Large enhancement of the in-field critical current density of YBCO coated conductors due to composite pinning landscape

Proton irradiation has been extensively used to enhance the vortex pinning in superconductors [39, 40]. Earlier TEM work on YBCO showed that p⁺ irradiation produces a hierarchy of randomly distributed defects with sizes ranging from atomic scale (Frenkel pairs), mostly on the O and Cu sites, to clusters that are 2–5 nm in diameter [35, 48, 51]. A typical TEM image for a p⁺-irradiated sample [48] similar to the pieces used in this study is shown in figure 1(b). Ultimately, the reason for the effectiveness of p⁺ or other light-ion irradiations (such as O) is that pinning in the pristine AMSC CC is dominated by the Dy₂O₃ NPs, which are particularly effective at low fields where the intervortex distance is of the order of, or larger than, the average distance among NPs. At higher H there are not enough NPs and their effectiveness decreases. At near-optimum p⁺ doses the densities of the smaller irradiation-induced defects are orders of magnitude higher than that of the NPs, allowing the irradiation induced defects to remain effective pinning centers at high H.

Figure 2 shows the dose dependence of J_c in our proton-irradiated CC sample. Due to the competition between increasing pinning force and decreasing superconducting volume fraction, a non-monotonic dependence of J_c on irradiation dose, i.e. pinning sites concentration, is theoretically expected [61, 62]. This behavior is observed in figure 2. We found that, although J_c reaches its maximum at a dose that is temperature and field dependent, a dose of ∼18 × 10¹⁶ p⁺ cm⁻² is a good compromise over a broad T and H range that is technologically relevant. Note that this relatively high dose of irradiation only induces a modest reduction of T_c. As shown in figure 3(a), the suppression rate of T_c is only 0.2 K per 10¹⁶ p⁺ cm⁻², which is much less than in single crystals. Also, no broadening appears in the magnetization curves around T_c (figure 3(b)) evidencing the homogeneity of the irradiations. A possible reason for this small suppression rate of T_c in coated conductors is that the numerous big defects and nanoparticles, which are already present in the pristine sample, act as sinks for the mobile point defects induced during irradiation. Isolated point defects are indeed the type of defects with the strongest impact on T_c (pair-breaking from electronic scattering in a d-wave), whereas the large columnar defects and clusters are much bigger and thus are weaker scattering centers, i.e. less 'pair-breaking' [63].

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Figure 4 shows J_c vs. H at four temperatures, as obtained from magnetization measurements for a pristine piece of CC (black squares) that was subsequently irradiated with Au (red circles) then protons (blue diamonds), as well as a piece from the same batch that was irradiated to 18 × 10¹⁶ p⁺ cm⁻² (green triangles). This last piece is the one that was studied after repeated irradiation in figure 2. We first note that at T= 5 K (figures 4(a)) and (H)∼ 0, the J_c of this CC is higher than the J_c reported for YBCO single crystals irradiated at any conditions. We also observe the typical fast decay in J_c(H, T) as H or T are increased.

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In figures 5(a–d) we plot the field dependence of the J_c enhancement factors, ${J_c}\left( {H,T} \right)/J_c^{pristine}\left( {H,T} \right)$ for the same temperatures as in figure 4 so as to facilitate the comparison of the effectiveness of proton, gold and gold + proton irradiations. Firstly, let us consider the optimum 4 MeV p⁺ irradiation: from figures 4(a–c) and 5(a–c), we see that for T ≤ 50 K the effect goes from detrimental to beneficial (i.e. J_c increases as compared to the pristine sample) above a crossover field H_cr, with µ₀ H_cr ∼ 0.6 T at 5 K (figures 4(a) and 5(a)), increasing to ∼1 T at 50 K (figures 4(c) and 5(c)). For T = 77 K, the effect of the (optimum) p⁺ irradiation is detrimental at all fields (figures 4(d) and 5(d)). This suppression of J_c at low H following p⁺ irradiation is likely caused by competing (as opposed to synergistic) pinning effects. Creep studies show that such competition arises at least in part from faster creep due to lower activation energies following irradiations [51].

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Now, let us consider the case of Au irradiation. Columnar defects (CDs) produced by swift heavy-ion irradiation are the most effective pinning centers for H||CDs and below the matching field (B_φ), because the whole length of the cores of all the vortices can be trapped [45]. They also retain their effectiveness up to higher T than point defects, due to their larger pinning energy. For both reasons, they are natural candidates to complement the effect of the p⁺ irradiations.

As a first step in our combined irradiation landscape engineering, we irradiated our sample with 250 MeV Au ions. We selected this relatively low energy heavy-ions to create CDs that are splayed and inhomogeneous along their length, because these features are known to produce the beneficial effect of slowing down the vortex dynamics due to low-energy kink excitations [15, 64, 65], as will be described below. The presence of CDs with these characteristics is clearly observed in figures 1(c and (d)), which were obtained on the piece of CC used in this study after all irradiations and measurements were completed. The diameter of the CDs is ∼7–8 nm, somewhat larger than the diameter of the vortex cores, $2\sqrt 2 {\xi _{ab}}\left( T \right)$, which is ∼5 nm for YBCO at T ≪ T_c, making them effective pins (here ξ_ab is the in-plane coherence length). We chose a dose-equivalent matching field B_φ = 3 T which is somewhat lower than the optimum B_φ for J_c enhancement reported in the literature for YBCO [66], and is also in the range of target magnetic fields for rotating machinery applications [1].

The red symbols in figures 4 and 5 show J_c and ${J_c}/J_c^{pristine}$ respectively, after the 250 MeV Au ions irradiation. The dissimilar effects of the p⁺ and Au irradiations are apparent. First, for T ≤ 27 K the Au irradiation produces no detrimental effect at low H; in fact, there is even a small increase in J_c(H= 0, T= 5 K) (figures 4(a, b) and 5(a, b)). For T= 50 K a slight deterioration occurs at low field, but it is less pronounced than for p⁺ and H_cr is much smaller (figures 4(c) and 5(c)). For T ≤ 50 K the enhancement factor for the Au irradiation first increases with H, similarly to the p⁺ irradiation, but then maximizes at an intermediate field ∼1.5 T–2 T and, in contrast to the p⁺ case, decreases for higher fields as most CDs become occupied and vortices in between the CDs start to proliferate. At T= 5 K, the 250 MeV Au processing becomes less effective than the 4 MeV p⁺ processing at ∼4 T, i.e. just above B_φ. However, as T increases the larger pinning energy of the CDs (due to their longer length) comes into play such that at 27 K the CDs remain better up to ∼5 T, and at 50 K they remain superior all the way up to our maximum field.

The T = 77 K results (figures 4(d) and 5(d)) deserve particular consideration. First, the low H deterioration is as bad for Au as for p⁺ irradiation, with ${J_c}\left( {H\sim 0,T = 77K} \right)/J_c^{pristine}\left( {H\sim 0,T = 77K} \right)\sim 0.5$, and T_c suppression is also similar in both cases: 88.4 K and 87.3 K respectively, see figure 3. However, at high H the Au irradiation does improve J_c, in sharp contrast to the p⁺ case. It must be recognized that the dramatic enhancement factors (>10) at high H are a consequence of the very small J_c of the pristine sample. Nevertheless, a critical current density J_c(H= 4 T, T= 77 K) ∼0.1 MA cm⁻² is encouraging and would enable applications of CC refrigerated by liquid N₂.

The fact that the Au irradiation has almost no effect at H∼ 0 and low T is not trivial and clearly evidences that pinning is not additive. At low fields, a material may have enough strong pinning centers to pin all the vortices very effectively. In a simple scenario, adding weaker defects will not create better pinning configurations; vortices will just 'ignore' them and J_c will be unaltered. The rich landscape of the pristine CC contains a small density of pinning centers (or combinations of them) that are very strong. As H increases those few defects become saturated and the much larger density of CDs progressively increase their fractional contribution to J_c, as we observed. We know, however, that this cannot be the complete picture, as, in contrast to Au irradiation, p⁺ irradiation decreases J_c at H ∼ 0 as already discussed.

After examining the effect of proton and Au irradiation independently, we combined both: the piece irradiated with Au was also irradiated with 4 MeV p⁺. We selected a dose of 4 × 10¹⁶ p⁺ cm⁻², well below the optimum for p⁺ irradiation alone to avoid excessive damage, but large enough to produce significant J_c enhancement in a pristine CC, as shown by the right dashed line in figure 2. The small defect clusters created by this second irradiation are visible in figure 1(d). Note that it is well-known that p⁺ irradiation also creates point defects, but these are not visible in these TEM images. The resulting J_c(H, T) and ${J_c}\left( {H,T} \right)/J_c^{pristine}\left( {H,T} \right)$ curves are shown as blue diamonds in figures 4 and 5, respectively. It is apparent that the mixed landscape created by this combined irradiation produces better performance than either the 250 MeV Au or the 4 MeV p⁺ alone. The yellow colored areas in figure 5 highlight the additional synergistic J_c enhancement produced by the combined irradiations, as compared to either of the individual ones. Below ∼1 T and for all T, the J_c resulting from the combined irradiation process is marginally smaller than the Au result, but for µ₀ H > 1 T and T ≤ 50 K it produces clearly stronger pinning. As seen in figure 5(b), for T = 27 K and fields in the 4–6 T range, a regime particularly relevant for superconducting rotatory machines, the combined irradiation exceeds the effect of the individual ones by roughly a factor of two. This unforeseen synergetic effect is the central result of this study. In figure 2, one can also see that at 27 K/4 T a proton irradiation dose of 4.10¹⁶ p cm⁻² should yield J_c ∼ 3.5 MA cm⁻² and from figure 4(b) one can see that the B_χ = 3 T Au irradiation also yields J_c ∼ 3.8 MA cm⁻² at 27 K/4 T. Hence, the value J_c ∼ 5.1 MA cm⁻² of the combined irradiations (B_χ = 3 T Au + 4.10¹⁶ p cm⁻²) is about 40% higher than either individual irradiations. We believe this synergy stems from the concept of a mixed pinning landscape [28, 48], in which the randomly distributed localized defects from proton irradiation catch stray vortices and suppress vortices jumping between CDs (for instance by hampering double kinks expansion, cf part 3.3). For T = 77 K, the combined irradiation just replicates the Au irradiation result, which confirms the ineffectiveness of p⁺ irradiation induced defects at 77 K, as already observed in figure 2.

In summary, at intermediate magnetic fields and all temperatures in figure 4, the blue curve of combined Au and proton irradiation is above all others thanks to the synergy between defects. Then at high magnetic field and low temperature the best pinning centers are the numerous clusters and Frenkel pairs generated by proton irradiation which can accommodate a large number of vortices [48], whereas the columnar defects from gold irradiation are saturated with vortices above the matching field of 3 T. Hence, in figure 4 the green curve (18 × 10¹⁶ p⁺ cm⁻²) shows higher J_c than the red curve (Au, B_φ = 3 T) at high magnetic field and low (a) or intermediate (b) temperature. At high temperature (77 K, figure 4(d)) however, the defects from proton irradiation are too small and weak to pin vortices efficiently whereas the long columnar defects retain their strong pinning properties.

Finally, to confirm that the CDs produced by Au irradiation indeed act as correlated pinning centers in our samples, we performed angular-dependent transport studies of J_c on a bridge patterned from the same CC batch. Figure 6 shows J_c vs. the angle between H and the c-axis (Θ), at T = 27 K and µ₀ H = 6 T, for that bridge before and after irradiation with 250 MeV Au to a dose equivalent B_φ = 3 T. In the pristine state, J_c(Θ) shows the typical anisotropy of AMSC CCs, with a large maximum centered at H||ab associated with correlated pinning by stacking faults, and a small c-axis peak due to twin boundaries. After irradiation, a much larger c-axis peak demonstrates the correlated pinning of the artificial CDs.

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Additional information about the pinning landscape can be obtained from the vortex dynamics, in particular from the normalized flux creep rates [67–69] S(T, H). Such information is complementary because of the quite different dependences of J_c and S on disorder. The former is very sensitive to the details of the pinning landscape, and consequently J_c values differing by orders of magnitude, as well as countless variations of the J_c(T, H, Θ) functional dependences, have been reported for YBCO. In contrast, creep rates in YBCO exhibit much less variability, with absolute values that are similar in all cases and functional dependences that typically fall into one of a few categories.

The reason for this is that S(T, H) is mainly defined by the type of the dominant depinning excitations, rather than by the quantitative values of the pinning parameters [68]. First, the dynamics can be either glassy or plastic [70–72]. In the first case the size of the excitation (either a vortex segment or a vortex bundle) diverges in the limit of J → 0, and consequently the flux creep activation energy diverges as U(J) ∝ U_p × (J_c/J)µ, where U_p(T, H) is the pinning energy and µ > 0 is the glassy exponent. In the second case, in contrast, the size and the activation energy of the excitation remain finite for J → 0 and the low J behavior U(J) ∝ U_p ×(J_c/J)^p is characterized by a plastic exponent p< 0. Within each category, different excitations produce different exponents. For instance, in collective pinning due to random point disorder: µ = 1/7, 3/2 or 7/9 depending on the regime [71]. Depinning due to the excitation of half-loops associated with CDs have [73] µ = 1. The traditional Anderson-Kim (AK) regime has [67] p = − 1. The numerical values of U_p and J_c have limited influence on the values of S. Mathematically, this stems from the fact that S is defined by logarithmic derivatives. These values determine the crossovers among creep regimes in the T-H phase diagram.

Several examples of the most common flux creep regimes for YBCO are illustrated in figure 7, where S(T) at 1 T for H||c is plotted for seven samples with dissimilar pinning landscapes. We first note that, for a given T, all the samples (with the exception of sample #C, discussed below) have S values within a factor of two of each other, in spite of the fact that their J_c's span a range of almost two orders of magnitude, particularly at high T.

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At low T up to ∼10 K, all samples have similar creep rates, with S(T) increasing monotonically with T. This is the AK regime in which, as we have shown recently [74], creep for all YBCO samples is close to the universal lower limit given by S_AK(T) ∼ Gi^1/2(T/T_c), where Gi is the Ginzburg number. In addition, there is a nonzero S(T→0) extrapolation that is frequently attributed to a T-independent quantum creep component S_Q. At high T (above ∼60 K), S(T) for all samples increases fast with increasing T, signalling the crossover from glassy to plastic creep [72] and the approach to the irreversibility line.

At intermediate T (between ∼10 K and ∼60 K), there are basically three types of S(T) curves. Many samples exhibit a large T-independent 'plateau' arising from the glassy 3D collective pinning regime of vortex bundles [75], S ∼ [µln(t/t₀)]⁻¹, where t₀ is a microscopic attempt time. Examples for this behavior are seen in samples A and E in figure 7, both of which have pinning dominated by random distributions of point defects or small clusters, although the density of such defects is far greater in E than in A. The second category consists of samples with CDs, which develop a maximum in S(T) at intermediate T arising from the expansion of double kinks [64, 65, 68, 73, 76]. In the case of perfectly parallel CDs, initial double-kink expansion should not be glassy [77] (because the kinks have finite sizes) and should turn glassy with a low µ ∼ 1/3 (at low H) as J decreases [64, 65, 73, 76, 77]. The result is a very large S(T) peak as in the case of the single crystal C, where CDs with negligible splay were produced by very energetic heavy-ions (1 GeV Au) [65]. A number of strategies can be used to reduce the height of the technologically undesirable S(T) peak by moderating the double-kinks expansion. The first option is to introduce splay among the CDs [64, 65] to geometrically constrain the kinks propagation. An example of this situation is realized in sample B, a single crystal with splayed CDs produced by less energetic ions (0.6 GeV Sn). The double kinks peak is still clearly visible, but it is smaller than in A. The second option is the incorporation of localized defects in between the CDs [15] to pin the kinks. Sample F, a film grown by Pulsed Laser Deposition containing splayed self-assembled BaZrO₃ nanorods as well as randomly distributed nanoparticles, is an example of combining both strategies, and consistently the height of the peak is even smaller than in B. The third category of S(T) curves are MOD films with pinning dominated by randomly dispersed nanoparticles [17, 51, 72], which exhibit a minimum in S(T) at low H and intermediate T, as our pristine film D (the minimum is more pronounced al lower H, see figure 6 in Eley et al [51].). In several previous studies, we have observed that irradiation of the MOD films with light particles that introduce point defects and small clusters increases S at low H and intermediate T, eliminating the minimum and recovering the plateau (sample E) [48–51].

Finally, curve G in figure 7 corresponds to our combined-irradiation CC. These data show the characteristic S(T) peak due to CDs, but the height is smaller than for sample B. Similarly to the case of sample F, this strongly reduced double-kink expansion, which is technologically desirable, is due to the combination of the two factors discussed above, namely, CDs that are splayed and inhomogeneous along their length as well as the presence of p-irradiation induced additional defects to pin the kinks.

Figure 8 shows S(T) curves for the combined irradiation sample at several fields, as well as the µ₀ H= 1 T curve for the pristine film D shown in figure 7 (dashed red curve). The double-kink peak is expected to be highest at the lowest fields, when vortex-vortex interactions can be neglected and each vortex pinned in a CD has plenty of nearby unoccupied CDs where kinks can propagate. This is the condition where the initial non-glassy and later glassy with µ = 1/3 dynamics is expected [64, 65, 73, 76, 77, 78]. It has been shown [64] that splay should increase the glassy exponent to µ ∼ 0.6, thus reducing the height of the peak from S ∼ [µln(t/t₀)]⁻¹ ∼0.11 to ∼0.05. Unfortunately, there are no theoretical estimates for µ in the presence of localized disorder in between the CDs, nor of how both effects would combine. In any case, we can take the maximum S ∼ 0.036 for µ₀ H= 0.3 T to estimate µ ∼ 0.9. Vortex-vortex interactions will stiffen the lattice, reducing S. Interactions will increase with increasing T, due to the increase of the transverse vortex localization length and the proliferation of kinks, producing the observed decrease in S(T) with increasing T after it peaks, see figures 7 and 8. Increases in H will also increase the interactions, producing two effects: the S(T) peak will shift to lower T and decrease in height. Both expectations are clearly observed in figure 8; in particular, as shown in the inset, the peak vanishes above B_φ = 4 T when all CDs are occupied and individual vortex double kink propagation stops (and are replaced by vortex bundle excitations).

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Comparison of the µ₀ H= 1 T curves for the pristine and irradiated CCs in figure 7 (curves D and G) and figure 8 shows that they are similar for T ≤ 15 K. This is fully consistent with the observation that the double irradiation does not significantly affect J_c at low T and H, as discussed before. It is also clear that the minimum in S(T) at ∼45 K associated with NPs, well developed in the pristine sample, disappears after irradiation. This is consistent with our previous finding that, for the S(T) minimum to occur, NPs not only have to be present, they must be the dominant pinning source [51]. Finally, it is worth noticing that in figure 8, outside the T-H regions where the dynamics is dominated by double kinks or NPs, all the S(T, H) data converges into a narrow plateau at S ∼ 0.025 (light yellow band) corresponding to the 'standard' collective creep of bundles (µ ∼ 1.3), and suggesting that the dynamics is dominated by point and small-clusters defects.