28 in the range of 30 < T < 150 K in accord with ref. 22. Shibauchi et al. have reported that the exponent n is unity at the quantum critical point (QCP) of the antiferromagnetic phase, where the maximum T c is observed at 33% of P content for bulk single crystals 23 . Based on those results, we infer that the P content of our Ba-122 thin film on IBAD-MgO is different from the optimal level. Chemical analysis by electron probe microanalysis revealed a P content of 0.31, high enough to induce superconductivity with an onset T c of 30 K for Ba-122 single crystal 22    substrates induce in-plane tensile strain to Ba-122 films due to a large lattice mismatch 24,25 . The lattice parameters a and c of our P-doped Ba-122 coated conductors are located between the single crystals and thin films deposited on MgO single crystalline substrates (Fig. 1b). The crystalline quality of IBAD-MgO affects mainly Δ φ Ba122 rather than Δ ω Ba122

17
, changing the amount of the in-plane strain and hence T c . The linearity of the Arrhenius plots of ρ(T, H) for both major crystallographic directions at a certain magnetic field ( Fig. 2a and b) reveals thermally activated flux motion under the assumption of a linear T-dependence of the activation energy, U 0 (H) 26 (See the method section). It can be seen from Fig. 2c that U 0 (H) for both H||c and ||ab are well described by H α (1 − H/H * ) β above 10 T, which has been used for analysing polycrystalline MgB 2 samples by Thompson et al. 27 H * is a characteristic field representing the irreversibility field at 0 K 27,28 . The evaluated values for H||c and ||ab are 48.9 T and 59.7 T, respectively (for H||c and ||ab α = 0.68 and 0.64, and β = 1.1 and 0.94).
A linear fit for lnρ(H) versus U 0 (H) using lnρ 0 (H) = lnρ 0f + U 0 (H)/T c , where ρ 0f is the prefactor, yields T c of 26.9 K for H||c and 27.2 K for H||ab, respectively (see Supplemental Fig. S2a). The T c values evaluated by this method are slightly lower than the T c,90 (see Fig. 1a). A plausible explanation for this difference is the increased transition width Δ T c due to the reduced texture quality compared to films on single crystal substrates or single crystal samples.
H c2 (T) was evaluated from the linear presentations of Fig. 2a and b (see Supplementary Fig. S2b and S2c) applying a ρ n,0.9 = 0.9ρ n resistivity criterion, where ρ n,0.9 is the normal state resistivity ρ n at 28.5 K. Shown in Fig. 2d is H c2 for H||c and ||ab. The dotted line in Fig. 2d is the fitting curve using (1 − T/T c ) k . An exponent k of 0.9 was obtained for H||ab, which is far from the expected value of 0.5 for layered compounds limited by Pauli pair breaking at given T close to the dimensional crossover temperature [29][30][31] , which confirms that P-doped Ba-122 is a 3D superconductor. Because of the lack of low temperature data, it is not possible to fit the H c2 (T) (and H c2 (θ), shown later unambiguously) with a proper model for FBS 32,33 .
The temperature dependence of the irreversibility field, H irr (T) (Fig. 2e) was evaluated from ρ(T, H) measurements using a resistivity criterion of ρ c = E c /J c,100 = 1.0 −8 Ω⋅ cm, where E c is the electric field criterion (1 mV/cm) for determining J c from E − J measurements and J c,100 is the criterion (100 A/cm 2 ) for determining H irr from J c (H) measurements (see Supplementary Fig. S2d and S2e). The H irr data at 0 K are estimated from the Arrhenius plots and they appear to match the low temperature limit of the H irr data directly determined from the ρ(T, H) using The angular dependence of H c2 at 20 K, which was derived from ρ(H) curves at constant angles with ρ n,0.9 (Fig. 3a) shows a minimum at θ = 90° (H||c) and a maximum at θ = 180° (H||ab), as shown in Fig. 3b. The single-band anisotropic Ginzburg-Landau (AGL) theory 35 Fig. 3b), cannot describe the measured H c2 (θ) due to the multi-band nature of this material, similarly to Co-doped Ba-122 28 . A fairly good description of the data is, however, achieved by the empirical formulae 28 , with δ = 1.47 and γ = 1.62 (solid line). The parameter γ is the H c2 anisotropy, whereas δ is a measure for the ab-peak width whose physical meaning is still unclear. These two values will be used later for scaling the angular dependence of J c (θ) data. The angular dependence of H irr at 20 K derived using the same resistivity criterion ρ c = 1.0 −8 Ω⋅ cm shows almost the same trend as H c2 (θ). Unlike the angular dependence of J c (see next section), no clear peak at θ = 90° (H||c) is observed in H irr (θ).
In-field critical current density J c (T, H, θ). The E − J curves of the P-doped Ba-122 coated conductor sample at 4.2 K (Fig. 4) show different behaviour at high and low magnetic fields for both major field directions. Up to 10 T they exhibit a non-Ohmic linear differential (NOLD) signature (i.e., E is linearly changing with J in linear scale, see Supplemental Fig. S3), indicative of J c limitation by GBs 36 . Here NOLD behaviour is due to viscous flux flow along the GBs 37 . On the other hand, NOLD signature is almost absent above 12.5 T, suggesting that J c is limited by intra-grain depinning of flux lines. This pinning crossover field is observed to decrease with increasing temperature (not shown), which is consistent with the cuprate YBCO reported in refs 38,39. Pinning-improved YBCO 2nd-generation (2G) tape shows the highest J c at entire magnetic fields, however, a well textured template is necessary. The P-doped Ba-122 coated conductor exceeds a self-field J c of 4 MA/cm 2 and maintains a high J c value of 50 kA/cm 2 at 20 T. For the entire field range, J c of P-doped Ba-122 coated conductor sample is larger than for MgB 2 and NbTi. Above 20 T, the P-doped Ba-122 coated conductor sample shows comparable properties to Nb 3 Sn. Although lower-field J c of P-doped Ba-122 on IBAD-MgO is higher than that of Fe(Se, Te) on RABiTS, the latter shows the better performance at medium and high fields. By analysing the pinning force density F p = m 0 H × J c , information on vortex pinning can be obtained. In general, the normalised pinning force, f p = F p /F p,max , is plotted as a function of reduced field h 1 = H/H irr at a given temperature for high-T c superconductors. However, we plot f p as a function of h = H/H max , where H max is the field at which F p shows the maximum [46][47][48][49] , since J c could not be measured up to H irr at all temperatures. As can be seen in Fig. 5c, the f p curves at different temperatures for H||c almost fall onto a master curve in the range of 0 < h < 3 described by This formula is analogous to − h h (1 ) p q 1 1 (p = 0.5 and q = 2) found by Dew-Hughes 50 for pinning by planar defects such as GB and twin boundaries, and by Kramer for line defect arrays 51 . In high-T c superconductors with extremely short coherence lengths ξ, a further classification of the defect size with respect to ξ is necessary. It has been recently found by Paturi et al. that the exponent p is 0.5 irrespective of q for a defect size of the order of ξ and especially for dislocations in undoped YBCO films 49 . On the contrary, p increases towards 1 with increasing defect size. This confirms the finding that pinning in our sample is dominated by the dislocations with nano-size. Here, it should be noted that a sign of NOLD signature does not contradict GB pinning. In fact it has been reported for YBCO that the dislocations in GBs can work as vortex pinning centres 52,53 . The flux preferentially flows across the dislocation cores in the GB plane, which explains the E − J curves with a NOLD sign.
Abrikosov-Josephson vortices (AJV) are present in low-angle GBs in both YBCO 54 and FBS. Unlike Josephson vortices (JV), AJV have normal cores and can be trapped by flux pinning. Furthermore, the presence of an interaction between Abrikosov vortices (AV) in the grain and AJV at the GBs has been experimentally found in ref. 55: an increase in pinning potential for AV leads to the enhancement of the pinning potential for AJV.
For H||ab the f p curves at both 10 and 15 K follow well the GB pinning line (red solid line) up to 16 T (corresponding to h = 2 and 3.2 in Fig. 5d, respectively). In contrast, f p at 20 K neither follows the GB pinning nor point-like pinning (red solid and blue dashed lines, respectively) in high field regime, although the f p curve lies on the GB pinning line below h < 2. Similarly, the f p curve at 4.2 K follows the GB pinning curve up to h < 1.5 and then approaches the point-like pinning curve beyond h > 1.5. Hence, differently from the H||c case, the dominant pinning mechanism for H||ab is varying with temperature and field strength.
The angular dependence of the critical current density, J c (θ) (Fig. 6a-d), shows two distinct peaks: a relatively sharp peak at H||ab and a broad maximum at H||c, which arises from the network of threading dislocations comprising the low-angle GBs 17 . Surprisingly, the c-axis peaks [J c (90°)] remain visible even close to H irr at all temperatures. Unlike single band superconductors, the anisotropy of coherence length, γ ξ = ξ ab /ξ c , and penetration depth, γ λ = λ c /λ ab , of FBS exhibit opposite behaviour with temperature 56 . For an optimally doped Ba-122 system, γ λ > γ ξ holds at all temperature. In this case even occasional uncorrelated defects slightly larger than ξ yield a strong c-axis pinning 57 . Such an effect in combination with threading dislocations along the c-axis may enhance enormously the average pinning potential for applied fields parallel to the c-axis.
Shown in Fig. 6e is the scaling behaviour of J c (θ) as a function of the effective field [i.e.,  θ γ δ µ × H ( , , ) 0 ] at 20 K. Here δ = 1.47 and γ = 1.62 were used as obtained by the H c2 (θ) fit. As can be seen, all J c (θ) curves collapse onto a master curve in a wide angular range around H||ab. Differences between the master curve and the measured J c (H) for H||c are correlated pinning contributions. Here we emphasise that the J c peak at θ = 180° is fully determined by the electronic anisotropy at 20 K and no intrinsic pinning or pinning by planar defects is observed.

Discussions and Conclusions
In order to realise FBS coated conductors, high J c values with low anisotropy in high fields are necessary. J c of our P-doped Ba-122 coated conductor nearly reached the practical level of ~0.1 MA/cm 2 at 15 T for any applied field directions at 4.2 K [see Fig. 5a)], which shows superior properties over MgB 2 and NbTi. Above 20 T the level of J c is comparable to Nb 3 Sn. Additionally, the intrinsic anisotropy estimated at 20 K from the H c2 data is below 2. Moreover the correlated defects increase J c for H||c substantially suppressing the effective J c anisotropy.
As stated above, the inequality of ξ and λ anisotropy in combination with a large density of threading dislocations along the c-axis significantly enhances the average pinning potential. It is worth mentioning that the population of threading dislocations can be controlled by the processing conditions only, without any modification of the PLD target 15 . Compared to optimally P-doped Ba-122 films on MgO single crystal substrates by MBE 12 and PLD 15 , the level of J c of the P-doped Ba-122 coated conductor still needs to be improved. Film stoichiometry especially for P content should be controlled precisely. As stated before, the P content of our Ba-122 film slightly differs from the optimal level, where the QCP causes a sharp maximum for the vortex core energy 11 . As a consequence, the slight deviation from the optimal P level in our sample results in a lower vortex core energy, which directly reduces J c .
Unlike in electron and hole doped Ba-122 systems, aliovalent disorder that contributes to pinning in the Co or K cases is absent in P-doped Ba-122. However, J c can be further enhanced by introducing growth defects (e.g. intragrain dislocations since the PLD processing conditions strongly affect their density 15 ) and artificial structures (e.g. nanoparticles). Moreover the thermal conductivity of single crystalline MgO is different from that of IBAD-MgO template, which infers the optimum deposition temperature may change.
The introduction of artificial pinning centres is effective for further improvement of J c . In fact, Miura et al. have reported the introduction of BaZrO 3 into P-doped Ba-122 matrix 58 in analogy to the addition of BaZrO 3 to YBCO. Hence, a combination of the introduction of artificial pinning centres and the precise control of P content will yield better performing P-doped Ba-122 coated conductors.
An attempt to fabricate a long length P-doped Ba-122 coated conductor has started quite recently. As a result, a 15 cm long P-doped Ba-122 coated conductor has been realised by PLD using a reel-to-reel system 16 . Albeit the resultant P-doped Ba-122 showed a small self-field I c of 0.47 mA (corresponding to a J c of 4.7 × 10 4 A/cm 2 ) at 4.2 K, an improvement of I c is foreseen by applying the aforementioned methods.
In summary, we have investigated in-field transport properties of a P-doped Ba-122 thin film grown by PLD on technical substrate in a wide range of temperature and DC magnetic field up to 35 T. The P-doped Ba-122 coated conductor exceeds a transport J c of 10 5 A/cm 2 at 15 T for both major crystallographic directions of the applied field. Additionally, the J c peaks for H||c remain visible even close to H irr at all temperatures by the enhanced vortex pinning due to the combination of large population of threading dislocations and the inequality of ξ and λ anisotropy. This leads to a lower J c anisotropy. By analysing pinning force densities, we established that the GB pinning contribution is dominant for H||c, whereas for H||ab, the dominant pinning is varying with temperature. The results obtained through this study are considered promising for future high-field-magnet applications of AE-122 systems.  consists of first a planarising bottom bed-layer amorphous Y 2 O 3 on the Hastelloy, second a biaxially textured MgO layer formed by IBAD, and a top homoepitaxial MgO layer. The IBAD-MgO substrate with a large in-plane distribution angle of Δ φ MgO = 8° was investigated because higher J c with isotropic properties can be achieved compared to the film on the well in-plane-aligned IBAD-MgO metal-tapes (i.e., Δ φ MgO = 4°) 17 . A polycrystalline BaFe 2 (As 0.65 P 0.35 ) 2 disk was used as the PLD target. We employed a higher growth temperature of 1200 °C than for optimised P-doped Ba-122 films on MgO single-crystal substrates (1050 °C) 15 , since the P concentration increases with increasing growth temperature for a given target composition. As expected, a higher P concentration closer to the optimum P concentration than in previous studies was achieved 15,17 . The other growth parameters [e.g., the excitation source and the laser fluence of the second harmonics (wavelength: 532 nm) of a Nd-doped yttrium-aluminum-garnet pulsed laser and 3 J/cm 2 , respectively] were the same as reported in ref. 15.

Methods
To determine the crystalline phases, ω-coupled 2θ scan X-ray diffraction measurements were performed. The asymmetric 103 diffraction of the P-doped Ba-122 film was measured to confirm the in-plane crystallographic four-fold symmetry without in-plane rotational domains. The crystallinity of the film was characterised on the basis of the full widths at half maximum (FWHMs) of the out-of-plane 004 (Δ ω) and the in-plane 200 rocking curves (Δ φ). The results of those XRD measurements can be found in Supplementary Information Fig. S1. The chemical composition was determined with an electron-probe microanalyser. The acceleration voltage of the electron beam was optimised while monitoring the Ni Kα spectrum to avoid the matrix effect from the Ni-containing Hastelloy metal-tapes.
In-plane transport measurements. A small bridge of 15 mm width and 500 mm length was patterned by photolithography, followed by ion-beam etching. Au electrodes with 50 nm thickness were formed by sputtering and lift-off. Transport properties using the resultant bridge were measured by a standard four-probe method.
The temperature dependence of the resistivity of the P-doped Ba-122 coated conductor shows a T c,90 of 28.3 K (Fig. 1a), which is about 3 K lower than that of the optimally P-doped Ba-122 single crystals. T c,90 is defined as the intersection between the steepest slope of the superconducting transition and a 90% reduction of the fit of the normal state resistivity using ρ n = ρ 0 + AT n . On the other hand, the onset T c is defined as the intersection between the fit curve as stated above and the steepest slope of the superconducting transition. The difference between T c,90 and the onset T c is negligible.
The activation energy U 0 (H) for vortex motion was evaluated by the temperature dependence of the resistivity measurements in various field strengths up to DC 35 T at the National High Magnetic Field Laboratory, Tallahassee, FL, USA. According to the model of thermally activated flux flow 26 , the slope of linear fit yields the pinning potential for vortex motion at given fields (Fig. 2c). On the assumption that U(T, H) = U 0 (H)(1 − T/T c ), both equations, lnρ(T, H) = lnρ 0 (H) − U 0 (H)/T and lnρ 0 (H) = lnρ 0f + U 0 (H)/T c , are obtained, where ρ 0f is a prefactor.
In order to further understand the H c2 anisotropy for a P-doped Ba-122 coated conductor sample, the angular dependence of the magnetoresistivity was measured at 20 K. Using the same constant criterion ρ n,0.9 for evaluating H c2 , the angular dependent upper critical field [H c2 (θ)] was derived (Fig. 3b).
A criterion of 1 mV/cm was employed for evaluating J c . In J c measurement, the magnetic field was always applied in the maximum Lorentz force configuration. Low-field measurements were performed in a Quantum Design physical property measurement system (PPMS) in magnetic fields up to 16 T. For high field measurements up to DC 35 T, the experiments were conducted at the National High Magnetic Field Laboratory, Tallahassee, FL, USA.