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 landscapes54–56; all films have an oxygen doping state close to optimal doping, deduced from the temperature evaluation of the normalized resistivity57.
Here, we consider the identification of defect contributions according to angular pinning performance and the associated pinning strength, as described previously58. As explained in detail in figure S2, in CSD YBCO we find, typically, isotropic defects (0D and 3D) such as copper-oxygen vacancy clusters38,59, small nanoparticles, or nanostrain generated in partial dislocations surrounding the stacking faults35. On the other hand, we observe planar anisotropic defects such as stacking faults parallel to the a-b planes60 or twin boundaries parallel to the c-axis61,42. 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 pinning62, 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 Jc(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 Jc(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 Jc(T) (i.e., Jcwk(T) and Jcstr(T), respectively). Whereas weak pinning centres yield a fast temperature decay of the Jc in the collective pinning model65, strong pinning centres account for a smoother temperature decay in the Bose glass model24. In a first approximation and neglecting interactions between both types, we can describe Jc(T) by the direct sum28:
J c(T)=Jcwk(T)+Jcstr(T)= Jc(0)wk exp(-T/T0) +Jc(0)str exp(-3(T/T*)2), (1)
where Jc(0)wk and Jc(0) str refer to contributions at 0 K, whereas T0 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 Jc(H,T) representation illustrates an enlargement of the (reddish) high critical current density region (> 1 MA/cm2) 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 Jc is visible at lower H-T values for H||c, but not for H||ab.
The enlargement of the reddish high Jc(H,T) region is concurrent with the shift to larger magnetic fields of the µ0H*(T) curve, where µ0 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 defects66,67 - and the vortex-vortex interaction regime. Therefore, H* is related to the density of defects. Here, it is defined as in other works58,68 by the equation Jc(µ0H*) = 0.9Jc(sf), where sf stands for self-field. Figure 2 shows a comparison between µ0H*(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 (Jciso) and anisotropic (Jcaniso) contributions of the Jc(H) curves shown in figure 1 we applied the Blatter scaling approach28,69 to angular Jc(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 Jciso/Jc in the H-T diagram (equivalent to 1- Jcaniso/Jc 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 µ0H*(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 Hirr(T) for the nanocomposite, especially at H||c, which can be associated to a lower pinning performance of the anisotropic defects (mainly twin boundaries42).
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 nanocomposites35. Hence, we macroscopically measured the nanostrain (ε) for each sample by XRD analysis, following the Williamson-Hall method70.
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 Jcaniso(θ) ab-peak; we approximated its half width-half-maximum with the trapping angle θT that limits the vortex staircase regime63,71 (θT 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 θT versus µ0H* for Jc(θ) curves measured at a field of 9 T and temperatures of 77, 50 and 5 K, and for Jc(H) curves measured for both H*||c and H*||ab. The linear trend of the θT(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 θT(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 Jc(T) curves obtained for a wide range of magnetic fields with Jc(θ) curves obtained at specific temperatures, and applied the Blatter scaling approach28,69. Thus, we determined the Jciso(T) and Jcaniso(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 Ba2YTaO6 (BYTO), BaZrO3 (BZO), Y2O3 (YO), or BaHfO3 (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 (<ØNP>) and density (σNP), stacking fault (SF) average length (<dSF>) and density (λSF) and main electrical transport properties – Tc, ΔTc (transition width), Jcsf,77K and Hirr77K,H||c – of each of the samples we analysed.
All samples display Tc > 88 K, ΔTc < 6 K, and Jcsf,77K ≈ 2-4.5 MA/cm2. We evaluated Hirr77K,H||c from Jc(H) measurements fulfiling the relation Jc(Hirr)=10−4Jc(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 nNP is the number of nanoparticles and AYBCO 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. σNP ranges: low (σNP < 1E-4 nm−2), medium (1E-4 nm−2 < σNP < 5E-4 nm−2), high (σNP > 5E-4 nm−2). λSF ranges: low (λSF < 0.1 nm−1), medium (0.1 nm−1 < λSF < 0.15 nm−1), high (λSF > 0.15 nm−1).
NAME
|
COMPOSITION
|
t (nm)
|
Tc (K)
|
ΔTc (K)
|
Jcsf,77K (MA/cm2)
|
µ0Hirr77K,H||c (T)
|
ε (%)
|
<ØNP> (nm)
|
σNP
(nm−2)
|
<dSF> (nm)
|
λSF
(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 Jc(T) can be described by the linear sum of three contributions:
J c(T)=Jciso−wk(T)+Jciso−str(T)+ Jcaniso−str(T)=
=Jc(0)iso−wk exp(-T/T0) +Jc(0)iso−str exp(-3(T/T*iso−str)2)+ Jc(0)aniso−str exp(-3(T/T*aniso−str)2), (2)
where the Jcstr contribution from equation (1) is substituted now by the sum of the isotropic-strong (iso-str) contribution Jciso−str and the anisotropic-strong (aniso-str) contribution Jcaniso−str (corresponding directly to Jcaniso); the isotropic-weak (iso-wk) contribution Jciso−wk corresponds to the overall Jcwk 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 T0, T*iso−str, and T*aniso−str, and the contributions at 0 K Jc(0)iso−wk, Jc(0)iso−str, and Jc(0)aniso−str. T0, 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 kBT, where kB is the Boltzmann constant. Instead, Jc(0)iso−wk, Jc(0)iso−str, and Jc(0)aniso−str are the Jc 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 µ0H*(0K) obtained in Jc(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., T0= 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 faults42,61, also provoking a decrease of the irreversibility line Hirr. In contrast, the pristine sample shows the highest T*aniso−str values and largest Hirr (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 Jc, 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 µ0H*iso−wk(0K), specially the pn-nc-thin, which is ascribed to a high density of Cu-O vacancy clusters hosted in the stacking faults38,59. The best Jc(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 T0 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 Jc(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 Jcaniso−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 Jc 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 Jc of nanocomposites in comparison to pristine films, especially at high temperatures due to the high T*aniso−str values developed by pristine films. The Jc(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 Jc associated with its lower irreversibility field.
We observe in figure 8(a) that although the pn-nc-thin sample exhibits a fast Jc(H) decay at 30K with lower Jc 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 Jc 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 applications18 refrigerated with cryocooler technology21, nanocomposites also offer substantially larger Jc 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 Ic values in comparison with the pristine thin film up to 35 T, despite of their lower Jc values. This reinforces the need to further understand and optimize the growth of thick films (using inkjet printing in this case73). 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 Ic 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 Fp(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 Fp value at each condition: the thick pn-nanocomposite provides 45 GN/m2 at [50K,15T], the pristine thick film 4 GN/m2 at [50K,35T] and the thin pn-nanocomposite 0.55 TN/m2 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 T0, T*iso−str and T*aniso−str and the Jc contributions at 0 K, Jc(0)iso−wk, Jc(0)iso−str and Jc(0)aniso−str, in figure 10. Interestingly, figure 10(a) shows that T0 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 Jc(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/m2 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 Jc(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 Jc(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 Ic 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 θT to accommodate vortices by stacking faults. Below the crossover magnetic field of about 20 T, where Jc 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 Jc 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 T0, 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 Jciso are obtained for effective anisotropies (γeff) 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 γeff 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.