You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


Although the critical temperature (*T*~c~) and upper critical field (*H*~c2~) of high temperature superconductors are extremely high, superconductors only become technically useful at a much lower field-temperature boundary, called the melting, or irreversibility, line. This is due to the appearance of the vortex liquid phase, one of the unique characteristics of these superconductors. In this liquid phase, superconductors have finite resistivity behaving much like a normal metal, thus the need to move the melting line to higher fields/temperatures. Defects can move the melting line, with random point-like defects[@b1] pushing it down and correlated defects moving this line up. The positive effect of correlated disorder is restricted to an angular range near the defects' orientation, and usually only up to a characteristic field related to the density of the defects (the matching field, typically a few tesla)[@b2][@b3][@b4][@b5]. Pushing up this upper limit is both technologically and scientifically important; given the interest in high magnetic field magnets. This requires finding ways to immobilize vortex densities much higher than the highest defect density that can be introduced without compromising the material integrity.

Recently, a third kind of disorder (neither correlated nor point-like) has been demonstrated to be effective at improving both *J*~c~ and *H*~irr~ at a very wide range of field orientations[@b6][@b7][@b8][@b9][@b10][@b11][@b12][@b13][@b14]. A deeper and more quantitative understanding of the effect of nanoparticles in a mixed pinning landscape (as they often work together with correlated defects) is necessary for assessing the potential of Cu-based superconducting wires for applications at high fields[@b15].

In particular, it is important to establish the behavior of *H*~irr~ when the vortex density is much higher than that of the defects. Most REBa~2~Cu~3~O~*y*~ (REBCO) films (RE = rare earth) with self-assembled nanorods[@b4][@b5] and YBCO crystals with columnar defects[@b2][@b3] show improved *H*~irr~ and a "kink" in the vortex liquid-glass transition for **H**\|\|*c*. This occurs when vortices stop populating columnar defects and start filling interstitial positions, at a density related to that of the defects at the so-called matching field (μ~0~*H*~ϕ~). These findings lead to the validation of the simple argument that once the pinning centers have been outnumbered by vortices, their effect on increasing *H*~irr~ decreases or may even be washed out. However, this idea overlooks the fact that vortices are interacting elastic objects, which form a lattice with different degrees of order depending on the underlying pinning landscape. The understanding of the physical system adds a layer of complexity when pinning centers of different dimensions (point defects, lines, planes or nanoparticles) are taken into account.

In this paper, we show that the combination of planar twin boundaries (TBs) and a higher density of three dimensional (3D) nanoparticles (NPs) increases *H*~irr~ at up to 60 T. In the case of TBs there is a clear signature of the matching field at very low fields (0.5 T) but nevertheless, their presence continues to increase *H*~irr~ up to 60 T. The effect of the NPs is also seen up to 60 T with the additional benefit of their being effective in the entire angular range. We find no signs of saturation in the improvement of *H*~irr~ up to 3 wt% BaZrO~3~ (BZO) added to REBCO wire up to the highest field measured (60 T), and obtain record high values.

Results
=======

The results shown are distributed as follows. We start by explaining the growth methods and show superconducting and microstructural studies. We find that the use of (Y,Gd)BCO is beneficial (as compared to YBCO) and that the addition of BZO NPs does not degrade the general properties, and increases twin boundary density. Then we focus on transport measurements in DC and pulsed fields as a function of temperature and field orientation. For the upper critical field, (*H*~c2~), the addition of NPs produces no significant changes. For *H*~irr~, the scenario is complex and depends on the field magnitude and orientation. For **H**\|\|*c*, at low fields, twin boundaries dominate the irreversibility line with a matching field observed and a peak as function of field orientation. As the field increases the effects of TBs are less prominent as nanoparticles compete in the vortex localization. At high fields, NPs and TBs cooperate to enhance the *H*~irr~. At intermediate angles (e.g. **H**\|\|45°) nanoparticles produce the greatest increase in *H*~irr~, showing no saturation up to the highest fields measured. Furthermore, at high fields we obtain a constant improvement of 25% with respect to YBCO films. For **H**\|\| *ab*, the changes due to NPs addition are small as compared to other orientations.

Uniformly dispersed BaZrO~3~ nanoparticles in (Y~0.77~Gd~0.23~)Ba~2~Cu~3~O~*y*~ wires
-------------------------------------------------------------------------------------

The samples used in this study were 0.5 μ thick films of standard YBCO, (Y~0.77~Gd~0.23~)Ba~2~Cu~3~O~*y*~ ((Y,Gd)BCO) and BZO-doped (Y,Gd)BCO ((Y,Gd)BCO+BZO) derived from the metal organic deposition (MOD) process, grown on metal substrates. The content of BZO in the films was 1--3 wt%. The film microstructure was studied by several techniques (see Methods). The planar view transmission electron microscopy (TEM) images of standard YBCO, (Y,Gd)BCO with 1wt% BZO (+1BZO) and 3wt% BZO (+3BZO) wires are shown in [Fig. 1a--c](#f1){ref-type="fig"}, respectively. For clarity, the corresponding bottom panels in those figures show schematics of the main defects. All films have a low density (∼0.1 × 10^21^/m^3^) of large RE~2~Cu~2~O~5~ (225) precipitates (shown as open circles in the bottom panels) formed during REBCO crystallization from the precursors containing BaF~2~, RE~2~Cu~2~O~5~ and CuO. In both +1BZO and +3BZO wires, BZO NPs (modal size ∼23 nm) are randomly distributed and uniformly dispersed. The average density of these nanoparticles was determined to be *n* = 2.9 × 10^21^/m^3^ for +1BZO, *n* = 7.1 × 10^21^/m^3^ for +2BZO (not shown), and *n* = 13 × 10^21^/m^3^ for +3BZO wires, respectively. Note that the greater than linear dependence of *n* on BZO% derives from the slight decrease in size of the NPs with increasing BZO density. In addition to the uniformly randomly distributed 3D defects (BZO NPs), all samples, including the standard YBCO, contain high densities of two types of planar (2D) defects, namely *c*-axis correlated TBs ([Fig. 1a--d](#f1){ref-type="fig"}) and stacking faults (SFs) parallel to the *ab* plane ([Fig. 1e](#f1){ref-type="fig"}). In some previous studies of MOD REBCO with nanoparticles, it was observed that the SFs cut into the TBs, resulting in discontinuous short length TBs[@b14]. In contrast, although our +3BZO wire has a high density of SFs as shown in [Fig. 1e](#f1){ref-type="fig"}, the TBs remain connected from the bottom to the surface ([Fig. 1d](#f1){ref-type="fig"}), indicating that the TBs in the BZO NP-doped wire are *c*-axis correlated pinning centers.

[Table 1](#t1){ref-type="table"} shows a summary of the crystallographic and superconducting properties for the YBCO, (Y,Gd)BCO, +1BZO, +2BZO and +3BZO films. No decrease in *T*~c~, or increase of *δω* or *δϕ* is observed for the films with BZO inclusions. The only difference found is positive, being that films with Y,Gd have higher *T*~c~ and *self-field J*~c~(*J*~c~^s.f.^) than the YBCO film, consistent with good crystallinity (unchanged *δω, δϕ*). The *J*~c~^s.f.^ values of the +3BZO film at 65 and 77 K are 12.5 and 4.0 MA cm^−2^, respectively. These *J*~c~^s.f.^ values are almost as high as those of nanocomposite MOD-YBCO thin films on a single crystal substrate[@b6]. The fact that we maintained (or even improved) *J*~c~^s.f.^ and *T*~c~ after adding defects is significant given that in some cases, for films grown by pulsed laser deposition (PLD), *T*~c~ and *J*~c~^s.f^ decreased with increasing BZO content due to poor crystallinity, local strain and oxygen deficiency near second phases[@b16]. The difference in *T*~*c*~ and *J*~c~^s.f^ behavior with BZO% between MOD and PLD processes comes from differences in the formation mechanisms of the BZO/REBCO matrix[@b17].

Irreversibility line at low and intermediate DC magnetic fields
---------------------------------------------------------------

To investigate the influence of the density of BZO NPs on the superconducting properties of the glassy phase, we measured the irreversibility temperature *T*~irr~ (*H*,*θ*). [Figure 2a--c](#f2){ref-type="fig"} show *T*~irr~ (*θ*) at 0.5, 4 and 15 T for standard YBCO, (Y,Gd)BCO and (Y,Gd)BCO+BZO wires, where *θ* is the angle between the magnetic field and the *c* axis.

For the YBCO and (Y,Gd)BCO wires, at low magnetic fields we observe two maxima in *T*~irr~, centered at **H**\|\|*c* (*θ* = 0°) and **H**\|\|*ab* (*θ* = 90°). The peak at **H**\|\|*c* comes from *c*-axis correlated defects. The maximum at **H**\|\|*ab* originates from the electronic-mass anisotropy and the SFs. At intermediate fields (see [Fig. 2b](#f2){ref-type="fig"}), the *c*-axis peak of *T*~irr~ in both YBCO and (Y,Gd)BCO becomes very weak, but is evident again at higher fields (see [Fig. 2c](#f2){ref-type="fig"}). We note that the *T*~irr~(θ)/*T*~c~ for the YBCO and (Y,Gd)BCO wires are almost identical as shown in inset of [Fig. 2](#f2){ref-type="fig"}, which validates the use of YBCO for the comparison that we are making.

All wires with BZO NPs show an enhanced *T*~irr~(*θ*) as compared to that of the YBCO and (Y,Gd)BCO wires, and the magnitude of the *T*~irr~(*θ*) enhancement increases with increasing BZO NP content at all magnetic fields (0.5, 4 and 15 T) and at all angles. The *T*~irr~ anisotropy, *T*~irr~(\|\|*ab*)/*T*~irr~(\|\|*c*), is also smaller for the +BZO samples and decreases monotonically with BZO NP content. At low fields, the +3BZO wire exhibits nearly isotropic properties with a small (in height) *c*-axis peak. At 15 T, *T*~irr~ (*θ*) shows a small *c*-axis peak indicating a contribution from correlated pinning. This is consistent with *J*~c~(*θ*) data[@b10] at high fields where a *c*-axis peak is also found. In both cases (*J*~c~ and *T*~irr~) the *c*-axis peak height is less pronounced in samples with BZO additions, partially because of the general increase in *J*~c~ and *T*~irr~ produced by the nanoparticles.

The results in [Fig. 2](#f2){ref-type="fig"} can be interpreted as follows. At low fields, below the matching field of the TBs (μ~0~*H*~*ϕ,*TB~) given by μ~0~*H*~*ϕ,*TB~ = (*ϕ*~0~/*d*~TB~^2^), where *ϕ*~0~ and *d*~TB~ are the flux quantum and TB spacing respectively, most vortices get localized by the TBs ([Fig. 3a](#f3){ref-type="fig"}). At intermediate *H,* above μ~0~*H*~*ϕ,*TB~, the density of vortices is high enough that the TBs become "saturated", the extra vortices sit outside them and become localized by the randomly distributed NPs which are strong pinning centers ([Figs 2](#f2){ref-type="fig"}b and [3](#f3){ref-type="fig"}b). At even higher fields, once all the NPs are saturated, no elastic energy is lost by achieving pinning at the TBs, allowing for the localization effect of the TBs to be observed through the caging effect ([Fig. 3c](#f3){ref-type="fig"}), similar to what happens for the standard YBCO sample ([Fig. 2c](#f2){ref-type="fig"}).

To better determine the effects of the *c*-axis correlated defects, we measured μ~0~*H*~irr~(*T*) at low fields for different *θ* (see [Fig. 4](#f4){ref-type="fig"}). The *c*-axis irreversibility lines of the wires with and without BZO NPs exhibit a pronounced kink indicating a crossover field (see *H*~cr~ arrows). For fields smaller than μ~0~*H*~cr~, *H*~irr~ shows a rapid increase with decreasing *T*; above μ~0~*H*~cr~ the irreversibility line is closer to a linear temperature dependence. For the +3BZO wire, μ~0~*H*~cr~ is 0.55 T, which is 1.6 times higher than that of YBCO (μ~0~*H*~cr~ = 0.34 T). From TEM images, we observe that this correlates with the higher TB density found in +3BZO as compared to YBCO wires. Indeed, we obtain μ~*0*~*H*~*ϕ*,TB~ = 2.3T and 1.0T, for +3BZO and YBCO, respectively. This cross-over is remarkably similar to that observed in YBCO bulk with nanoscale TBs[@b18][@b19] and columnar defects[@b20]. For TBs and columnar defects, the cross over field is usually not observed precisely at the matching field but around 1/3-1/2 of *H*~*ϕ*~. This also correlates very well with our observation of the crossover fields with *H*~cr~/*H*~ϕ,TB~ ∼ 1/3 for samples with and without BZO NPs, namely 0.34 and 0.24 for YBCO and +3BZO, respectively. To further corroborate that the observed crossover field arises from correlated defects and is not an artifact, we confirmed that no kink is found in *H*~irr~-*T* at **H**\|\|45° (see [Fig. 4](#f4){ref-type="fig"}). Therefore, we can conclude that the array of TBs is the main source of correlated pinning at **H**\|\|*c* in our MOD REBCO wires. Note that the TBs continue to contribute at μ~0~*H* ≫ μ~0~*H*~cr~ as seen in the peak of *T*~irr~(*θ*) around **H**\|\|*c* in [Fig. 2c](#f2){ref-type="fig"} and the inset of [Fig. 5d](#f5){ref-type="fig"}.

Irreversibility lines and upper critical fields in pulsed fields
----------------------------------------------------------------

To obtain the temperature and angular dependence of μ~0~*H*~c2~ and μ~0~*H*~irr~ for the YBCO and (Y,Gd)BCO + BZO wires at even higher fields, we measured *ρ*(*T*) and *ρ*(*H*) at various *θ* values by using pulsed fields up to 60 T (see insert [Fig. 5b](#f5){ref-type="fig"}). See Methods for further details.

[Figure 5a](#f5){ref-type="fig"} shows μ~0~*H*~c2~(*T*) at **H**\|\|*c*, **H**\|\|45°, and **H**\|\|*ab*. The results demonstrate that μ~0~*H*~c2~(*T*) is remarkably similar for all samples in spite of their very different pinning landscapes. The inset of [Fig. 5a](#f5){ref-type="fig"} shows the electronic-mass anisotropy (*γ*) vs. *T* obtained from the *H*~c2~ measurements for the YBCO and (Y,Gd)BCO+BZO wires (see ref. [@b9] for details). The average values for *γ* are 5.1, 4.6 and 4.7 for the YBCO, +1BZO and +3BZO wires, respectively. Although *γ* is slightly smaller for the wires with BZO, all values are very close to 5. Further confirmation of the obtained value of *γ*, comes from the angular-dependent *H*~c2~ shown in [Fig. 5b](#f5){ref-type="fig"}. The angular dependence of *H*~c2~ can be fit very well using *Hε*(*θ*) = *H*(cos^2^(*θ*)+*γ*^-2^sin^2^(*θ*)) (see ref. [@b21]) with *γ* = 4.7, in agreement with the experimental result shown in the inset of [Fig. 5a](#f5){ref-type="fig"}. This is also in accordance with our previous work, where we reported that the μ~0~*H*~c2~(*θ*) dependence follows a single curve consistent with *γ* \~ 5 even with different additions and growth methods[@b22]. From the μ~0~*H*~c2~ data, we conclude that μ~0~*H*~c2~ is not greatly affected by the pinning landscape. It is worth noting that the value of *γ* \~ 5 is indeed smaller than the values found for YBCO single crystals[@b23][@b24], as previously noted[@b25]. The lack of sensitivity in *H*~c2~ upon increase of disorder can be found in the small coherence length of REBCO (also the reason for high *H*~c2~). The small coherence length places REBCO in the clean limit, thus making its superconducting properties less sensitive to disorder.

On the other hand, the changes in pinning landscape do influence *H*~irr~, as a clear enhancement is found for all +BZO wires compared with YBCO wire (see [Fig. 5c,d](#f5){ref-type="fig"}). [Figure 5c](#f5){ref-type="fig"} displays the μ~0~*H*~irr~-*T* at various angles for the YBCO and (Y,Gd)BCO+BZO wires. For **H**\|\|*c* and **H**\|\|45°, wires with BZO NPs show a higher μ~0~*H*~irr~(*T*) than that of standard YBCO. Furthermore, we observe that μ~0~*H*~irr~(*T*) continues to increases with higher densities of BZO NPs. For **H**\|\|*ab*, +BZO samples show a much smaller increase in μ~0~*H*~irr~(*T*).

The changes can be better understood by analyzing the *H*~irr~(*θ*) as shown in [Fig. 5d](#f5){ref-type="fig"}. Consistent with [Fig. 5c](#f5){ref-type="fig"}, the addition of BZO NPs produces a small increase near **H**\|\|*ab* and a much bigger enhancement for **H**\|\|*c* and intermediate orientations. The resulting angular dependence of *H*~irr~ for the +3BZO wire cannot be described using the electronic-mass anisotropy scaling model, unlike *H*~c2~(*θ*) or YBCO's *H*~irr~(*θ*), which do follow *ε*(*θ*) for most of its angular dependence (see [Fig. 5b,d](#f5){ref-type="fig"}). More information on the effect of the nanoparticles on *H*~irr~ can be observed in the inset to [Fig. 5d](#f5){ref-type="fig"}. In this inset we plot the difference of μ~0~*H*~irr~(*θ*)--*ε*(*θ*)μ~0~*H*~irr~ for the YBCO and +3BZO sample. For YBCO we observe that, except for the peaks around **H**\|\|*c* and **H**\|\|*ab* due to correlated disorder (TBs and SFs, respectively), over most of the angular range *H*~irr~(*θ*) can be very well described by the electronic-mass anisotropy, *γ* = 5 indicating that most of the angular dependence of *H*~irr~ can be explained by pinning arising from weak random point defects such as oxygen vacancies (with diameter in the angstrom scale ≪ 2ξ(*T*)). For +3BZO we find very similar behavior near the *ab*-plane, where it shows a peak almost identical to that of the YBCO wire indicating similar *ab*-plane correlated pinning like SFs (consistent with *H*~irr~(*T*) in [Fig. 5c](#f5){ref-type="fig"}). However, a much broader maximum is found for \|*θ*\| \< 80°. This is the consequence of the higher density of TBs coupled with the presence of strong random pinning from BZO NPs as shown in the TEM of [Fig. 1b](#f1){ref-type="fig"},c, and the schematics of [Fig. 3](#f3){ref-type="fig"}. The NPs are responsible for the increases in the wider angular range and the TBs are more effective near the *c* axis. The broad dome-shape like increase in μ~0~*H*~irr~(*θ*)--*ε*(*θ*)μ~0~*H*~irr~ due to the NPs resembles the increases found in *J*~c~ in samples with nanosized inclusions, both in YBCO and Fe-based superconductors[@b10][@b26][@b27][@b28][@b29]. The reason for this dome shape (or inverse anisotropy) is found in the fact that while NPs are randomly dispersed, they are not point defects, thus do not follow the electronic mass anisotropy scaling as point defects do[@b21]. Recently Mishev *et al.* proposed a model to explain this effect based on the relative size of the vortex core compared to the inclusion size[@b29].

The leveling off observed in *H*~irr~(*θ*) due to nanoparticles translates into an smaller ratio of *H*~irr~(\|\|*ab*)/*H*~irr~(\|\|*c*), with values of 2.9 for +3BZO as compared to 5.0 for YBCO. The decrease in the *H*~irr~ ratio (also found in *J*~c~) has been analyzed using an 'effective anisotropy" (*γ*~eff~) both for of *J*~c~(*θ*) and *H*~irr~(*θ*)[@b6][@b7][@b30][@b31]. We attempted to scale the *H*~irr~(*θ*) data of our BZO NPs doped wires using *γ*~eff~. Using intermediate angles we obtain *γ*~eff~ \~ 2, but the scaling is not successful, as the data do not collapse onto a single curve as shown in the literature[@b6][@b7][@b30][@b31]. It is worth mentioning that although in principle the samples in references [@b6],[@b7],[@b14] are also MOD with NPs, there are some differences in the microstructure with the wires in this study. Specifically, with the addition of BZO our samples have a higher density of twin boundaries, but the opposite is found in ref. [@b14].

As shown in [Fig. 5c](#f5){ref-type="fig"}, overall the +3BZO wire shows an extremely high μ~0~*H*~irr~ at 65 K, at 30 T (**H**\|\|45°) and 24 T (**H**\|\|*c*) and at 50 K, 58 T (**H**\|\|45°) and 45 T (**H**\|\|*c*), values which to our knowledge are the highest reported for practical HTS wires[@b31] as well as for thin films on single-crystal substrates[@b32]. Recently, very high μ~0~*H*~irr~ = 14.8 and 15.8 T at 77 K (**H**\|\|*c*) were observed in a heavily BZO nanorod-doped (Y,Gd)BCO wire grown by metal organic chemical vapor deposition[@b33][@b34] and BaHfO~3~ doped PLD GdBCO wire[@b35]; these methods could also translate to great improvements of *H*~irr~ at high fields. This indicates that a high density of NPs/columns is beneficial not only for MOD prepared materials but is a general trend for REBCO wires.

Discussion
==========

In order to pinpoint *H*-*T* regions where the BZO additions are more effective, in [Fig. 6](#f6){ref-type="fig"} we plot the *H*~irr~ enhancement Δμ~0~*H*~irr~ = μ~0~*H*~irr,BZO~−μ~0~*H*~irr,Y~ for different concentrations of BZO NPs. This also set the bases to determine possible *H-T* saturation regions and if so, the dependence with magnetic field orientation. The improvement, Δμ~0~*H*~irr,~ is bigger for higher BZO NP densities. We also find that Δ*H*~irr~ shows similar temperature dependences for samples with +1BZO, +2BZO (not shown) and +3BZO for all orientations measured. At **H**\|\|45°, Δμ~0~*H*~irr~ curves have a greater increase with respect to **H**\|\|*c* for both concentrations, consistently with [Fig. 5c](#f5){ref-type="fig"}, showing no signs of saturation up to the highest magnetic field measured.

The lack of saturation is also apparent in the inset of [Fig. 6](#f6){ref-type="fig"}, which shows the ratio μ~0~*H*~irr,BZO~/μ~0~*H*~irr,Y~ for the **H**\|\|45° orientation for two different concentrations of BZO NPs, 1% and 3%. The enhancement factor is largest at low fields and initially decays with *H*, but then becomes constant up the highest accessible fields. In particular, *H*~irr~ for +3BZO is about 25% higher than for YBCO up to \~45 T.

Also observed in [Fig. 6](#f6){ref-type="fig"} is a steeper growth in *H*~irr~ at *T* \> 80 K for both +1BZO and +3BZO wires. This temperature corresponds to μ~0~*H* ∼ 5 T, where the inter-vortex distance is *a*~f~ ∼ 22 nm, which is close to the average BZO NP spacing (*d*~BZO~ ∼ 30 nm) observed in TEM images. This suggests that NPs are most effective in increasing μ~0~*H*~irr~ (at **H**\|\|45°) when the intervortex spacing is similar the distance between NPs. This behavior is analogous to the *J*~c~ enhancement we observed as function of field for different NP densities in ref. [@b36].

The fact that improvements are smaller for **H**\|\|*c* compared to **H**\|\|45°, is partly due to the fact that *H*~irr~ is already higher due to the presence of correlated defects (insert [Fig. 5d](#f5){ref-type="fig"}). After an initial increase of *H*~irr~, Δμ~0~*H*~irr~ flattens around 75 K and appears to increase again for *T* \< 60 K. The initial increase can be related to the higher density of NPs and/or of TBs, with the latter being 2.3 times more numerous in samples with BZO than in standard YBCO. However, the increase at lower temperatures is most likely related solely to the presence of nanoparticles, given the similarity of the behavior found at **H**\|\|45°.

The lack of saturation in the increase of *H*~irr~ is remarkable. For +3BZO at **H**\|\|45° we have achieved a 25% enhancement up to the highest fields measured, with no sign of decrease. This corresponds to an absolute increase over 9 T for μ~0~*H*~irr~ \~ 50 T, implying an increase of \~4--6 K in operational temperature (depending on the orientation). This enhancement is particularly significant knowing that at μ~0~*H* ∼ 60 T the inter-vortex spacing is at least 7 times smaller than the average distance between nanoparticles. These findings indicate that further improvement of *H*~irr~ in practical REBCO wires is still possible, thus pushing the technically relevant region up to even higher magnetic fields.

In summary, we find that up to the highest BZO NPs density we tested, *H*~irr~ can be increased further, with no indication of saturation up to 60 T. This allows us to report extremely high μ~0~*H*~irr~, the highest values reported so far for REBCO films and wires. Our results suggest that higher densities of NPs will increase *H*~irr~ even more, and that the high-field limit is far from being reached in nanoengineered REBCO wires. These results are further proof that REBCO wire is an enabling technology for several high field applications.

Methods
=======

HTS wires based on epitaxial REBCO nanocomposite films of standard YBCO and (Y,Gd)BCO + BZO were grown from metal organic solutions including Y-, Gd-, and Ba-trifluoroacetates and Cu-naphthenate with the cation ratio of 0.77 : 0.23 : 1.5 : 3 on ion-beam-assist deposited metal templates[@b37]. We added Zr-naphthenate into the (Y, Gd)BCO solutions; the content of BZO was 1--3wt%, and the concentration of starting solution was 1.2 mol/L. The total thickness of the superconductive layer for all samples was 0.5 μm, which was confirmed by cross sectional transmission electron microscopy (TEM). The details of the calcinations and conversion steps have been published elsewhere[@b17].

Films were patterned using photolithography and ion milling into bridges of ∼50 μm width. The crystalline quality was examined by x-ray diffraction (XRD). The resistivity measurements, *ρ* vs. *H*, were realized in pulsed fields up to 60 T at the Pulsed Field Facility of the National High Magnetic Field Laboratory at Los Alamos National Laboratory. The four-probe technique was applied in AC mode with a low current corresponding to 400 A/cm^2^ and a frequency of 100 kHz. Pulsed field measurements were performed at fixed orientations (*θ*), and the angular orientation was changed using a mechanical rotator. Additional *ρ* vs. *T* measurements were performed in a Quantum Design PPMS with a superconducting magnet (DC magnetic field) generating fields μ~0~**H** up to 15 T. For the transport measurements the current was always perpendicular to **H**. Criteria of 0.9*ρ*~n~ and 0.01*ρ*~n~, where *ρ*~n~ is the normal state resistivity, were used to define *H*~c2~ and *H*~irr~, respectively. Both planar and cross sectional TEM images were taken to evaluate the microstructure of the film.

The microstructures and elemental concentration mappings of the films were analyzed by transmission electron microscopy (TEM) and energy-dispersive x-ray spectroscopy (EDS), respectively.

Additional Information
======================

**How to cite this article**: Miura, M. *et al.* Upward shift of the vortex solid phase in high-temperature-superconducting wires through high density nanoparticle addition. *Sci. Rep.* **6**, 20436; doi: 10.1038/srep20436 (2016).

Work by B.M. and L.C. was supported by the U.S. DOE, Office of Science, BES, Materials Sciences and Engineering Division. Work by M.M. at LANL was supported by the LANL LDRD program, and at Seikei Univ. by JSPS KAKENHI (26709076). Work by F.F.B. was supported by NSF Cooperative Agreement No. DMR-1157490 and the State of Florida. A part of the work at ISTEC-SRL was supported by METI and NEDO as a Collaborative Research. M.M. would like to thank Jeffrey O. Willis for helpful discussions and a critical reading of the manuscript.

**Author Contributions** M.M. grew the films, carried out the experimental design, performed the superconducting property measurements and prepared the manuscript. B.M. carried out superconducting property measurements, data analysis, provided advice and consultation on flux pinning and assisted in preparing the manuscript and coordinated the research. F.F.B. carried out superconducting properties measurement. T.K. carried out microstructural studies. M.S. carried out superconducting property measurements. Y.T. carried out photolithography preparations. T.I. provided advice and consultation on film preparation. L.C. contributed to discussion and manuscript preparation. All authors discussed the results and implications and commented on the manuscript.

![Microstructural characterization for YBCO and (Y,Gd)BCO+BZO wires.\
Top panels of (**a--c**): High magnification planar view TEM images of (**a**) YBCO, (**b**) +1BZO and (**c**) +3BZO wires, respectively. Bottom row: corresponding positions of TBs and BZO NPs. In the bottom panels, some of the RE~2~Cu~2~O~5~ precipitates are indicated by open circles. (**d**) Wide areas of cross-section TEM image of +3BZO wires. The TBs are indicated by arrows. (**e**) Cross-section high-magnification TEM image of +3BZO wire showing randomly dispersed BZO NPs and a high density of SFs (white arrows). Horizontal bars in Fig. 1 (a,b,c,d) and Fig. 1 (e) represent 100 nm and 30 nm, respectively.](srep20436-f1){#f1}

![Angular dependent irreversibility temperature *T*~irr~.\
Angular dependence of *T*~irr~ for YBCO, (Y,Gd)BCO and (Y,Gd)BCO+BZO wires at (**a**) 0.5 T, (**b**) 4 T and (**c**) 15 T, respectively. Inset of Fig. 2 indicates the angular dependent normalized *T*~irr~ (*T*~irr~/*T*~c~) for YBCO and (Y,Gd)BCO wires.](srep20436-f2){#f2}

![Diagrams of vortex pinning for configurations involving different defects at H\|\|c.\
(**a**) Diagram of vortex and *c*-axis parallel correlated TBs and BZO NPs at μ~0~*H*\<μ~0~*H*~ϕ,TB~. (**b**) Diagram of a vortex and BZO NPs and TBs at μ~0~*H* ∼ μ~0~*H*~BZO~(*a*~f~ = *d*~BZO~), showing that above μ~0~*H*~ϕ,TB~ vortices are localized not only by TBs but also by BZO NPs. (**c**) Diagram of a vortex and hybrid defects at μ~0~*H* ≫ μ~0~*H*~BZO~, showing how a large number of vortices are arrested by BZO NPs and TBs.](srep20436-f3){#f3}

![Temperature dependence of *H*~irr~ at low magnetic fields.\
Red open and solid symbol show μ~0~*H*~irr~(*T*/*T*~c~) at **H**\|\|45° and **H**\|\|*c*, respectively, for the +3BZO wire. Black solid symbols indicate μ~0~*H*~irr~(*T*/*T*~c~) for the YBCO wire at **H**\|\|*c*. A clear kink (*H*~cr~) is observed only for **H**\|\|*c* for the wires.](srep20436-f4){#f4}

![Temperature and angular dependence of the upper critical field and irreversibility field.\
(**a**) Temperature and (**b**) angular dependence of μ~0~*H*~c2.~ The inset of Fig. 5(a) shows the temperature dependence of *γ* calculated using and . The inset of Fig. 5(b) shows *ρ*~n~(*T*) with **H**\|\|*c* for YGdBCO + 1BZO wire. Solid lines in Fig. 5(b) are *ε*(*θ*)μ~0~*H*~c2~ using *γ* values from the inset of Fig. 5(a). (**c**) Temperature and (d) angular dependence of μ~0~*H*~irr~. Solid lines in Fig. 5(d) are *ε*(*θ*)μ~0~*H*~irr~ for the YBCO and +3BZO wires using *γ* = 5.1 and 4.7, respectively.](srep20436-f5){#f5}

![Temperature dependence of *H*~irr~ enhancement.\
Temperature dependence of Δμ~0~*H*~irr~ = μ~0~*H*~irr,BZO~−μ~0~*H*~irr,Y~ at **H**\|\|*c* and **H**\|\|45° for +1BZO and +3BZO wires. The inset shows the ratio of μ~0~*H*~irr,BZO~/μ~0~*H*~irr,Y~ for + 1 and + 3BZO for **H**\|\|45°.](srep20436-f6){#f6}

###### Structural and superconducting properties.

  Sample                                            YBCO                              (Y,Gd)BCO                 +1BZO       +2BZO         +3BZO
  ---------------------------------- ----------------------------------- ----------------------------------- ----------- ------------ -------------
  *δω* (deg.)                                       1.07                                1.10                    1.05         1.08         1.11
  *δϕ* (deg.)                                       2.89                                2.85                    2.88         2.84         2.83
  Average NP diameter (nm)            \~108[\*](#t1-fn2){ref-type="fn"}   \~113[\*](#t1-fn2){ref-type="fn"}   23 ± 4.8     23 ± 4.6     22 ± 4.7
  Average NP density (10^21^/m^3^)    \~0.1[\*](#t1-fn2){ref-type="fn"}   \~0.1[\*](#t1-fn2){ref-type="fn"}   2.9 ± 0.1   7.1 ± 0.14   13.0 ± 0.13
  Average TB spacing (nm)                         45 ± 4.8                           38.5 ± 5.2               34 ± 2.5    32.5 ± 3.2    30 ± 3.1
  *T*~c~ (K)                                        89.9                                90.2                    90.3         90.4         90.4
  *J*~c~^s.f.^ (77 K) (MA/cm^2^)                     2.8                                 3.8                     4.0         3.9           4.0

Sample data for the reference YBCO wire and for the (Y,Gd)BCO + BZO wires. *δω* and *δϕ* denote the full-width at half-maximum (FWHM) values of the out-of-plane rocking curves (*ω* scans) of the 005 diffraction peaks and in-plane rocking curves (*ϕ* scans) of the 103 diffraction peaks, respectively. The particle-size distribution was extracted from high-magnification planar- and cross-section views of several TEM images. The size of the BZO NPs ranged from 17 to 28 nm with a modal size of ∼23 nm. The average TB spacing was estimated from several planar view TEM images. *T*~c~ was determined using a criterion of 0.01*ρ*~*n*~.

^\*^225 precipitates.