Optimal Vortex Pinning in YBa2Cu3O7-x Superconducting Films Up to Very High Magnetic Fields

Optimal Vortex Pinning in YBa2Cu3O7-x Superconducting Films Up to Very High Magnetic Fields | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Optimal Vortex Pinning in YBa 2 Cu 3 O 7-x Superconducting Films Up to Very High Magnetic Fields Ferran Vallès, Anna Palau, Dmytro Abraimov, Jan Jaroszynski, Anca-Monia Constantinescu, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1138719/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Jul, 2022 Read the published version in Communications Materials → Version 1 posted You are reading this latest preprint version Abstract The magnetic flux pinning capabilities of YBa 2 Cu 3 O 7−x (YBCO) coated conductors (CCs) vary strongly between different regions of the magnetic field-temperature (H-T) diagram and with the orientation of the magnetic field (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-field to very high magnetic fields (35 T). Our systematic analysis reveals the best directions to target to artificially 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 fields and low temperatures. Moreover, we demonstrate that twin boundaries preserve a high pinning energy in thick YBCO films, which is beneficial for the pinning performance at high magnetic fields and high temperatures. Materials Theory and Modeling Electronic Materials and Devices coated conductors (CCs) magnetic flux twin boundaries YBCO films. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction The successful development of suitable methods to grow epitaxial REBa 2 Cu 3 O 7−x (REBCO, RE = Rare Earth) films 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 fields and temperatures 1 – 6 . Among investigated superconductors, the REBCO superconductors do not exhibit either the highest critical temperature T c or upper critical magnetic field H c2 . However, they do provide the highest irreversibility line H irr (see figure S1 in the supplementary information for YBCO). Therefore, besides being suitable for power cables and fault current limiters at low magnetic fields and high temperatures 7 , REBCO CCs have been included in the design and fabrication of new coil architectures for high magnetic field applications such as research magnets 8 – 12 , NMR/MRI magnets 13 , magnets for fusion energy 14 – 16 , and high energy physics accelerator magnets 17 . They are excellent candidates not only for superconducting large currents in high field magnets at very low temperatures, but also in the intermediate magnetic fields 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 field - 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 field 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-field J c at all magnetic field orientations at any temperature and in some cases self-field (sf) J c . The presence of random point defects 37 , 38 also improved the in-field 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 fields 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 – 50 have also been investigated, with the aim of merging gains. However, only a few studies cover large magnetic field and temperature ranges 6,51−53 . In this article, we offer a broad study so as to determine the optimal microstructure for specific 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 fields. To do so, we analyse films 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 fields (0-35 T), combined with detailed microstructural investigations by scanning transmission electron microscopy (STEM) and x-ray diffraction (XRD). 2. Results The epitaxial solution-deposited YBCO films 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 (ss-nanocomposites), and YBCO with preformed nanoparticles (pn-nanocomposites). We grew samples with distinctive amounts of nanoparticles (0%-12% mol) and diverse processing conditions (i.e., film deposition, heating ramp), yielding to very different defect landscapes 54 – 56 ; all films have an oxygen doping state close to optimal doping, deduced from the temperature evaluation of the normalized resistivity 57 . Here, we consider the identification of defect contributions according to angular pinning performance and the associated pinning strength, as described previously 58 . As explained in detail in figure S2 , in CSD YBCO we find, typically, isotropic defects (0D and 3D) such as copper-oxygen 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 c-axis 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 field H||c and H||ab for pristine and nanocomposite films, as shown in figure 1 . This was achieved by measuring J c (H) curves at 5, 20, 50, 65 and 77 K, linearly interpolating, and subsequently fitting 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 . In a first approximation and neglecting interactions between both types, we can describe J c (T) by the direct sum 28 : J c (T)=J c wk (T)+J c str (T)= J c (0) wk exp(-T/T 0 ) +J c (0) str exp(-3(T/T*) 2 ), (1) 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 final temperature interpolation is explained in detail in figure 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 fields; the appealing region for high-current applications. On the other hand, at high temperatures and high magnetic fields, 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 fields of the µ 0 H*(T) curve, where µ 0 is the vacuum permeability and H* is the accommodation magnetic field, which sets the limit between the single vortex pinning regime - where vortices interact weakly with each other but strongly with defects 66 , 67 - and the vortex-vortex interaction regime. Therefore, H* is related to the density of defects. Here, it is defined as in other works 58 , 68 by the equation J c (µ 0 H*) = 0.9J c (sf), where sf stands for self-field. Figure 2 shows a comparison between µ 0 H*(T) curves for several nanocomposites and a pristine sample, for both H||c and H||ab, highlighting the presence of the two regimes in the H-T diagram. In comparison to the pristine YBCO, all nanocomposites share the capability of enlarging the single vortex pinning regime up to high fields; this was observed for both magnetic field orientations, 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 figure 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 fields of 0.1, 0.3, 0.5, 1, 3, 5, 7 and 9 T. Subsequently, we fitted their temperature dependence through the procedure explained in the supplementary information ( figure 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 figure 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 field, 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 fields 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 figure 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 field (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 field 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 figure 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. Figure 4 (g-i) presents θ T versus µ 0 H* for J c (θ) curves measured at a field of 9 T and temperatures of 77, 50 and 5 K, and for J c (H) curves measured for both H*||c and H*||ab. The linear trend of the θ T (H*) combined with the exponential trend of H*(ε) indicates that the introduction of stacking faults leads to a vortex trapping widening and an increase of isotropic pinning centres by means of nanostrain. Some deviations from the θ T (H*) trend are observed when H*||ab, which can be associated with H* enhancement provided by stacking faults themselves, additional to the pinning of small nanoparticles already commented in the previous paragraph. b. Density, strength and energy scale of vortex pinning centres up to 9 T To separate the characteristics of different vortex pinning centres, we combined J c (T) curves obtained for a wide range of magnetic fields with J c (θ) curves obtained at specific temperatures, and applied the Blatter scaling approach 28 , 69 . Thus, we determined the J c iso (T) and J c aniso (T) components. We determined curves up to 35 T for a broad variety of samples that are representative of different microstructures, consisting of pristine and nanocomposite films with Ba 2 YTaO 6 (BYTO), BaZrO 3 (BZO), Y 2 O 3 (YO), or BaHfO 3 (BHO) nanoparticles (note that in this subsection we present only the results obtained up to 9 T; the results up to 35 T are summarized in the next subsection). In Table 1 are shown the thickness, nanostrain, nanoparticle (NP) average diameter () and density (σ NP ), stacking fault (SF) average length () 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 fulfiling the relation J c (H irr )=10 −4 J c (sf). We inferred the NP and SF average densities from high-angle annular dark field (HAADF) STEM images (see figure 5 ) using the formulae \({{\sigma }}_{\text{N}\text{P}}={n}_{NP}/{A}_{YBCO}\) and \({{\lambda }}_{\text{S}\text{F}}=\sum {\text{d}}_{SF}/{A}_{YBCO}\) , where n NP is the number of nanoparticles and A YBCO is the area of the image corresponding to the analysed YBCO film. Table 1 Sample properties. Name, composition, thickness and main electrical and microstructural properties of the studied films. 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 ). λ SF ranges: low (λ SF < 0.1 nm −1 ), medium (0.1 nm −1 < λ SF 0.15 nm −1 ). NAME COMPOSITION t (nm) T c (K) ΔT c (K) J c sf,77K (MA/cm 2 ) µ 0 H irr 77K,H||c (T) ε (%) (nm) σ NP (nm −2 ) (nm) λ SF (nm −1 ) pr-thin-1 Pristine YBCO 250 90.0 1.4 4.2 9.4 0.13 - none 140 low pr-thin-2 Pristine YBCO 250 92.7 3.1 4.3 n.m. 0.13 - none 140 low pr-thick Pristine YBCO 600 91.4 2.4 2 9 n.m. 58 low 150 low ss-nc-thin-1 YBCO+8%BYTO 250 90.2 1.0 3.5 7.7 0.20 13 medium 140 high ss-nc-thin-2 YBCO+10%BZO&5%YO 250 91.7 1.8 3.0 7 n.m. 17 medium 45 high pn-nc-thin YBCO+20%BHO 150 88.6 5.7 3.0 5.4 0.24 8 high 8 medium pn-nc-thick YBCO+20%BZO 700 92.5 2.7 3.4 9.25 0.26 19 high 95 medium From Table 1 , one observes that pristine films display a larger irreversibility magnetic field than nanocomposite films (except for pn-nc-thick); this indicates a significant change of the dominating pinning defect at high magnetic fields. Further, all nanocomposites exhibit a medium or high density of nanoparticles and stacking faults. However, each sample displays significant changes of the distribution and sizes of these defects. The ss-nc-thin-2 and pn-nc-thin films show signficantly shorter stacking faults than the rest of the films; this indicates a larger presence of partial dislocations. Furthermore, the pn-nc-thin film 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: J c (T)=J c iso−wk (T)+J c iso−str (T)+ J c aniso−str (T)= =J c (0) iso−wk exp(-T/T 0 ) +J c (0) iso−str exp(-3(T/T* iso−str ) 2 )+ J c (0) aniso−str exp(-3(T/T* aniso−str ) 2 ), (2) 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 films 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 sufficiently small (below 8 nm) 36 , 56 , 72 . By fitting equation (2) to the experimental results obtained at different magnetic fields, we determined the field dependence of the fitting 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 . T 0 , T* iso−str and T* aniso−str are associated with the characteristic pinning energy of the defects, they account for the effecitivness of their pinning potential in relation with the thermal energy k B T, where k B is the Boltzmann constant. Instead, J c (0) iso−wk , J c (0) iso−str , and J c (0) aniso−str are the J c values at 0 K of each pinning contribution, in the absence of creep, thus they are proportional to the density and strength of pinning centres. On the other hand, the accommodation magnetic field µ 0 H*(0K) obtained in J c (0) vs. magnetic field curves is exclusively associated to the density of pinning centres. In figure 6 (a) are shown the characteristic temperatures vs. the applied magnetic field. Coloured bands highlight the dispersion range of the characteristic temperatures obtained for different samples (i.e., T 0 = 5-20 K, T* iso−str = 50-90 K and T* aniso−str =70-130 K). 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 significant 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 fields) 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 figure 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 figure 6 (a) ). In the case of iso-str pinning in figure 6 (c) , nanocomposites exhibit altogether a distinguishable behaviour with respect to the pristine film due to the nanostrain already mentioned in the previous subsection, resulting in enhanced J c (0) iso−str at any magnetic field. In addition, nanoparticles that are sufficiently small will also contribute to enhance iso-str pinning. Last, the aniso-str pinning in figure 6 (b) , mainly attributed to the pinning performance of twin boundaries, shows that pn-nc-thin and ss-nc-thin-2 films 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 films (see figure 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. c. Density, strength and energy scale of vortex pinning centres up to 35T Nanocomposites improve J c primarily in magnetic field regions where the isotropic pinning contribution is enhanced. However, studies up to very high magnetic fields highlight that a crossover may occur, resulting in lower J c of nanocomposites in comparison to pristine films, especially at high temperatures due to the high T* aniso−str values developed by pristine films. The J c (H,T) surfaces of pr-thin-2 and pn-nc-thin are compared in figure 7 at 5-60 K and 10-35 T. It is recognized that the pn-nanocomposite displays larger critical current densities in a large H-T region, especially at low temperatures and intermediate fields. In contrast, at high temperatures and large magnetic fields, the nanocomposite presents a more prominent decay of J c associated with its lower irreversibility field. We observe in figure 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 fields, it shows the best performance at 4.2 K at the entire analysed magnetic field range. A crossover between the J c values from pn-nc-thin and pr-thin-2 is expected to take place at a magnetic field higher than 35 T. Such a crossover is on the other hand observed at 21 T for pn-nc-thick. At 30K, a desirable temperature for superconducting rotating machinery applications 18 refrigerated with cryocooler technology 21 , nanocomposites also offer substantially larger J c values than pristine films in the magnetic field region of 5-20 T, strengthening the fact that nanocomposites are very appropriate for the development of CCs for in-field applications. On the other hand, as depicted in figure 8 (b) , thick films offer at 4.2 K higher total critical current I c values in comparison with the pristine thin film up to 35 T, despite of their lower J c values. This reinforces the need to further understand and optimize the growth of thick films (using inkjet printing in this case 73 ). Our study on CSD films suggests that the selection of thick nanocomposite films is especially beneficial for the design of CCs operating at the range of 5-10 T offering 6 and 2.5 times larger I c values than the thin and thick pristine films respectively. Additionally, in the high magnetic field facilities, we have been able to analyse the isothermal magnetic field 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 figure 9 . In these plots, we focus at three H-T conditions: [50K,15T], [50K,35T] and [4.2K,35T], indicated with circles. Notice that different samples provide the best F p value at each condition: the thick pn-nanocomposite provides 45 GN/m 2 at [50K,15T], the pristine thick film 4 GN/m 2 at [50K,35T] and the thin pn-nanocomposite 0.55 TN/m 2 at [4.2K,35T]. In order to understand the responsible pinning contributions at the different H-T conditions, we have extended the study from the previous section to magnetic fields up to 35 T, obtaining the magnetic field 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 figure 10 . Interestingly, figure 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 field. The performance at 30-50 K in very high magnetic fields is therefore very much influenced 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 (figures 10 (b-d) ), which makes nanocomposites very appealing for the application of superconducting films 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 figure 10 (a) cause a strong J c (H) decay at higher temperatures, as already observed in figures 7 - 9 . On the other hand, the thick pn-nanocomposite exhibits higher T* iso−str and T* aniso−str (figure 10 (a) ) than the thin pn-nanocomposite and ss-nanocomposites (figure 6 (a)) . Actually, this T* iso−str coincides with that for the pristine samples (note that the different thin pristine samples display in general very similar results), indicating that nanoparticles and nanostrained regions have not effectively modified the typology of pinning centres in the thick pn-nanocomposite, also manifested by the similar J c (0) iso−str (H) dependence in figure 10 (c) . T* aniso−str in this sample is also closer to the one of pristine samples, indicating a regain in vertical coherence length of twin boundaries in comparison to thin nanocomposites. If we also consider the high T* aniso−str obtained by the thick pristine, which is the highest at 35 T, all the signs are that larger thickness favours twin boundary coherence and yields to higher value of T* aniso−str . For this reason, pr-thick and pn-nc-thick exhibit the best pinning force densities at [50K,35T] and [50K,15T] respectively. Moreover, given the larger I c in thicker films (figure 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 fields 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 fields of 15, 25 and 35 T. Results are plotted in figure 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 field of about 20 T, where J c values of nanocomposites fall below the ones of pristine films (in figure 8 (a) at 30 K), nanocomposites offer higher performance throughout the angular range. In contrast, above 20 T, the pristine film 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 fields (see figure 10 (a) ). Notice in figure 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 fields. Thus, confirming that γ eff remains constant at very high magnetic fields and that the effective anisotropy of the nanocomposite films is certainly approaching very low values, making them very appealing for high field magnets where the isotropic characteristics of CC are a strong demand. 3. Discussion The thorough study undertaken at wide temperature and magnetic field ranges up to 35 T has demonstrated that the performance of solution-derived nanocomposites is excellent at very high magnetic fields 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 films. This suggests that additional pinning centres should be induced at these conditions to overcome the existing performances of pristine CSD films, as for example a reinforcement of the density of small nanoparticles which can act as pinning centres themselves. The pinning characteristics observed in CSD films are specially ascribed to the shape, density and length of the most extended defect in these films, 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 fields and intermediate temperatures and is responsible for the general enlargement of the single vortex pinning regime defined 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 fields. 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 figure 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. At intermediate T and intermediate H: a large density of strong isotropic and anisotropic defects, the latter with a long vertical coherence (e.g., nanoparticles, nanostrain and twin boundaries or a mixed landscape of long nanorods combined with nanoparticles and nanostrain). At intermediate T and high H: a high density of anisotropic strong defects with a very long vertical coherence (like long twin boundaries in thick nanocomposites or elongated nanorods), if possible combined with other auxiliary strong or weak isotropic defects in order to sum pinning gains and avoid vortex creep excitations in parallel correlated defects 36 , 45 , 74 . 4. Conclusions Overall, the analysis presented here demonstrates the capacity to artificially modify the pinning landscape with solution-derived nanocomposites due to the benefits 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 field 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 fields. 5. Methods YBCO film growth. Epitaxial c-axis oriented YBCO films were grown by chemical solution deposition from metal organic decomposition of trifluoroacetate (TFA) salts in solution following previous works 75 – 77 . The solution was deposited on 5 x 5 mm LaAlO 3 single crystal substrates whether by spin coating for thin films (150-250 nm) or by inkjet printing for thick films (> 600 nm) 78 , 79 . Subsequently, films were pyrolized and thermal treated at high temperatures. All films 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 flash 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 , 56 , 81 , 82 . Nanoparticle concentrations are expressed by the percentage of the molar concentration of nanoparticles with respect to the YBCO molar concentration. For example, for YBCO+8%BYTO there are 8 mols of BYTO for 100 mols of YBCO. 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 field which was rotated with the angle θ from the c-axis (0°) to the ab-plane (90°), ensuring maximum Lorentz force configuration. Critical currents were determined for a 10 µV/cm electric field. 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 figure S6 in the supplementary information) and a temperature control system operating in the 4.2-60 K range. Microstructural characterisation. Nanostrain (ε) was quantified 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: \({\beta }^{2}{cos}^{2}\left(\vartheta \right)=\frac{{\lambda }_{\alpha 1}}{{L}_{\perp }}+16{\epsilon }^{2}{sin}^{2}\left(\vartheta \right)\) , 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 filter TRIDIEM 866 ERS and a monochromator. Declarations Data availability The data that support the findings of this study are available from the corresponding authors on reasonable request. Acknowledgements The authors acknowledge financial support from Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” Programme for Centres of Excellence in R&D (Grant No. SEV-2015-0496), ULTRASUPERTAPE (ERC-2014-ADG-669504), EUROTAPES project (FP7-NMP-Large-2011-280432), the CONSOLIDER Excellence Network (Grant No. MAT2015-68994-REDC), COACHSUPENERGY project (Grant No. MAT2014-56063-C2-1- R and SuMaTe RTI2018-095853-B-C21, co-financed by the European Regional Development Fund), and from the Catalan Government with Grant No. 2014-SGR-753 and 2017-SGR-1519. Authors also thank the network collaboration of EU COST action NANOCOHYBRI CA16218. We also acknowledge the Scientific Services at ICMAB and Z. Li and P. Cayado for the growth of the studied samples. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida. 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Superconducting YBa 2 Cu 3 O 7− δ Nanocomposites Using Preformed ZrO 2 Nanocrystals: Growth Mechanisms and Vortex Pinning Properties. Adv. Electron. Mater. 2 , 1600161 (2016). Additional Declarations There is NO Competing Interest. Supplementary Files optimalvortexpinningsupplementaryinfocommmat.pdf Cite Share Download PDF Status: Published Journal Publication published 08 Jul, 2022 Read the published version in Communications Materials → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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16:30:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1138719/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1138719/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s43246-022-00266-y","type":"published","date":"2022-07-08T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":17021721,"identity":"2baf73c0-562e-4d19-bed8-80be958f6351","added_by":"auto","created_at":"2022-01-05 15:53:12","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":439004,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e(H,T) surfaces. \u003c/strong\u003eJ\u003csub\u003ec\u003c/sub\u003e(H,T) for (above) a pristine and (below) a nanocomposite for (left) H||c and (right) H||ab. Spherical symbols represent the measured J\u003csub\u003ec\u003c/sub\u003e(H) curves and solid lines correspond to the accommodation magnetic field μ\u003csub\u003e0\u003c/sub\u003eH*(T) curve.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/66ac9c9d467b33cfdfa6564c.png"},{"id":17022229,"identity":"32ae7fdf-740c-4439-a57c-cceb5f5c1c57","added_by":"auto","created_at":"2022-01-05 15:56:12","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":165754,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePinning regimes in the H-T diagram.\u003c/strong\u003e Temperature dependence of μ\u003csub\u003e0\u003c/sub\u003eH* for (a) H||c and (b) H||ab for pristine and ss-nanocomposites. μ\u003csub\u003e0\u003c/sub\u003eH*(T) separates single vortex pinning from vortex-vortex interactions regimes in the H-T diagram.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/93f6816a77adf35d390b068f.png"},{"id":17021728,"identity":"28a35055-d467-43f6-819d-a704bae28e04","added_by":"auto","created_at":"2022-01-05 15:53:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":248150,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003csup\u003e\u003cstrong\u003eiso\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e/J\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e and J\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003csup\u003e\u003cstrong\u003eaniso\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e/J\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e in the H-T diagram\u003c/strong\u003e. μ\u003csub\u003e0\u003c/sub\u003eH-T color map of the ratios J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u003c/sup\u003e/J\u003csub\u003ec\u003c/sub\u003e and J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u003c/sup\u003e/J\u003csub\u003ec\u003c/sub\u003e for (left) a pristine and (right) a nanocomposite for (above) H||c and (below) H||ab. Solid lines with circles and triangles mark the μ\u003csub\u003e0\u003c/sub\u003eH\u003csub\u003eirr\u003c/sub\u003e(T) and μ\u003csub\u003e0\u003c/sub\u003eH*(T) curves, respectively.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/9780d2d3be640fbee9bdfd61.png"},{"id":17021724,"identity":"6e23762e-2fab-4a76-ba2e-30adc7edb059","added_by":"auto","created_at":"2022-01-05 15:53:12","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":153799,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExponential H*(ε) and linear θ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eT\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e(H*) trends.\u003c/strong\u003e For (black) pristine, (red) ss-nanocomposites and (blue) pn-nanocomposites:\u0026nbsp;μ\u003csub\u003e0\u003c/sub\u003eH* at (a-b) 77 K, (c-d) 50 K and (e-f) 5 K ε for (a,c,e) H*||c and (b,d,f) H*||ab versus nanostrain and θ\u003csub\u003eT\u003c/sub\u003e at 9 T as a function of μ\u003csub\u003e0\u003c/sub\u003eH* at (g) 77 K, (h) 50 K and (i) 5 K for H*||c (closed symbols) and H*||ab (open symbols). Dashed curves are guides to the eye.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/adbf0b7050af992046b74e25.png"},{"id":17021727,"identity":"660aed82-00de-4ae9-a658-74cb7bf2c84c","added_by":"auto","created_at":"2022-01-05 15:53:12","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":323320,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSTEM images.\u003c/strong\u003e HAADF STEM images obtained from (a) pr-thin-1*, (b) pr-thick, (c) ss-nc-thin-1*, (d) ss-nc-thin-2, (e) pn-nc-thin and (f) pn-nc-thick. (g,h,i) are magnified images of the same samples from (d,e,f) respectively. *: STEM images were taken in other samples with same composition and growth process.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/874529152977c6b899e5e253.png"},{"id":17022230,"identity":"96e38b85-a9c7-4b07-bced-fc3878faf7b4","added_by":"auto","created_at":"2022-01-05 15:56:12","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":158220,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCharacteristic temperatures and J\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e contributions at 0 K. \u003c/strong\u003eApplied magnetic field dependence of characteristic temperatures (a) T\u003csub\u003e0\u003c/sub\u003e (solid lines, green region), T*\u003csub\u003eiso-str\u003c/sub\u003e (solid lines, blue region) and T*\u003csub\u003eaniso-str\u003c/sub\u003e (dashed lines, red region), and J\u003csub\u003ec\u003c/sub\u003e contributions at 0 K (b) J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eaniso-str\u003c/sup\u003e, (c) J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso-str\u003c/sup\u003e and (d) J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso-wk\u003c/sup\u003e for pr-thin-1, ss-nc-thin1, ss-nc-thin2 and pn-nc-thin samples for H||c.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/3798215a08e1cdb90190bfb0.png"},{"id":17022232,"identity":"71342fe9-61f9-402a-bb94-a7fb6e2dea84","added_by":"auto","created_at":"2022-01-05 15:56:12","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":282619,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e(H,T) surfaces at very high magnetic fields.\u003c/strong\u003e They are shown for (a) pr-thin-2 and (b) pn-nc-thin for H||c.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig7.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/26edfe30349b59f3d5f379d6.png"},{"id":17022352,"identity":"e68f4c5d-3339-47e7-8457-b8b53a66404a","added_by":"auto","created_at":"2022-01-05 15:59:12","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":126724,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e(H) and I\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e(H) at very high magnetic fields.\u003c/strong\u003e Magnetic field dependence for H||c of (a) J\u003csub\u003ec\u003c/sub\u003e at 4.2 K (blue region) and 30 K (red region) for pr-thin-2, pr-thick, pn-nc-thin and pn-nc-thick samples and of (b) I\u003csub\u003ec\u003c/sub\u003e at 4.2 K for pr-thin-2, pr-thick and pn-nc-thick samples.\u003c/p\u003e","description":"","filename":"fig8.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/3690826a9afb3809f90c9e3a.png"},{"id":17022233,"identity":"5c3b703b-8c8b-40b2-95ca-c9c40d43ded0","added_by":"auto","created_at":"2022-01-05 15:56:12","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":165294,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePinning force densities at very high magnetic fields.\u003c/strong\u003e Magnetic field dependence of F\u003csub\u003eP\u003c/sub\u003e for H||c from 6 T up to 35 T at temperatures of 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10 and 4.2 K for (a) pr-thin-2, (b) pr-thick, (c) pn-nc-thin and (d) pn-nc-thick. Results at [50K,15T], [50K,35T] and [4.2K,35T] are marked with circles.\u003c/p\u003e","description":"","filename":"fig9.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/4eb15a96c2103890d1a2026c.png"},{"id":17022353,"identity":"ba983ab0-dd42-48dd-9305-b2b57658bd36","added_by":"auto","created_at":"2022-01-05 15:59:12","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":185620,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCharacteristic temperatures and J\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e contributions at 0 K at very high magnetic fields. \u003c/strong\u003eMagnetic field dependence of characteristic temperatures (a) T\u003csub\u003e0\u003c/sub\u003e (solid lines), T*\u003csub\u003eiso-str\u003c/sub\u003e (solid lines) and T*\u003csub\u003eaniso-str\u003c/sub\u003e (dashed lines), and J\u003csub\u003ec\u003c/sub\u003e contributions at 0 K (b) J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso-str\u003c/sup\u003e, (c) J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso-str\u003c/sup\u003e and (d) Jc\u003csup\u003eiso-wk\u003c/sup\u003e for pr-thin-1, pr-thin-2, pr-thick, pn-nc-thin and pn-nc-thick samples for H||c at very high magnetic fields.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig10.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/f03bfd48fb822555ddc0e9ce.png"},{"id":17021730,"identity":"932022a5-3512-4729-b937-1e5af304c419","added_by":"auto","created_at":"2022-01-05 15:53:12","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":166663,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAngular J\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e at very high magnetic fields.\u003c/strong\u003e (a) J\u003csub\u003ec\u003c/sub\u003e(θ) at 20 K for pr-thin-2, pn-nc-thin and pn-nc-thick samples at magnetic fields of 15, 25 and 35 T. Dashed lines correspond to the J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u003c/sup\u003e(θ) contributions, obtained from the collapses shown in (b) of J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u003c/sup\u003e versus the effective magnetic field μ\u003csub\u003e0\u003c/sub\u003eH\u003csub\u003eeff\u003c/sub\u003e (dashed lines), plotted for the determined γ\u003csub\u003eeff\u003c/sub\u003e, where H\u003csub\u003eeff\u003c/sub\u003e=H(cos\u003csup\u003e2\u003c/sup\u003eθ + γ\u003csub\u003eeff\u003c/sub\u003e\u003csup\u003e−2\u003c/sup\u003esin\u003csup\u003e2\u003c/sup\u003eθ)\u003csup\u003e1/2\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig11.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/f3fcdbd95661b39886d70d46.png"},{"id":17022234,"identity":"db1735fc-2af7-41d5-82cf-bb236b821a19","added_by":"auto","created_at":"2022-01-05 15:56:12","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":173455,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eOptimized pinning landscapes for H||c.\u003c/strong\u003e H-T diagram with three optimized pinning landscapes in the regions of: low temperatures from low magnetic fields up to ~35 T, intermediate temperatures and intermediate magnetic fields (~15 T) and intermediate temperatures and very high magnetic fields (~35 T).\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"fig12.png","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/bd17d7213bb8170658099de1.png"},{"id":23855937,"identity":"235fafff-f0d7-48b4-ba24-8fb51fc4fb90","added_by":"auto","created_at":"2022-07-14 12:42:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3026023,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/ddab9c5a-768d-4f8c-9355-504e2725ad7b.pdf"},{"id":17021733,"identity":"26909257-5eab-4a86-ab4b-12a8ffe3af8c","added_by":"auto","created_at":"2022-01-05 15:53:12","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1344481,"visible":true,"origin":"","legend":"","description":"","filename":"optimalvortexpinningsupplementaryinfocommmat.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1138719/v1/9488b4d9d897dd810e61f661.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eOptimal Vortex Pinning in YBa\u003csub\u003e2\u003c/sub\u003eCu\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e7-x\u003c/sub\u003e Superconducting Films Up to Very High Magnetic Fields\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe successful development of suitable methods to grow epitaxial REBa\u003csub\u003e2\u003c/sub\u003eCu\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e7\u0026minus;x\u003c/sub\u003e (REBCO, RE = Rare Earth) films 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 fields and temperatures\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Among investigated superconductors, the REBCO superconductors do not exhibit either the highest critical temperature T\u003csub\u003ec\u003c/sub\u003e or upper critical magnetic field H\u003csub\u003ec2\u003c/sub\u003e. However, they do provide the highest irreversibility line H\u003csub\u003eirr\u003c/sub\u003e (see \u003cb\u003efigure S1\u003c/b\u003e in the supplementary information for YBCO). Therefore, besides being suitable for power cables and fault current limiters at low magnetic fields and high temperatures\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, REBCO CCs have been included in the design and fabrication of new coil architectures for high magnetic field applications such as research magnets\u003csup\u003e\u003cspan additionalcitationids=\"CR9 CR10 CR11\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, NMR/MRI magnets\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e, magnets for fusion energy\u003csup\u003e\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, and high energy physics accelerator magnets\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. They are excellent candidates not only for superconducting large currents in high field magnets at very low temperatures, but also in the intermediate magnetic fields generated in rotating machines\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e or superconducting magnetic energy storage systems\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e at temperatures in the range of 20-50 K, which can be effectively driven by cryocoolers\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAt present, the magnetic field - 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\u003csub\u003ec\u003c/sub\u003e, shows a strong variation in different regions of the H-T diagram and with the orientation of the magnetic field 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\u003csup\u003e22\u0026minus;25\u003c/sup\u003e. A quest for an adequate microstructure that favours vortex pinning and enhances J\u003csub\u003ec\u003c/sub\u003e 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\u003csup\u003e4,5,26\u0026minus;32\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eVortex 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\u003csub\u003ec\u003c/sub\u003e enhancement. Nanoparticles\u003csup\u003e16,27,33\u0026minus;36\u003c/sup\u003e improved the in-field J\u003csub\u003ec\u003c/sub\u003e at all magnetic field orientations at any temperature and in some cases self-field (sf) J\u003csub\u003ec\u003c/sub\u003e. The presence of random point defects\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e also improved the in-field J\u003csub\u003ec\u003c/sub\u003e, especially at temperatures below 40 K. Secondary phase nanorods/nanocolumns\u003csup\u003e29,39,40\u003c/sup\u003e or irradiated columnar defects\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e enhanced J\u003csub\u003ec\u003c/sub\u003e mainly when H is parallel to the c-axis (H||c), especially at high magnetic fields and high temperatures; the same occured for natural defects such as twin boundaries\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e and dislocations\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. Lately, hybrid nanostructures combining various defects\u003csup\u003e\u003cspan additionalcitationids=\"CR46 CR47 CR48 CR49\" citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e have also been investigated, with the aim of merging gains. However, only a few studies cover large magnetic field and temperature ranges\u003csup\u003e6,51\u0026minus;53\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this article, we offer a broad study so as to determine the optimal microstructure for specific 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 fields. To do so, we analyse films 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\u003csub\u003ec\u003c/sub\u003e(H,θ,T) over a very broad range of temperatures (5-77 K) and applied magnetic fields (0-35 T), combined with detailed microstructural investigations by scanning transmission electron microscopy (STEM) and x-ray diffraction (XRD).\u003c/p\u003e"},{"header":"2. Results","content":"\u003cp\u003eThe epitaxial solution-deposited YBCO films we study in this work are ranging in thickness from 100 nm to 1 \u0026micro;m. These have been grown by CSD with various precursor solutions: pristine YBCO, YBCO with additives for spontaneous segregation of nanoparticles (ss-nanocomposites), and YBCO with preformed nanoparticles (pn-nanocomposites). We grew samples with distinctive amounts of nanoparticles (0%-12% mol) and diverse processing conditions (i.e., film deposition, heating ramp), yielding to very different defect landscapes\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e; all films have an oxygen doping state close to optimal doping, deduced from the temperature evaluation of the normalized resistivity\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eHere, we consider the identification of defect contributions according to angular pinning performance and the associated pinning strength, as described previously\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e. As explained in detail in \u003cstrong\u003efigure S2\u003c/strong\u003e, in CSD YBCO we find, typically, isotropic defects (0D and 3D) such as copper-oxygen vacancy clusters\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e, small nanoparticles, or nanostrain generated in partial dislocations surrounding the stacking faults\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. On the other hand, we observe planar anisotropic defects such as stacking faults parallel to the a-b planes\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e or twin boundaries parallel to the c-axis\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e61\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. 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\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/sup\u003e, originated in the layered structure of the YBCO itself, coexists with stacking fault pinning for H parallel to the a-b planes (H||ab)\u003csup\u003e63,64\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eWe 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.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea. Pinning regimes up to 9 T in the H-T phase diagram\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eWe obtained accurate surfaces of J\u003csub\u003ec\u003c/sub\u003e(H,T) for the main orientations of the magnetic field H||c and H||ab for pristine and nanocomposite films, as shown in figure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. This was achieved by measuring J\u003csub\u003ec\u003c/sub\u003e(H) curves at 5, 20, 50, 65 and 77 K, linearly interpolating, and subsequently fitting the curves as a function of temperature considering both the weak and strong pinning contributions of J\u003csub\u003ec\u003c/sub\u003e(T) (i.e., J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003ewk\u003c/sup\u003e(T) and J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003estr\u003c/sup\u003e(T), respectively). Whereas weak pinning centres yield a fast temperature decay of the J\u003csub\u003ec\u003c/sub\u003e in the collective pinning model\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e65\u003c/span\u003e\u003c/sup\u003e, strong pinning centres account for a smoother temperature decay in the Bose glass model\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. In a first approximation and neglecting interactions between both types, we can describe J\u003csub\u003ec\u003c/sub\u003e(T) by the direct sum\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e:\u003c/p\u003e\n\u003cp\u003eJ \u003csub\u003ec\u003c/sub\u003e(T)=J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003ewk\u003c/sup\u003e(T)+J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003estr\u003c/sup\u003e(T)= J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003ewk\u003c/sup\u003e exp(-T/T\u003csub\u003e0\u003c/sub\u003e) +J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003estr\u003c/sup\u003e exp(-3(T/T*)\u003csup\u003e2\u003c/sup\u003e), (1)\u003c/p\u003e\n\u003cp\u003ewhere J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003ewk\u003c/sup\u003e and J\u003csub\u003ec\u003c/sub\u003e(0) \u003csup\u003estr\u003c/sup\u003e refer to contributions at 0 K, whereas T\u003csub\u003e0\u003c/sub\u003e and T* refer to temperatures associated to the characteristic vortex pinning energy of weak and strong defects, respectively. The final temperature interpolation is explained in detail in \u003cstrong\u003efigure S3\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eFor the nanocomposite, the 3D J\u003csub\u003ec\u003c/sub\u003e(H,T) representation illustrates an enlargement of the (reddish) high critical current density region (\u0026gt; 1 MA/cm\u003csup\u003e2\u003c/sup\u003e) at low temperatures and low magnetic fields; the appealing region for high-current applications. On the other hand, at high temperatures and high magnetic fields, a rapid decay of J\u003csub\u003ec\u003c/sub\u003e is visible at lower H-T values for H||c, but not for H||ab.\u003c/p\u003e\n\u003cp\u003eThe enlargement of the reddish high J\u003csub\u003ec\u003c/sub\u003e(H,T) region is concurrent with the shift to larger magnetic fields of the \u0026micro;\u003csub\u003e0\u003c/sub\u003eH*(T) curve, where \u0026micro;\u003csub\u003e0\u003c/sub\u003e is the vacuum permeability and H* is the accommodation magnetic field, which sets the limit between the single vortex pinning regime - where vortices interact weakly with each other but strongly with defects\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e66\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e - and the vortex-vortex interaction regime. Therefore, H* is related to the density of defects. Here, it is defined as in other works\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e68\u003c/span\u003e\u003c/sup\u003e by the equation J\u003csub\u003ec\u003c/sub\u003e(\u0026micro;\u003csub\u003e0\u003c/sub\u003eH*) = 0.9J\u003csub\u003ec\u003c/sub\u003e(sf), where sf stands for self-field. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows a comparison between \u0026micro;\u003csub\u003e0\u003c/sub\u003eH*(T) curves for several nanocomposites and a pristine sample, for both H||c and H||ab, highlighting the presence of the two regimes in the H-T diagram. In comparison to the pristine YBCO, all nanocomposites share the capability of enlarging the single vortex pinning regime up to high fields; this was observed for both magnetic field orientations, suggesting that the origin of this enlargement is effective at any orientation and, therefore, is isotropic.\u003c/p\u003e\n\u003cp\u003eIn order to separate the isotropic (J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u003c/sup\u003e) and anisotropic (J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u003c/sup\u003e) contributions of the J\u003csub\u003ec\u003c/sub\u003e(H) curves shown in figure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e we applied the Blatter scaling approach\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e69\u003c/span\u003e\u003c/sup\u003e to angular J\u003csub\u003ec\u003c/sub\u003e(\u0026theta;) measurements at temperatures of 5, 20, 50, 65 and 77 K, and applied magnetic fields of 0.1, 0.3, 0.5, 1, 3, 5, 7 and 9 T. Subsequently, we fitted their temperature dependence through the procedure explained in the supplementary information (\u003cstrong\u003efigure S3\u003c/strong\u003e), aiming to establish the weight of each contribution within the full range of the H-T diagram.\u003c/p\u003e\n\u003cp\u003eWe, thus, obtained the colour maps presented in figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, which show the ratio J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u003c/sup\u003e/J\u003csub\u003ec\u003c/sub\u003e in the H-T diagram (equivalent to 1- J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u003c/sup\u003e/J\u003csub\u003ec\u003c/sub\u003e 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 field, 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 fields of the order of 1 T, especially at low temperatures.\u003c/p\u003e\n\u003cp\u003eIt is worth noting that the \u0026micro;\u003csub\u003e0\u003c/sub\u003eH*(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\u003csub\u003eirr\u003c/sub\u003e(T) for the nanocomposite, especially at H||c, which can be associated to a lower pinning performance of the anisotropic defects (mainly twin boundaries\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003eTo 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 \u003cstrong\u003efigure S2(c,d))\u003c/strong\u003e, and it has been signalled as a characteristic defect emerging in large quantities in nanocomposites\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. Hence, we macroscopically measured the nanostrain (\u0026epsilon;) for each sample by XRD analysis, following the Williamson-Hall method\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e70\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cstrong\u003e(a-f)\u003c/strong\u003e shows the above-mentioned correlation between the H* accomodation magnetic field (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 \u0026epsilon; increases; this is clear at all temperatures and orientations of the magnetic field 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.\u003c/p\u003e\n\u003cp\u003eFurther, we analysed the widening of the J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u003c/sup\u003e(\u0026theta;) ab-peak; we approximated its half width-half-maximum with the trapping angle \u0026theta;\u003csub\u003eT\u003c/sub\u003e that limits the vortex staircase regime\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e63\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e71\u003c/span\u003e\u003c/sup\u003e (\u0026theta;\u003csub\u003eT\u003c/sub\u003e calculation presented in \u003cstrong\u003efigure S4\u003c/strong\u003e), 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. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cstrong\u003e(g-i)\u003c/strong\u003e presents \u0026theta;\u003csub\u003eT\u003c/sub\u003e versus \u0026micro;\u003csub\u003e0\u003c/sub\u003eH* for J\u003csub\u003ec\u003c/sub\u003e(\u0026theta;) curves measured at a field of 9 T and temperatures of 77, 50 and 5 K, and for J\u003csub\u003ec\u003c/sub\u003e(H) curves measured for both H*||c and H*||ab. The linear trend of the \u0026theta;\u003csub\u003eT\u003c/sub\u003e(H*) combined with the exponential trend of H*(\u0026epsilon;) indicates that the introduction of stacking faults leads to a vortex trapping widening and an increase of isotropic pinning centres by means of nanostrain. Some deviations from the \u0026theta;\u003csub\u003eT\u003c/sub\u003e(H*) trend are observed when H*||ab, which can be associated with H* enhancement provided by stacking faults themselves, additional to the pinning of small nanoparticles already commented in the previous paragraph.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eb. Density, strength and energy scale of vortex pinning centres up to 9 T\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eTo separate the characteristics of different vortex pinning centres, we combined J\u003csub\u003ec\u003c/sub\u003e(T) curves obtained for a wide range of magnetic fields with J\u003csub\u003ec\u003c/sub\u003e(\u0026theta;) curves obtained at specific temperatures, and applied the Blatter scaling approach\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e69\u003c/span\u003e\u003c/sup\u003e. Thus, we determined the J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u003c/sup\u003e(T) and J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u003c/sup\u003e(T) components.\u003c/p\u003e\n\u003cp\u003eWe determined curves up to 35 T for a broad variety of samples that are representative of different microstructures, consisting of pristine and nanocomposite films with Ba\u003csub\u003e2\u003c/sub\u003eYTaO\u003csub\u003e6\u003c/sub\u003e (BYTO), BaZrO\u003csub\u003e3\u003c/sub\u003e (BZO), Y\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e (YO), or BaHfO\u003csub\u003e3\u003c/sub\u003e (BHO) nanoparticles (note that in this subsection we present only the results obtained up to 9 T; the results up to 35 T are summarized in the next subsection).\u003c/p\u003e\n\u003cp\u003eIn Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e are shown the thickness, nanostrain, nanoparticle (NP) average diameter (\u0026lt;\u0026Oslash;\u003csub\u003eNP\u003c/sub\u003e\u0026gt;) and density (\u0026sigma;\u003csub\u003eNP\u003c/sub\u003e), stacking fault (SF) average length (\u0026lt;d\u003csub\u003eSF\u003c/sub\u003e\u0026gt;) and density (\u0026lambda;\u003csub\u003eSF\u003c/sub\u003e) and main electrical transport properties \u0026ndash; T\u003csub\u003ec\u003c/sub\u003e, \u0026Delta;T\u003csub\u003ec\u003c/sub\u003e (transition width), J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003esf,77K\u003c/sup\u003e and H\u003csub\u003eirr\u003c/sub\u003e\u003csup\u003e77K,H||c\u003c/sup\u003e \u0026ndash; of each of the samples we analysed.\u003c/p\u003e\n\u003cp\u003eAll samples display T\u003csub\u003ec\u003c/sub\u003e \u0026gt; 88 K, \u0026Delta;T\u003csub\u003ec\u003c/sub\u003e \u0026lt; 6 K, and J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003esf,77K\u003c/sup\u003e \u0026asymp; 2-4.5 MA/cm\u003csup\u003e2\u003c/sup\u003e. We evaluated H\u003csub\u003eirr\u003c/sub\u003e\u003csup\u003e77K,H||c\u003c/sup\u003e from J\u003csub\u003ec\u003c/sub\u003e(H) measurements fulfiling the relation J\u003csub\u003ec\u003c/sub\u003e(H\u003csub\u003eirr\u003c/sub\u003e)=10\u003csup\u003e\u0026minus;4\u003c/sup\u003eJ\u003csub\u003ec\u003c/sub\u003e(sf). We inferred the NP and SF average densities from high-angle annular dark field (HAADF) STEM images (see figure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e) using the formulae \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}_{\\text{N}\\text{P}}={n}_{NP}/{A}_{YBCO}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\lambda }}_{\\text{S}\\text{F}}=\\sum {\\text{d}}_{SF}/{A}_{YBCO}\\)\u003c/span\u003e\u003c/span\u003e, where n\u003csub\u003eNP\u003c/sub\u003e is the number of nanoparticles and A\u003csub\u003eYBCO\u003c/sub\u003e is the area of the image corresponding to the analysed YBCO film.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003e\u003cstrong\u003eSample properties.\u003c/strong\u003e Name, composition, thickness and main electrical and microstructural properties of the studied films. pr: pristine, nc: nanocomposite, ss: spontaneous segregated nanoparticles, pn: preformed nanoparticles, n.m.: not measured. \u0026sigma;\u003csub\u003eNP\u003c/sub\u003e ranges: low (\u0026sigma;\u003csub\u003eNP\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1E-4 nm\u003csup\u003e\u0026minus;2\u003c/sup\u003e), medium (1E-4 nm\u003csup\u003e\u0026minus;2\u003c/sup\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u0026sigma;\u003csub\u003eNP\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;5E-4 nm\u003csup\u003e\u0026minus;2\u003c/sup\u003e), high (\u0026sigma;\u003csub\u003eNP\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;5E-4 nm\u003csup\u003e\u0026minus;2\u003c/sup\u003e). \u0026lambda;\u003csub\u003eSF\u003c/sub\u003e ranges: low (\u0026lambda;\u003csub\u003eSF\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.1 nm\u003csup\u003e\u0026minus;1\u003c/sup\u003e), medium (0.1 nm\u003csup\u003e\u0026minus;1\u003c/sup\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u0026lambda;\u003csub\u003eSF\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.15 nm\u003csup\u003e\u0026minus;1\u003c/sup\u003e), high (\u0026lambda;\u003csub\u003eSF\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.15 nm\u003csup\u003e\u0026minus;1\u003c/sup\u003e).\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNAME\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCOMPOSITION\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003et (nm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eT\u003csub\u003ec\u003c/sub\u003e (K)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026Delta;T\u003csub\u003ec\u003c/sub\u003e (K)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eJ\u003csub\u003ec\u003c/sub\u003e\u003csup\u003esf,77K\u003c/sup\u003e (MA/cm\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026micro;\u003csub\u003e0\u003c/sub\u003eH\u003csub\u003eirr\u003c/sub\u003e\u003csup\u003e77K,H||c\u003c/sup\u003e (T)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026epsilon; (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026lt;\u0026Oslash;\u003csub\u003eNP\u003c/sub\u003e\u0026gt; (nm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026sigma;\u003csub\u003eNP\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e(nm\u003csup\u003e\u0026minus;2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026lt;d\u003csub\u003eSF\u003c/sub\u003e\u0026gt; (nm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026lambda;\u003csub\u003eSF\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e(nm\u003csup\u003e\u0026minus;1\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epr-thin-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePristine YBCO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e90.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003enone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elow\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epr-thin-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePristine YBCO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e92.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003en.m.\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003enone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elow\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epr-thick\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePristine YBCO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e91.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003en.m.\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elow\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ess-nc-thin-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYBCO+8%BYTO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e90.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003emedium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ehigh\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ess-nc-thin-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYBCO+10%BZO\u0026amp;5%YO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e91.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003en.m.\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003emedium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ehigh\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epn-nc-thin\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYBCO+20%BHO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e88.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ehigh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003emedium\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epn-nc-thick\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYBCO+20%BZO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e700\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e92.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ehigh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003emedium\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eFrom Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, one observes that pristine films display a larger irreversibility magnetic field than nanocomposite films (except for pn-nc-thick); this indicates a significant change of the dominating pinning defect at high magnetic fields. Further, all nanocomposites exhibit a medium or high density of nanoparticles and stacking faults. However, each sample displays significant changes of the distribution and sizes of these defects. The ss-nc-thin-2 and pn-nc-thin films show signficantly shorter stacking faults than the rest of the films; this indicates a larger presence of partial dislocations. Furthermore, the pn-nc-thin film 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.\u003c/p\u003e\n\u003cp\u003eAnisotropic 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\u003csub\u003ec\u003c/sub\u003e(T) can be described by the linear sum of three contributions:\u003c/p\u003e\n\u003cp\u003eJ \u003csub\u003ec\u003c/sub\u003e(T)=J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u0026minus;wk\u003c/sup\u003e(T)+J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u0026minus;str\u003c/sup\u003e(T)+ J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u0026minus;str\u003c/sup\u003e(T)=\u003c/p\u003e\n\u003cp\u003e=J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;wk\u003c/sup\u003e exp(-T/T\u003csub\u003e0\u003c/sub\u003e) +J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;str\u003c/sup\u003e exp(-3(T/T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e)+ J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eaniso\u0026minus;str\u003c/sup\u003e exp(-3(T/T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e), (2)\u003c/p\u003e\n\u003cp\u003ewhere the J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003estr\u003c/sup\u003e contribution from \u003cstrong\u003eequation (1)\u003c/strong\u003e is substituted now by the sum of the isotropic-strong (iso-str) contribution J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u0026minus;str\u003c/sup\u003e and the anisotropic-strong (aniso-str) contribution J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u0026minus;str\u003c/sup\u003e (corresponding directly to J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u003c/sup\u003e); the isotropic-weak (iso-wk) contribution J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u0026minus;wk\u003c/sup\u003e corresponds to the overall J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003ewk\u003c/sup\u003e contribution. For the films 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 sufficiently small (below 8 nm)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e72\u003c/span\u003e\u003c/sup\u003e. By fitting \u003cstrong\u003eequation (2)\u003c/strong\u003e to the experimental results obtained at different magnetic fields, we determined the field dependence of the fitting parameters; these are the characteristic temperatures T\u003csub\u003e0\u003c/sub\u003e, T*\u003csub\u003eiso\u0026minus;str,\u003c/sub\u003e and T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e, and the contributions at 0 K J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;wk\u003c/sup\u003e, J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;str\u003c/sup\u003e, and J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eaniso\u0026minus;str\u003c/sup\u003e. T\u003csub\u003e0\u003c/sub\u003e, T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e and T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e are associated with the characteristic pinning energy of the defects, they account for the effecitivness of their pinning potential in relation with the thermal energy k\u003csub\u003eB\u003c/sub\u003eT, where k\u003csub\u003eB\u003c/sub\u003e is the Boltzmann constant. Instead, J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;wk\u003c/sup\u003e, J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;str\u003c/sup\u003e, and J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eaniso\u0026minus;str\u003c/sup\u003e are the J\u003csub\u003ec\u003c/sub\u003e values at 0 K of each pinning contribution, in the absence of creep, thus they are proportional to the density and strength of pinning centres. On the other hand, the accommodation magnetic field \u0026micro;\u003csub\u003e0\u003c/sub\u003eH*(0K) obtained in J\u003csub\u003ec\u003c/sub\u003e(0) vs. magnetic field curves is exclusively associated to the density of pinning centres.\u003c/p\u003e\n\u003cp\u003eIn figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e are shown the characteristic temperatures vs. the applied magnetic field. Coloured bands highlight the dispersion range of the characteristic temperatures obtained for different samples (i.e., T\u003csub\u003e0\u003c/sub\u003e= 5-20 K, T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e = 50-90 K and T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e =70-130 K).\u003c/p\u003e\n\u003cp\u003eWe 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 significant changes. The larger dispersion in the pinning energy values was obtained for T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e. In this case, much lower values are found for all nanocomposites (T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e\u0026asymp;70-80 K at high fields) as compared with the pristine, which we associate to the segmentation of twin boundaries due to a large density of stacking faults\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e, also provoking a decrease of the irreversibility line H\u003csub\u003eirr\u003c/sub\u003e. In contrast, the pristine sample shows the highest T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e values and largest H\u003csub\u003eirr\u003c/sub\u003e (9.4 T at 77 K, see Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), indicative of coherent long twin boundaries. Another remarkable difference is the one obtained for T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e, 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.\u003c/p\u003e\n\u003cp\u003eRegarding the 0 K contributions of J\u003csub\u003ec\u003c/sub\u003e, we also observe remarkable differences between nanocomposites and the pristine sample. In the case of iso-wk (see figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e\u003cstrong\u003e(d)\u003c/strong\u003e), we observe that nanocomposites show an enhanced \u0026micro;\u003csub\u003e0\u003c/sub\u003eH*\u003csub\u003eiso\u0026minus;wk\u003c/sub\u003e(0K), specially the pn-nc-thin, which is ascribed to a high density of Cu-O vacancy clusters hosted in the stacking faults\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e. The best J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;wk\u003c/sup\u003e 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\u003csub\u003e0\u003c/sub\u003e in figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e). In the case of iso-str pinning in figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e\u003cstrong\u003e(c)\u003c/strong\u003e, nanocomposites exhibit altogether a distinguishable behaviour with respect to the pristine film due to the nanostrain already mentioned in the previous subsection, resulting in enhanced J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso\u0026minus;str\u003c/sup\u003e at any magnetic field. In addition, nanoparticles that are sufficiently small will also contribute to enhance iso-str pinning. Last, the aniso-str pinning in figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e\u003cstrong\u003e(b)\u003c/strong\u003e, mainly attributed to the pinning performance of twin boundaries, shows that pn-nc-thin and ss-nc-thin-2 films excel at exhibiting the largest J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eaniso\u0026minus;str\u003c/sup\u003e 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 films (see figure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e\u003cstrong\u003e(d,e,g,h)\u003c/strong\u003e). 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*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e due to the lack of vertical defect coherence.\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ec. Density, strength and energy scale of vortex pinning centres up to 35T\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eNanocomposites improve J\u003csub\u003ec\u003c/sub\u003e primarily in magnetic field regions where the isotropic pinning contribution is enhanced. However, studies up to very high magnetic fields highlight that a crossover may occur, resulting in lower J\u003csub\u003ec\u003c/sub\u003e of nanocomposites in comparison to pristine films, especially at high temperatures due to the high T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e values developed by pristine films. The J\u003csub\u003ec\u003c/sub\u003e(H,T) surfaces of pr-thin-2 and pn-nc-thin are compared in figure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e at 5-60 K and 10-35 T. It is recognized that the pn-nanocomposite displays larger critical current densities in a large H-T region, especially at low temperatures and intermediate fields. In contrast, at high temperatures and large magnetic fields, the nanocomposite presents a more prominent decay of J\u003csub\u003ec\u003c/sub\u003e associated with its lower irreversibility field.\u003c/p\u003e\n\u003cp\u003eWe observe in figure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e that although the pn-nc-thin sample exhibits a fast J\u003csub\u003ec\u003c/sub\u003e(H) decay at 30K with lower J\u003csub\u003ec\u003c/sub\u003e values at very high fields, it shows the best performance at 4.2 K at the entire analysed magnetic field range. A crossover between the J\u003csub\u003ec\u003c/sub\u003e values from pn-nc-thin and pr-thin-2 is expected to take place at a magnetic field higher than 35 T. Such a crossover is on the other hand observed at 21 T for pn-nc-thick.\u003c/p\u003e\n\u003cp\u003eAt 30K, a desirable temperature for superconducting rotating machinery applications\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e refrigerated with cryocooler technology\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e, nanocomposites also offer substantially larger J\u003csub\u003ec\u003c/sub\u003e values than pristine films in the magnetic field region of 5-20 T, strengthening the fact that nanocomposites are very appropriate for the development of CCs for in-field applications. On the other hand, as depicted in figure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e\u003cstrong\u003e(b)\u003c/strong\u003e, thick films offer at 4.2 K higher total critical current I\u003csub\u003ec\u003c/sub\u003e values in comparison with the pristine thin film up to 35 T, despite of their lower J\u003csub\u003ec\u003c/sub\u003e values. This reinforces the need to further understand and optimize the growth of thick films (using inkjet printing in this case\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e73\u003c/span\u003e\u003c/sup\u003e). Our study on CSD films suggests that the selection of thick nanocomposite films is especially beneficial for the design of CCs operating at the range of 5-10 T offering 6 and 2.5 times larger I\u003csub\u003ec\u003c/sub\u003e values than the thin and thick pristine films respectively.\u003c/p\u003e\n\u003cp\u003eAdditionally, in the high magnetic field facilities, we have been able to analyse the isothermal magnetic field dependent current-voltage characteristics for four different samples: pr-thin-2, pr-thick, pn-nc-thin and pn-nc-thick, whose F\u003csub\u003ep\u003c/sub\u003e(H) curves are plotted in figure \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. In these plots, we focus at three H-T conditions: [50K,15T], [50K,35T] and [4.2K,35T], indicated with circles. Notice that different samples provide the best F\u003csub\u003ep\u003c/sub\u003e value at each condition: the thick pn-nanocomposite provides 45 GN/m\u003csup\u003e2\u003c/sup\u003e at [50K,15T], the pristine thick film 4 GN/m\u003csup\u003e2\u003c/sup\u003e at [50K,35T] and the thin pn-nanocomposite 0.55 TN/m\u003csup\u003e2\u003c/sup\u003e at [4.2K,35T]. In order to understand the responsible pinning contributions at the different H-T conditions, we have extended the study from the previous section to magnetic fields up to 35 T, obtaining the magnetic field dependence of the characteristic temperatures T\u003csub\u003e0\u003c/sub\u003e, T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e and T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e and the J\u003csub\u003ec\u003c/sub\u003e contributions at 0 K, J\u003csub\u003ec\u003c/sub\u003e(0)\u003csub\u003eiso\u0026minus;wk\u003c/sub\u003e, J\u003csub\u003ec\u003c/sub\u003e(0)\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e and J\u003csub\u003ec\u003c/sub\u003e(0)\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e, in figure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e. Interestingly, figure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e shows that T\u003csub\u003e0\u003c/sub\u003e tends to slightly increase, whereas both T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e and T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e tend to decrease with increasing magnetic field. The performance at 30-50 K in very high magnetic fields is therefore very much influenced by the pinning characteristic temperatures.\u003c/p\u003e\n\u003cp\u003eThe analysis of the pinning contributions extrapolated to 0 K shows in general larger J\u003csub\u003ec\u003c/sub\u003e(0) for pn-nanocomposites than for pristine samples (figures \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e\u003cstrong\u003e(b-d)\u003c/strong\u003e), which makes nanocomposites very appealing for the application of superconducting films 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\u003csup\u003e2\u003c/sup\u003e at [4.2K,35T]. However, the low T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e and especially the low T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e possessed by this thin pn-nanocomposite plotted in figure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e cause a strong J\u003csub\u003ec\u003c/sub\u003e(H) decay at higher temperatures, as already observed in figures \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e-\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eOn the other hand, the thick pn-nanocomposite exhibits higher T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e and T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e (figure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e) than the thin pn-nanocomposite and ss-nanocomposites (figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e\u003cstrong\u003e(a))\u003c/strong\u003e. Actually, this T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e coincides with that for the pristine samples (note that the different thin pristine samples display in general very similar results), indicating that nanoparticles and nanostrained regions have not effectively modified the typology of pinning centres in the thick pn-nanocomposite, also manifested by the similar J\u003csub\u003ec\u003c/sub\u003e(0)\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e(H) dependence in figure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e\u003cstrong\u003e(c)\u003c/strong\u003e. T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e in this sample is also closer to the one of pristine samples, indicating a regain in vertical coherence length of twin boundaries in comparison to thin nanocomposites. If we also consider the high T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e obtained by the thick pristine, which is the highest at 35 T, all the signs are that larger thickness favours twin boundary coherence and yields to higher value of T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e. For this reason, pr-thick and pn-nc-thick exhibit the best pinning force densities at [50K,35T] and [50K,15T] respectively. Moreover, given the larger I\u003csub\u003ec\u003c/sub\u003e in thicker films (figure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e\u003cstrong\u003e(b)\u003c/strong\u003e), the total pinning force strongly improves and therefore it is strongly recommended to take steps forward in the direction of gaining thickness.\u003c/p\u003e\n\u003cp\u003eFinally, the study of current-voltage curves at very high magnetic fields has been extended at magnetic orientations different to H||c at the temperature of 20 K, covering an angular range of 180\u0026deg; centred at H||ab for the magnetic fields of 15, 25 and 35 T. Results are plotted in figure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e 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 \u0026theta;\u003csub\u003eT\u003c/sub\u003e to accommodate vortices by stacking faults. Below the crossover magnetic field of about 20 T, where J\u003csub\u003ec\u003c/sub\u003e values of nanocomposites fall below the ones of pristine films (in figure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e at 30 K), nanocomposites offer higher performance throughout the angular range. In contrast, above 20 T, the pristine film starts to exhibit larger J\u003csub\u003ec\u003c/sub\u003e 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\u003csub\u003e0\u003c/sub\u003e, T*\u003csub\u003eiso\u0026minus;str\u003c/sub\u003e and T*\u003csub\u003eaniso\u0026minus;str\u003c/sub\u003e get closer at very high magnetic fields (see figure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e\u003cstrong\u003e(a)\u003c/strong\u003e). Notice in figure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e\u003cstrong\u003e(b)\u003c/strong\u003e, that the collapses of J\u003csub\u003ec\u003c/sub\u003e\u003csup\u003eiso\u003c/sup\u003e are obtained for effective anisotropies (\u0026gamma;\u003csub\u003eeff\u003c/sub\u003e) 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 fields. Thus, confirming that \u0026gamma;\u003csub\u003eeff\u003c/sub\u003e remains constant at very high magnetic fields and that the effective anisotropy of the nanocomposite films is certainly approaching very low values, making them very appealing for high field magnets where the isotropic characteristics of CC are a strong demand.\u003c/p\u003e"},{"header":"3. Discussion","content":"\u003cp\u003eThe thorough study undertaken at wide temperature and magnetic field ranges up to 35 T has demonstrated that the performance of solution-derived nanocomposites is excellent at very high magnetic fields and very low temperatures. However, at temperatures above 20 K, there is a crossover of J\u003csub\u003ec\u003c/sub\u003e values in nanocomposites with respect to the pristine films. This suggests that additional pinning centres should be induced at these conditions to overcome the existing performances of pristine CSD films, as for example a reinforcement of the density of small nanoparticles which can act as pinning centres themselves. The pinning characteristics observed in CSD films are specially ascribed to the shape, density and length of the most extended defect in these films, 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:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThey increase the isotropic-strong contribution by means of increasing J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso-str\u003c/sup\u003e 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 fields and intermediate temperatures and is responsible for the general enlargement of the single vortex pinning regime defined by the increase of \u0026micro;\u003csub\u003e0\u003c/sub\u003eH*.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThey increase the isotropic-weak contribution by means of increasing J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eiso-wk\u003c/sup\u003e due to the formation of Cu-O vacancy clusters among stacking faults. This increase is very effective at low temperatures.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThey increase the anisotropic-strong contribution by means of increasing J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eaniso-str\u003c/sup\u003e due to the multiplication of twin boundaries given by the segmentation provoked by the appearance of stacking faults. The increase of J\u003csub\u003ec\u003c/sub\u003e(0)\u003csup\u003eaniso-str\u003c/sup\u003e is very effective at low temperatures up to very high magnetic fields. However, the segmentation of twin boundaries causes in parallel a breaking of their vertical coherence, which yields a reduction of the pinning energy T*\u003csub\u003eaniso-str\u003c/sub\u003e and therefore a decrease of the irreversibility line \u0026micro;\u003csub\u003e0\u003c/sub\u003eH\u003csub\u003eirr\u003c/sub\u003e(T), which can be recovered in the case of thick nanocomposites.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eTherefore, 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 figure \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eAt 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.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAt intermediate T and intermediate H: a large density of strong isotropic and anisotropic defects, the latter with a long vertical coherence (e.g., nanoparticles, nanostrain and twin boundaries or a mixed landscape of long nanorods combined with nanoparticles and nanostrain).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAt intermediate T and high H: a high density of anisotropic strong defects with a very long vertical coherence (like long twin boundaries in thick nanocomposites or elongated nanorods), if possible combined with other auxiliary strong or weak isotropic defects in order to sum pinning gains and avoid vortex creep excitations in parallel correlated defects\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e,\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eOverall, the analysis presented here demonstrates the capacity to artificially modify the pinning landscape with solution-derived nanocomposites due to the benefits 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 field 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 fields.\u003c/p\u003e"},{"header":"5. Methods","content":"\u003cp\u003e \u003cb\u003eYBCO film growth.\u003c/b\u003e Epitaxial c-axis oriented YBCO films were grown by chemical solution deposition from metal organic decomposition of trifluoroacetate (TFA) salts in solution following previous works\u003csup\u003e\u003cspan additionalcitationids=\"CR76\" citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e\u003c/sup\u003e. The solution was deposited on 5 x 5 mm LaAlO\u003csub\u003e3\u003c/sub\u003e single crystal substrates whether by spin coating for thin films (150-250 nm) or by inkjet printing for thick films (\u0026gt; 600 nm)\u003csup\u003e\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e,\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e\u003c/sup\u003e. Subsequently, films were pyrolized and thermal treated at high temperatures. All films in Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e have been grown following a conventional thermal annealing (25\u0026deg;C/min heating ramp)\u003csup\u003e\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e\u003c/sup\u003e, except the pn-nc-thin sample, which followed a flash heating process (1200\u0026deg;C/min heating ramp)\u003csup\u003e\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e\u003c/sup\u003e. 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)\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e or by the mixing of a previously stabilized colloidal solution containing preformed nanoparticles with the TFA precursor solution (pn-nanocomposites)\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e,\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e,\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e,\u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e82\u003c/span\u003e\u003c/sup\u003e. Nanoparticle concentrations are expressed by the percentage of the molar concentration of nanoparticles with respect to the YBCO molar concentration. For example, for YBCO+8%BYTO there are 8 mols of BYTO for 100 mols of YBCO.\u003c/p\u003e \u003cp\u003e \u003cb\u003eElectric transport measurements.\u003c/b\u003e 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 \u0026micro;Ω\u0026middot;cm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Samples were trimmed into 10-100 \u0026micro;m narrow bridges with lengths of 200-400 \u0026micro;m by standard lithography with a Micro-Writer from Durham Magneto Optics LTD and wet etching in H\u003csub\u003e3\u003c/sub\u003ePO\u003csub\u003e4\u003c/sub\u003e. The current was applied parallel to the a-b plane, always perpendicularly to the magnetic field which was rotated with the angle θ from the c-axis (0\u0026deg;) to the ab-plane (90\u0026deg;), ensuring maximum Lorentz force configuration. Critical currents were determined for a 10 \u0026micro;V/cm electric field. 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 \u003cb\u003efigure S6\u003c/b\u003e in the supplementary information) and a temperature control system operating in the 4.2-60 K range.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMicrostructural characterisation.\u003c/b\u003e Nanostrain (ε) was quantified along the c-axis by analysing the symmetric (00l) 2ϴ Bragg diffraction integral breadth acquired in a Siemens D5000 diffractometer using Cu K\u003csub\u003eα\u003c/sub\u003e radiation. Following the Williamson-Hall method\u003csup\u003e\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e\u003c/sup\u003e, ε was obtained following the equation: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }^{2}{cos}^{2}\\left(\\vartheta \\right)=\\frac{{\\lambda }_{\\alpha 1}}{{L}_{\\perp }}+16{\\epsilon }^{2}{sin}^{2}\\left(\\vartheta \\right)\\)\u003c/span\u003e\u003c/span\u003e, 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\u003csub\u003eα1\u003c/sub\u003e is the wavelength of the Cu K\u003csub\u003eα1\u003c/sub\u003e radiation and L\u003csub\u003e\u0026perp;\u003c/sub\u003e 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 filter TRIDIEM 866 ERS and a monochromator.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eData availability\u003c/h2\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding authors on reasonable request.\u003c/p\u003e\n\u003ch2 id=\"isPasted\"\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThe authors acknowledge financial support from Spanish Ministry of Economy and Competitiveness through the \u0026ldquo;Severo Ochoa\u0026rdquo; Programme for Centres of Excellence in R\u0026amp;D (Grant No. SEV-2015-0496), ULTRASUPERTAPE (ERC-2014-ADG-669504), EUROTAPES project (FP7-NMP-Large-2011-280432), the CONSOLIDER Excellence Network (Grant No. MAT2015-68994-REDC), COACHSUPENERGY project (Grant No. MAT2014-56063-C2-1- R and SuMaTe RTI2018-095853-B-C21, co-financed by the European Regional Development Fund), and from the Catalan Government with Grant No. 2014-SGR-753 and 2017-SGR-1519. Authors also thank the network collaboration of EU COST action NANOCOHYBRI CA16218. We also acknowledge the Scientific Services at ICMAB and Z. Li and P. Cayado for the growth of the studied samples. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida.\u003c/p\u003e\n\u003ch2\u003eAuthor Contributions\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eF.V., A.P. and T.P. designed the experimental study. F.V. performed the main experimental work and analysed the data. D.A., A-M.C., J.J. and F.V. prepared the experimental setup and performed the measurements at very high magnetic fields. B.M. performed and analysed the STEM observations. \u0026nbsp;F.V. and T.P. prepared the manuscript with contributions from co-authors. All authors contributed to the scientific discussion.\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eParanthaman, M. P. \u0026amp; Izumi, T. High-Performance YBCO-Coated Superconductor Wires. \u003cem\u003eMRS Bull. \u003c/em\u003e\u003cstrong\u003e29\u003c/strong\u003e, 533\u0026ndash;541 (2004).\u003c/li\u003e\n\u003cli\u003eLarbalestier, D., Gurevich, A., Feldmann, D. M. \u0026amp; Polyanskii, A. High-T\u003csub\u003ec\u003c/sub\u003e superconducting materials for electric power applications. \u003cem\u003eNature\u003c/em\u003e\u003cstrong\u003e414\u003c/strong\u003e, 368\u0026ndash;377 (2001).\u003c/li\u003e\n\u003cli\u003eShiohara, Y., Yoshizumi, M., Takagi, Y. \u0026amp; Izumi, T. Future prospects of high T\u003csub\u003ec\u003c/sub\u003e superconductors-coated conductors and their applications. \u003cem\u003ePhys. 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Mater.\u003c/em\u003e\u003cstrong\u003e2\u003c/strong\u003e, 1600161 (2016).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"coated conductors (CCs), magnetic flux, twin boundaries, YBCO films.","lastPublishedDoi":"10.21203/rs.3.rs-1138719/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1138719/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe magnetic flux pinning capabilities of YBa\u003csub\u003e2\u003c/sub\u003eCu\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e7\u0026minus;x\u003c/sub\u003e (YBCO) coated conductors (CCs) vary strongly between different regions of the magnetic field-temperature (H-T) diagram and with the orientation of the magnetic field (θ). Here, we determine the optimal pinning landscape for a given H-T region by investigating the critical current density J\u003csub\u003ec\u003c/sub\u003e(H,θ,T) in the 5-77 K temperature range, from self-field to very high magnetic fields (35 T). Our systematic analysis reveals the best directions to target to artificially 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 fields and low temperatures. Moreover, we demonstrate that twin boundaries preserve a high pinning energy in thick YBCO films, which is beneficial for the pinning performance at high magnetic fields and high temperatures.\u003c/p\u003e","manuscriptTitle":"Optimal Vortex Pinning in YBa2Cu3O7-x Superconducting Films Up to Very High Magnetic Fields","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-01-05 15:53:10","doi":"10.21203/rs.3.rs-1138719/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"communications-materials","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"commsmat","sideBox":"Learn more about [Communications Materials](https://www.nature.com/commsmat/)","snPcode":"","submissionUrl":"","title":"Communications Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Communications Series","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d0e5236b-f798-4888-9c54-9d51a8c114f4","owner":[],"postedDate":"January 5th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":9541904,"name":"Materials Theory and Modeling"},{"id":9541905,"name":"Electronic Materials and Devices"}],"tags":[],"updatedAt":"2022-07-14T12:42:20+00:00","versionOfRecord":{"articleIdentity":"rs-1138719","link":"https://doi.org/10.1038/s43246-022-00266-y","journal":{"identity":"communications-materials","isVorOnly":false,"title":"Communications Materials"},"publishedOn":"2022-07-08 04:00:00","publishedOnDateReadable":"July 8th, 2022"},"versionCreatedAt":"2022-01-05 15:53:10","video":"","vorDoi":"10.1038/s43246-022-00266-y","vorDoiUrl":"https://doi.org/10.1038/s43246-022-00266-y","workflowStages":[]},"version":"v1","identity":"rs-1138719","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1138719","identity":"rs-1138719","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}