Optimal Vortex Pinning in YBa 2 Cu 3 O 7-x Superconducting Films Up to Very High Magnetic Fields

The magnetic ux pinning capabilities of YBa 2 Cu 3 O 7−x (YBCO) coated conductors (CCs) vary strongly between different regions of the magnetic eld-temperature (H-T) diagram and with the orientation of the magnetic eld (θ). Here, we determine the optimal pinning landscape for a given H-T region by investigating the critical current density J c (H,θ,T) in the 5-77 K temperature range, from self-eld to very high magnetic elds (35 T). Our systematic analysis reveals the best directions to target to articially engineer CCs in any region of interest. In solution-derived nanocomposites, we identify the relevance of coexisting high amounts of short stacking faults, Cu-O vacancy clusters and segmentation of twin boundaries, in combination with nanoparticles, for enhanced pinning performance at very high magnetic elds and low temperatures. Moreover, we demonstrate that twin boundaries preserve a high pinning energy in thick YBCO lms, which is benecial for the pinning performance at high magnetic elds and high temperatures. to identify relevant vortex pinning contributions in the widest possible range of the H-T diagram of YBCO, with special focus on very high magnetic elds. To do so, we analyse lms that display a manifold microstructure, which we achieved with the versatile chemical solution deposition (CSD) technique to grow nanostructured superconducting nanocomposites. Our analysis involves a thorough evaluation of over very broad range of temperatures (5-77 K) and applied magnetic elds (0-35 T), combined with detailed microstructural investigations by scanning transmission electron microscopy (STEM) and x-ray diffraction (XRD).


Introduction
The successful development of suitable methods to grow epitaxial REBa 2 Cu 3 O 7−x (REBCO, RE = Rare Earth) lms on top of bi-axially textured substrates following a multi-layered architecture (i.e., coated conductors/CCs), opened the way to promote practical and scalable conductors for power applications at high magnetic elds and temperatures [1][2][3][4][5][6] . Among investigated superconductors, the REBCO superconductors do not exhibit either the highest critical temperature T c or upper critical magnetic eld H c2 . However, they do provide the highest irreversibility line H irr (see gure S1 in the supplementary information for YBCO). Therefore, besides being suitable for power cables and fault current limiters at low magnetic elds and high temperatures 7 , REBCO CCs have been included in the design and fabrication of new coil architectures for high magnetic eld applications such as research magnets 8-12 , NMR/MRI magnets 13 , magnets for fusion energy [14][15][16] , and high energy physics accelerator magnets 17 . They are excellent candidates not only for superconducting large currents in high eld magnets at very low temperatures, but also in the intermediate magnetic elds generated in rotating machines 18 or superconducting magnetic energy storage systems 19,20 at temperatures in the range of 20-50 K, which can be effectively driven by cryocoolers 21 .
At present, the magnetic eld -temperature (H-T) ranges attainable with REBCO CCs are much wider than the ones obtained using any other existing superconducting material. However, the intrinsic limit of the dissipation-free current, i.e., the critical current density J c , shows a strong variation in different regions of the H-T diagram and with the orientation of the magnetic eld θ. Such variations are determined by the different vortex pinning contributions that arise in each microstructure and lead to different phases of the vortex lattice 22−25 . A quest for an adequate microstructure that favours vortex pinning and enhances J c has been ongoing for the last decades, motivating the search for new nanoengineering approaches aimed at tuning the REBCO defect landscape with additional pinning centres 4,5,26−32 .
Vortex pinning investigations based on the correlation between the electrical transport and microstructural visualization techniques enabled the evaluation of how each type of defect affects J c enhancement. Nanoparticles 16,27,33−36 improved the in-eld J c at all magnetic eld orientations at any temperature and in some cases self-eld (sf) J c . The presence of random point defects 37,38 also improved the ineld J c , especially at temperatures below 40 K. Secondary phase nanorods/nanocolumns 29,39,40 or irradiated columnar defects 26,31 enhanced J c mainly when H is parallel to the c-axis (H||c), especially at high magnetic elds and high temperatures; the same occured for natural defects such as twin boundaries 41,42 and dislocations 43,44 . Lately, hybrid nanostructures combining various defects [45][46][47][48][49][50] have also been investigated, with the aim of merging gains. However, only a few studies cover large magnetic eld and temperature ranges 6,51−53 .
In this article, we offer a broad study so as to determine the optimal microstructure for speci c H-T conditions. We aim to identify relevant vortex pinning contributions in the widest possible range of the H-T diagram of YBCO, with special focus on very high magnetic elds. To do so, we analyse lms that display a manifold microstructure, which we achieved with the versatile chemical solution deposition (CSD) technique used to grow nanostructured superconducting nanocomposites. Our analysis involves a thorough evaluation of J c (H,θ,T) over a very broad range of temperatures (5-77 K) and applied magnetic elds (0-35 T), combined with detailed microstructural investigations by scanning transmission electron microscopy (STEM) and x-ray diffraction (XRD).

Results
The epitaxial solution-deposited YBCO lms we study in this work are ranging in thickness from 100 nm to 1 µm. These have been grown by CSD with various precursor solutions: pristine YBCO, YBCO with additives for spontaneous segregation of nanoparticles (ssnanocomposites), and YBCO with preformed nanoparticles (pn-nanocomposites). We grew samples with distinctive amounts of nanoparticles (0%-12% mol) and diverse processing conditions (i.e., lm deposition, heating ramp), yielding to very different defect landscapes [54][55][56] ; all lms have an oxygen doping state close to optimal doping, deduced from the temperature evaluation of the normalized resistivity 57 .
Here, we consider the identi cation of defect contributions according to angular pinning performance and the associated pinning strength, as described previously 58 . As explained in detail in gure S2, in CSD YBCO we nd, typically, isotropic defects (0D and 3D) such as copperoxygen vacancy clusters 38,59 , small nanoparticles, or nanostrain generated in partial dislocations surrounding the stacking faults 35 . On the other hand, we observe planar anisotropic defects such as stacking faults parallel to the a-b planes 60 or twin boundaries parallel to the caxis 61,42 . Regarding the associated pinning strength, point defects (i.e., oxygen and copper vacancies) are considered weak pinning centres, whereas nanoparticles, nanostrain, stacking faults and twin boundaries are considered strong pinning centres. Additionally, strong anisotropic intrinsic pinning 62 , originated in the layered structure of the YBCO itself, coexists with stacking fault pinning for H parallel to the a-b planes (H||ab) 63,64 .
We present our results in three sections: in section 2.a, we evaluate the pinning performance in the H-T region 0-9 T and 5-77 K for pristine YBCO and a large batch of YBCO nanocomposites, distinguishing different pinning regimes for H||c and H||ab; in sections 2.b and 2.c we evaluate for H||c the density, strength and energy scale of the pinning centres up to 9 T and to 35 T, respectively, in a group of samples possessing very disparate microstructures.
a. Pinning regimes up to 9 T in the H-T phase diagram We obtained accurate surfaces of J c (H,T) for the main orientations of the magnetic eld H||c and H||ab for pristine and nanocomposite lms, as shown in gure 1. This was achieved by measuring J c (H) curves at 5, 20, 50, 65 and 77 K, linearly interpolating, and subsequently tting the curves as a function of temperature considering both the weak and strong pinning contributions of J c (T) (i.e., J c wk (T) and J c str (T), respectively). Whereas weak pinning centres yield a fast temperature decay of the J c in the collective pinning model 65 , strong pinning centres account for a smoother temperature decay in the Bose glass model 24  where J c (0) wk and J c (0) str refer to contributions at 0 K, whereas T 0 and T* refer to temperatures associated to the characteristic vortex pinning energy of weak and strong defects, respectively. The nal temperature interpolation is explained in detail in gure S3.
For the nanocomposite, the 3D J c (H,T) representation illustrates an enlargement of the (reddish) high critical current density region (> 1 MA/cm 2 ) at low temperatures and low magnetic elds; the appealing region for high-current applications. On the other hand, at high temperatures and high magnetic elds, a rapid decay of J c is visible at lower H-T values for H||c, but not for H||ab.
The enlargement of the reddish high J c (H,T) region is concurrent with the shift to larger magnetic elds of the µ 0 H*(T) curve, where µ 0 is the vacuum permeability and H* is the accommodation magnetic eld, which sets the limit between the single vortex pinning regimewhere vortices interact weakly with each other but strongly with defects 66,67 -and the vortex-vortex interaction regime. Therefore, H* is  suggesting that the origin of this enlargement is effective at any orientation and, therefore, is isotropic.
In order to separate the isotropic (J c iso ) and anisotropic (J c aniso ) contributions of the J c (H) curves shown in gure 1 we applied the Blatter scaling approach 28,69 to angular J c (θ) measurements at temperatures of 5, 20, 50, 65 and 77 K, and applied magnetic elds of 0.1, 0.3, 0.5, 1, 3, 5, 7 and 9 T. Subsequently, we tted their temperature dependence through the procedure explained in the supplementary information ( gure S3), aiming to establish the weight of each contribution within the full range of the H-T diagram.
We, thus, obtained the colour maps presented in gure 3, which show the ratio J c iso /J c in the H-T diagram (equivalent to 1-J c aniso /J c by assuming a no interaction approximation), identifying regions of pinning dominance. For H||c we observe that the dominance of isotropic pinning is enhanced for the nanocomposite in both temperature and magnetic eld, leaving the region dominated by anisotropic pinning close to the irreversibility line. For H||ab, the dominance of isotropic pinning is also shifted to larger magnetic elds of the order of 1 T, especially at low temperatures.
It is worth noting that the µ 0 H*(T) curves fall inside the region mostly dominated by isotropic pinning, in agreement with an increase of H* related to the increase of isotropic pinning centres in nanocomposites. In contrast, we observe a slight decrease of H irr (T) for the nanocomposite, especially at H||c, which can be associated to a lower pinning performance of the anisotropic defects (mainly twin boundaries 42 ).
To elucidate the origin of the variation between the isotropic and anisotropic pinning contributions, let us consider the correlation between the increase of H* and the isotropic nanostrain; the nanostrain arises in the region surrounding the partial dislocations that envelope the stacking faults (see gure S2(c,d)), and it has been signalled as a characteristic defect emerging in large quantities in nanocomposites 35 .
Hence, we macroscopically measured the nanostrain (ε) for each sample by XRD analysis, following the Williamson-Hall method 70 . Figure 4(a-f) shows the above-mentioned correlation between the H* accomodation magnetic eld (measured at 5, 50 and 77 K for both H||c and H||ab) and nanostrain for a very broad variety of samples. Although the results do not fall exactly on a single curve, we observe a common trend of the exponential increase of H* when ε increases; this is clear at all temperatures and orientations of the magnetic eld considered. This correlation explains the importance of the isotropic nanostrain but, based on the deviations from the trend, it also reveals that this cannot be strictly distinguished as the unique cause of the enlargement of H*. Small nanoparticles able to pin vortices by themselves might well be an additional contribution of this enlargement.
Further, we analysed the widening of the J c aniso (θ) ab-peak; we approximated its half width-half-maximum with the trapping angle θ T that limits the vortex staircase regime 63,71 (θ T calculation presented in gure S4), which in this case can be interpreted as an additional capability of accommodating vortices parallel to the ab-planes due to a higher presence of stacking faults. In Table 1 are shown the thickness, nanostrain, nanoparticle (NP) average diameter (<Ø NP >) and density (σ NP ), stacking fault (SF) average length (<d SF >) and density (λ SF ) and main electrical transport properties -T c , ΔT c (transition width), J c sf,77K and H irr 77K,H||c -of each of the samples we analysed.
All samples display T c > 88 K, ΔT c < 6 K, and J c sf,77K ≈ 2-4.5 MA/cm 2 . We evaluated H irr 77K,H||c from J c (H) measurements ful ling the relation J c (H irr )=10 −4 J c (sf). We inferred the NP and SF average densities from high-angle annular dark eld (HAADF) STEM images (see gure 5) using the formulae σ NP = n NP /A YBCO and λ SF = ∑ d SF /A YBCO , where n NP is the number of nanoparticles and A YBCO is the area of the image corresponding to the analysed YBCO lm. Table 1 Sample properties. Name, composition, thickness and main electrical and microstructural properties of the studied lms. pr: pristine, nc: nanocomposite, ss: spontaneous segregated nanoparticles, pn: preformed nanoparticles, n.m.: not measured. σ NP ranges: low (σ NP < 1E-4 nm −2 ), medium (1E-4 nm −2 < σ NP < 5E-4 nm −2 ), high (σ NP > 5E-4 nm −2 ). λ SF ranges: low (λ SF < 0.1 nm −1 ), medium (0.1 nm −1 < λ SF < 0.15 sizes of these defects. The ss-nc-thin-2 and pn-nc-thin lms show sign cantly shorter stacking faults than the rest of the lms; this indicates a larger presence of partial dislocations. Furthermore, the pn-nc-thin lm is characterized by very small nanoparticles with diameters of the same order of magnitude (2 or 3 times) as the superconducting coherence length at the measured temperature.
Anisotropic defects act only as strong pinning centres, whereas isotropic defects can be either point or nanosized defects, promoting both weak and strong pinning. Therefore, the total J c (T) can be described by the linear sum of three contributions: where the J c str contribution from equation (1) is substituted now by the sum of the isotropic-strong (iso-str) contribution J c iso−str and the anisotropic-strong (aniso-str) contribution J c aniso−str (corresponding directly to J c aniso ); the isotropic-weak (iso-wk) contribution J c iso−wk corresponds to the overall J c wk contribution. For the lms that were studied in this work, we considered that iso-wk is generally associated to atom/cluster vacancies, iso-str to nanostrained regions and nanoparticles, and aniso-str to twin boundaries for H||c. Regarding the nanoparticles, they become effective pinning centres when their diameter is su ciently small (below 8 nm) 36,56,72 . By tting equation (2) to the experimental results obtained at different magnetic elds, we determined the eld dependence of the tting parameters; these are the characteristic temperatures T 0 , T* iso−str, and T* aniso−str , and the contributions at 0 K J c (0) iso−wk , J c (0) iso−str , and J c (0) aniso−str . We note that the characteristic temperatures for each contribution are characterized by similar ranges regardless of the sample type, indicating that the same type of defects contribute in different samples. However, differences in size and/or precise morphology of the defects induce signi cant changes. The larger dispersion in the pinning energy values was obtained for T* aniso−str . In this case, much lower values are found for all nanocomposites (T* aniso−str ≈70-80 K at high elds) as compared with the pristine, which we associate to the segmentation of twin boundaries due to a large density of stacking faults 42,61 , also provoking a decrease of the irreversibility line H irr . In contrast, the pristine sample shows the highest T* aniso−str values and largest H irr (9.4 T at 77 K, see Table 1), indicative of coherent long twin boundaries. Another remarkable difference is the one obtained for T* iso−str , which also shows lower values for nanocomposites than for the pristine, suggesting a change in the nature of isotropic-strong pinning centres, in agreement with the introduction of nanoparticles and the abundant pinning provided by nanostrain in nanocomposites.
Regarding the 0 K contributions of J c , we also observe remarkable differences between nanocomposites and the pristine sample. In the case of iso-wk (see gure 6(d)), we observe that nanocomposites show an enhanced µ 0 H* iso−wk (0K), specially the pn-nc-thin, which is ascribed to a high density of Cu-O vacancy clusters hosted in the stacking faults 38, 59 . The best J c (0) iso−wk contribution is found for ss-nc-thin2, in agreement with a large number of Cu-O vacancies which are stronger in this sample (see T 0 in gure 6(a)). In the case of iso-str pinning in gure 6(c), nanocomposites exhibit altogether a distinguishable behaviour with respect to the pristine lm due to the nanostrain already mentioned in the previous subsection, resulting in enhanced J c (0) iso−str at any magnetic eld. In addition, nanoparticles that are su ciently small will also contribute to enhance iso-str pinning. Last, the aniso-str pinning in gure 6(b), mainly attributed to the pinning performance of twin boundaries, shows that pn-nc-thin and ss-nc-thin-2 lms excel at exhibiting the largest J c aniso−str values along the entire studied range, which is certainly related to a very high density of twin boundaries due to their segmentation and therefore multiplication provoked by the presence of a high density of short stacking faults as observed in these lms (see gure 5(d,e,g,h)). Therefore, we evidence that a high density of short stacking faults always coexists with a high density of twin boundaries, which however, produce a lower T* aniso−str due to the lack of vertical defect coherence. In contrast, at high temperatures and large magnetic elds, the nanocomposite presents a more prominent decay of J c associated with its lower irreversibility eld.
We observe in gure 8(a) that although the pn-nc-thin sample exhibits a fast J c (H) decay at 30K with lower J c values at very high elds, it shows the best performance at 4.2 K at the entire analysed magnetic eld range. A crossover between the J c values from pn-nc-thin and pr-thin-2 is expected to take place at a magnetic eld higher than 35 T. Such a crossover is on the other hand observed at 21 T for pn-ncthick.
At 30K, a desirable temperature for superconducting rotating machinery applications 18 refrigerated with cryocooler technology 21  Additionally, in the high magnetic eld facilities, we have been able to analyse the isothermal magnetic eld dependent current-voltage characteristics for four different samples: pr-thin-2, pr-thick, pn-nc-thin and pn-nc-thick, whose F p (H) curves are plotted in gure 9. In these plots, we focus at three H- dependence of the characteristic temperatures T 0 , T* iso−str and T* aniso−str and the J c contributions at 0 K, J c (0) iso−wk , J c (0) iso−str and J c (0) aniso−str , in gure 10. Interestingly, gure 10(a) shows that T 0 tends to slightly increase, whereas both T* iso−str and T* aniso−str tend to decrease with increasing magnetic eld. The performance at 30-50 K in very high magnetic elds is therefore very much in uenced by the pinning characteristic temperatures.
The analysis of the pinning contributions extrapolated to 0 K shows in general larger J c (0) for pn-nanocomposites than for pristine samples ( gures 10(b-d)), which makes nanocomposites very appealing for the application of superconducting lms at helium temperature. The pn-nc-thin sample exhibits the largest values of iso-weak pinning due to the already mentioned Cu-O vacancies, and very large iso-str pinning up to 25 T due to the large density of nanostrained regions surrounding the short stacking faults and very likely due to the small BHO nanoparticles, and also a large aniso-str pinning due to the high density of segmented twin boundaries. Altogether, it makes pn-nc-thin the best sample to afford a pinning force density of 0.55 TN/m 2 at [4.2K,35T]. However, the low T* iso−str and especially the low T* aniso−str possessed by this thin pn-nanocomposite plotted in gure 10(a) cause a strong J c (H) decay at higher temperatures, as already observed in gures 7-9.
On the other hand, the thick pn-nanocomposite exhibits higher T* iso−str and T* aniso−str ( gure 10(a)) than the thin pn-nanocomposite and ss-nanocomposites ( gure 6(a)). Actually, this T* iso−str coincides with that for the pristine samples (note that the different thin pristine  8(b)), the total pinning force strongly improves and therefore it is strongly recommended to take steps forward in the direction of gaining thickness.
Finally, the study of current-voltage curves at very high magnetic elds has been extended at magnetic orientations different to H||c at the temperature of 20 K, covering an angular range of 180° centred at H||ab for the magnetic elds of 15, 25 and 35 T. Results are plotted in gure 11(a) for pr-thin-2, pn-nc-thin and pn-nc-thick. It is observed that the ab-peak is widened for nanocomposites, in agreement with a larger θ T to accommodate vortices by stacking faults. Below the crossover magnetic eld of about 20 T, where J c values of nanocomposites fall below the ones of pristine lms (in gure 8(a) at 30 K), nanocomposites offer higher performance throughout the angular range. In contrast, above 20 T, the pristine lm starts to exhibit larger J c than nanocomposites in the vicinity of H||c, where an intricate competition takes place between the three contributions (iso-wk, iso-str and aniso-str) since T 0 , T* iso−str and T* aniso−str get closer at very high magnetic elds (see gure 10(a)). Notice in gure 11(b), that the collapses of J c iso are obtained for effective anisotropies (γ eff ) of 6, 2.5 and 2 for pr-thin-2, pn-nc-thin and pn-nc-thick respectively, which are the same values that were obtained at lower magnetic elds. Thus, con rming that γ eff remains constant at very high magnetic elds and that the effective anisotropy of the nanocomposite lms is certainly approaching very low values, making them very appealing for high eld magnets where the isotropic characteristics of CC are a strong demand.

Discussion
The thorough study undertaken at wide temperature and magnetic eld ranges up to 35 T has demonstrated that the performance of solution-derived nanocomposites is excellent at very high magnetic elds and very low temperatures. However, at temperatures above 20 K, there is a crossover of J c values in nanocomposites with respect to the pristine lms. This suggests that additional pinning centres should be induced at these conditions to overcome the existing performances of pristine CSD lms, as for example a reinforcement of the density of small nanoparticles which can act as pinning centres themselves. The pinning characteristics observed in CSD lms are specially ascribed to the shape, density and length of the most extended defect in these lms, i.e. the stacking fault. In particular, from the analysis elaborated here we conclude that stacking faults in solution-derived YBCO nanocomposites have a triple effect in the pinning contributions for H||c: They increase the isotropic-strong contribution by means of increasing J c (0) iso-str due to the generation of isotropic nanosized strain regions located at the partial dislocations surrounding the stacking faults. This increase is very effective at low-intermediate magnetic elds and intermediate temperatures and is responsible for the general enlargement of the single vortex pinning regime de ned by the increase of µ 0 H*.
They increase the isotropic-weak contribution by means of increasing J c (0) iso-wk due to the formation of Cu-O vacancy clusters among stacking faults. This increase is very effective at low temperatures.
They increase the anisotropic-strong contribution by means of increasing J c (0) aniso-str due to the multiplication of twin boundaries given by the segmentation provoked by the appearance of stacking faults. The increase of J c (0) aniso-str is very effective at low temperatures up to very high magnetic elds. However, the segmentation of twin boundaries causes in parallel a breaking of their vertical coherence, which yields a reduction of the pinning energy T* aniso-str and therefore a decrease of the irreversibility line µ 0 H irr (T), which can be recovered in the case of thick nanocomposites.
Therefore, the intensity of each change in any of the pinning contributions will strongly depend on the precise distribution and size of the stacking faults present in each sample. To summarize, we propose general optimized defect landscapes to enhance pinning at distinctive H-T regions for H||c, depicted in gure 12: At low T and from low to very high H: a large density of isotropic defects (e.g., Cu-O vacancies, nanostrain and small nanoparticles) and anisotropic defects (e.g., segmented twin boundaries), no matter their length in defect coherence. Therefore, a landscape possessing large density of short stacking faults and small nanoparticles is very appropriate.

Conclusions
Overall, the analysis presented here demonstrates the capacity to arti cially modify the pinning landscape with solution-derived nanocomposites due to the bene ts of adding small nanoparticles and the relevance of stacking faults and their secondary effects (generation of strained nanoregions, generation of Cu-O vacancy clusters and segmentation of twin boundaries). Furthermore, this study urges the manufacturers to fabricate customized coated conductors for different applications depending on their magnetic eld and temperature operation range. Whereas the generation of a mixed landscape with plentiful kinds of defects of short length is desirable for enhancing pinning at low temperatures, the presence of strong elongated defects with long defect coherence in combination with other auxiliary defects is preferable for pinning at higher temperatures, and defects with even longer defect coherence in the case of very high magnetic elds.

Methods
YBCO lm growth. Epitaxial c-axis oriented YBCO lms were grown by chemical solution deposition from metal organic decomposition of tri uoroacetate (TFA) salts in solution following previous works [75][76][77] . The solution was deposited on 5 x 5 mm LaAlO 3 single crystal substrates whether by spin coating for thin lms (150-250 nm) or by inkjet printing for thick lms (> 600 nm) 78,79 . Subsequently, lms were pyrolized and thermal treated at high temperatures. All lms in Table 1 have been grown following a conventional thermal annealing (25°C/min heating ramp) 77 , except the pn-nc-thin sample, which followed a ash heating process (1200°C/min heating ramp) 80 .
Nanocomposites were obtained by promoting the formation of nanoparticles in the YBCO matrix, whether by including the salts directly to the solution leading to spontaneous segregation during growth (ss-nanocomposites) 28,35 or by the mixing of a previously stabilized colloidal solution containing preformed nanoparticles with the TFA precursor solution (pn-nanocomposites) 55 Electric transport measurements. Current-voltage (I-V) curves were obtained using the standard four-point method. Silver contacts were sputtered on YBCO with a TSST sputtering system and were post-annealed, ensuring contact resistivities below 10 µΩ·cm 2 . Samples were trimmed into 10-100 µm narrow bridges with lengths of 200-400 µm by standard lithography with a Micro-Writer from Durham Magneto Optics LTD and wet etching in H 3 PO 4 . The current was applied parallel to the a-b plane, always perpendicularly to the magnetic eld which was rotated with the angle θ from the c-axis (0°) to the ab-plane (90°), ensuring maximum Lorentz force con guration. Critical currents were determined for a 10 µV/cm electric eld. The I-V characteristics up to 9 T were conducted in a Quantum Design PPMS 9 T system, whereas the experiments carried out up to 35 T were conducted in a cryostat inside of a 35 T DC resistive magnet (32 mm bore) using a tight-vacuum probe provided with a rotating sample holder (see gure S6 in the supplementary information) and a temperature control system operating in the 4.2-60 K range.
Microstructural characterisation. Nanostrain (ε) was quanti ed along the c-axis by analysing the symmetric (00l) 2ϴ Bragg diffraction integral breadth acquired in a Siemens D5000 diffractometer using Cu K α radiation. Following the Williamson-Hall method 70 , ε was obtained following the equation: β 2 cos 2 (ϑ) = λ α1 L ⊥ + 16ϵ 2 sin 2 (ϑ), where β and ϑ are respectively the integrated breadth and the position of the (00l) YBCO Bragg peaks after the subtraction of the contribution from the instrument. λ α1 is the wavelength of the Cu K α1 radiation and L ⊥ is the coherent volume size perpendicular to the scattering vector. The scanning transmission electron microscopy observations were performed using an FEI Titan 60-300 kV microscope operated in STEM mode at 300kV, which is equipped with an X-FEG gun, a CESCOR Cs-probe corrector, a Gatan energy lter TRIDIEM 866 ERS and a monochromator.

Data availability
The data that support the ndings of this study are available from the corresponding authors on reasonable request.          J c (H) and I c (H) at very high magnetic elds. Magnetic eld dependence for H||c of (a) J c at 4.2 K (blue region) and 30 K (red region) for prthin-2, pr-thick, pn-nc-thin and pn-nc-thick samples and of (b) I c at 4.2 K for pr-thin-2, pr-thick and pn-nc-thick samples.

Figure 9
Pinning force densities at very high magnetic elds. Magnetic eld dependence of F P for H||c from 6 T up to 35   Characteristic temperatures and J c contributions at 0 K at very high magnetic elds. Magnetic eld dependence of characteristic temperatures (a) T 0 (solid lines), T* iso-str (solid lines) and T* aniso-str (dashed lines), and J c contributions at 0 K (b) J c aniso-str , (c) J c iso-str and (d) Jc iso-wk for pr-thin-1, pr-thin-2, pr-thick, pn-nc-thin and pn-nc-thick samples for H||c at very high magnetic elds.

Supplementary Files
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