Improvement of critical current density of REBa2Cu3O7-δ by increase in configurational entropy of mixing

REBa2Cu3O7-δ (RE123, RE: rare earth) is one of the high-temperature superconductors with a transition temperature (Tc) exceeding 90 K. Because of its high-Tc and large critical current density (Jc) under magnetic fields, RE123 superconductors have been expected to play a key role in superconductivity application. To accelerate application researches on RE123-based devices, further improvements of Jc characteristics have been desired. In this study, we investigated the effects of high-entropy alloying at the RE site on the superconducting properties, through the measurements of local (intra-grain) Jc (Jclocal) by a remanent magnetization method. We found that Jclocal shows a trend to be improved when four or five RE elements are mixed at the RE site, which results in high configurational entropy of mixing (ΔSmix). All samples exhibited an order of few MA cm−2 which is a criterion for practical application and the highest Jclocal resulted in a value of around 7.0 MA cm−2 at T = 2.0 K. Because high-entropy alloying can improve Jclocal of RE123 superconductors, our entropy-engineering strategy introduced here would be useful for the development of RE123 superconducting materials available under high magnetic fields.

REBa 2 Cu 3 O 7-δ (RE123, RE: rare earth) is one of the hightemperature superconductors with a transition temperature (T c ) exceeding 90 K. Because of its high-T c and large critical current density (J c ) under magnetic fields, RE123 superconductors have been expected to play a key role in superconductivity application. To accelerate application researches on RE123-based devices, further improvements of J c characteristics have been desired. In this study, we investigated the effects of high-entropy alloying at the RE site on the superconducting properties, through the measurements of local (intra-grain) J c (J local c ) by a remanent magnetization method. We found that J local c shows a trend to be improved when four or five RE elements are mixed at the RE site, which results in high configurational entropy of mixing (ΔS mix ). All samples exhibited an order of few MA cm −2 which is a criterion for practical application and the highest J local c resulted in a value of around 7.0 MA cm −2 at T = 2.0 K. Because highentropy alloying can improve J local c of RE123 superconductors, our entropy-engineering strategy introduced here would be useful for the development of RE123 superconducting materials available under high magnetic fields.
because of its high-T c exceeding 90 K and high critical current density (J c ) under magnetic fields [6]. To improve J c of RE123 films, nanoscale disorders such as nanoparticles, nanocomposite structure, defects etc. were introduced [7][8][9][10]. However, the current record of J c of RE123 films are far from the limit expected for an ideal RE123 material [11]. To achieve higher J c in RE123 materials, further development of the method for J c engineering is needed. Having considered the structural and physical properties of various Cu-oxide superconductors, we find that the RE123 system is relatively difficult to use in superconductivity applications because it contains structural and compositional fluctuations. High-T c and high-J c superconductivity of RE123 is generally observed in the orthorhombic structure with the space group of Pmmm (#47) [12]. Decrease in oxygen amount in RE123 in the blocking layer results in a decrease in hole carriers and suppression of high performance of RE123. Recently, the improvement of J c in RE123 film was achieved by over-doping of holes [13]. The improvement of J c by chemicalcomposition tuning would be a desired progress because that can be applied together with the nanoscale fabrication techniques mentioned above. Here, we show another strategy to improve local (intra-grain) J c (J local c ) by introducing high-entropy-alloy-type (HEA-type) RE site in RE123 superconductor. HEA is an alloy containing five or more elements with a concentration range between 5 and 35 at% and hence has a high configurational entropy of mixing (ΔS mix ), which is defined as ΔS mix = −R Σ i c i ln c i , where c i and R are compositional ratio and the gas constant, respectively [14,15]. Although the field of HEA had mostly focused on structural materials for the use under extreme conditions, various functionalities have been found in HEAs [15,16]. In 2014, superconductivity was observed in a HEA, Ti-Zr-Hf-Nb-Ta [17]. Although the expected pairing mechanisms of superconductivity for the HEA was a conventional type, the unique structural and compositional character were welcomed in the field of new superconducting materials. As reviewed in [18] and [19], many HEA superconductors were discovered after the first discovery by Koželj et al. [17]. Since 2018, we have developed HEAtype superconducting compounds, in which the HEA concept was applied to complicated compounds having two or more crystallographic sites [20]. Comparing the HEA effects for superconductors with various crystal structural dimensionality, we found that the disordering effects introduced by the HEA-type site in layered system (BiS 2 -based superconductor) [21] and quasi-two-dimensional system (tetragonal TrZr 2 , Tr: transition metals) [22,23] does not suppress its original T c in pure phases. By contrast, in three-dimensional systems (NaCl-type metal tellurides [24,25] and A15 niobium-based compounds [26]), T c of HEA-type phases was clearly lower than that for pure phases. Therefore, in a two-dimensional crystal structure, the introduction of HEA-type site does not negatively work on T c of the superconductor. As a result, we previously reported the synthesis of HEA-type RE123 polycrystalline samples and reported that the increase in ΔS mix does not suppress superconducting properties including J c [27]. Let us remind that the technique of mixing RE elements has been used for the improvement of J c in some RE123 materials [28]. To the best of our knowledge, however, superconducting properties including J c for RE123 with remarkably high ΔS mix at the RE site was examined in [27] for the first time. In this study, we expanded the study and synthesized various samples of RE123 using lighter RE elements including Dy, Ho, Yb and Lu. Here, we show that tuning ΔS mix at the RE site could improve intra-grain J c (J local c ) of RE123 superconductors.

Material and methods
Polycrystalline samples of REBa 2 Cu 3 O 7-δ (RE: Y, La, Nd, Sm, Eu, Dy, Ho, Yb and Lu) were prepared by solid-state reaction and all samples were prepared in air, as described in [26] (98%) and CuO (99.9%) were used for the synthesis. To obtain the best superconducting properties of each sample, two-step or three-step sintering was performed in air. Note that annealing in air at a low temperature around 350°C is performed because T c of RE123 decreases with lower oxygen amount. Three-step sintering was performed for all samples except for labelled RE-2 and RE-3 (table 1 for the  composition and electronic supplementary material, table S1 for the condition). We also confirmed that sample which showed enough high-T c exhibited almost same superconducting properties after the three-step sintering The raw chemicals with a nominal compositional ratio of RE : Ba : Cu = 1 : 2 : 3 were well mixed and pelletized with a diameter of 1 cm. The first sintering condition was 930°C for 20 h, followed by furnace cooling. For the second sintering process, the sample was ground, mixed, pelletized in the same manner as the first one and heated at 930°C for 8 h and 350°C for 18 h, followed by furnace cooling. The third sintering was performed in three-step sintering for samples royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211874 which showed low T c and shielding volume fraction (SVF) after the second sintering. The condition of the third sintering was 930°C for 8 h, 350°C for 18 h and 175°C for 12 h, followed by furnace cooling.
Powder X-ray diffraction (XRD) patterns were collected on MiniFlex-600 (RIGAKU), equipped with a D/tex-Ultra high-resolution detector, with a Cu-Kα radiation by a conventional θ−2θ method. Rietveld refinement was performed using RIETAN-FP [29]. Crystal structure images were drawn using VESTA [30]. The actual composition of the synthesized disc-shaped polycrystalline samples was investigated by energy-dispersive X-ray spectroscopy (EDX) on a scanning electron microscope (SEM), TM-3030 (Hitachi), with Swift-ED (Oxford). The compositions were estimated by averaging the EDX analysis result from four points on the surface of the examined samples. The obtained compositions are shown in electronic supplementary material, figure S1 with SEM images.
The superconducting properties were investigated using a superconducting quantum interference device magnetometer on MPMS-3 (Quantum Design). For the precise measurement, the disc-shaped samples were cut into the cube-shaped form with a typical size of 0.18 × 0.17 × 0.20 mm. The temperature dependence of magnetic susceptibility (4πχ) was measured after both zero-field cooling and field cooling with an applied field of approximately 10 Oe. , remanent magnetization (m R ) was measured. Remanent magnetization is defined to be a residual magnetization after the applied magnetic field is turned off [32]. When the field is applied to the sample, two full penetration fields at H p1 and H p2 appear at lower field and higher field. When the sample is partially penetrated by the lower field, the contribution to remanent magnetization or the total trapped flux by the pinning centres is only located in the thin penetrated layer. The sample is first fully penetrated with an increasing field at H p1 . As the applied field further raises, more flux lines get over the pinning barrier and enter the sample. The stronger the pinning strength or the higher the applied field, the more flux lines trapped. The trapped flux lines contribute highly to the remanent magnetization, which has a large value compared with the first full penetration field H p1 . Therefore, the remanent magnetization sharply increases with increasing applied field until the second full penetration field H p2 . The derivative of m R with maximum magnetic field (H m ) is given by the following equation with respect to the three different H m conditions [33] p2 Þ: H p2 < H m < 2H p2 , and 0: H m > 2H p . In the equation, dm R /dlogH m exhibits a peak at ÞHp2=7. Therefore, J local c can be calculated from H p2 ¼ J local c r, where r is average grain size. The H m dependence of dm R /dlogH m was measured using a sequence for remanent magnetization measurements. First of all, H m was applied to the sample, and the magnetic field was set to zero, followed by magnetization measurement, which gives m R (H m ). The same measurements were performed at different maximum fields and temperatures. From the H m dependence of dm R / dlogH m , H p2 was estimated from the peak position H peak . The cube-shaped samples were crushed into fine powders by grinding using mortar and pestle. The powders close to 20 µm were selected by micro sieves and used for remanent magnetization measurements. The diameter of powders was estimated using ImageJ [34]. Here, OP was used to discuss the superconducting properties because, as mentioned earlier, orthorhombicity is a key structural parameter to achieve higher superconducting characteristics in the RE123 system [12,27]. Since OP is a good scale for estimating oxygen deficiency in the RE123 system, the use of OP in plotting superconducting properties is useful to extract the effects of ΔS mix at the RE site of REBa 2 Cu 3 O 7-δ on the J c characteristics in the system. According to the data in figure 1b, we found that higher J global c s are achieved for samples containing four, six and seven RE elements. The results motivated us to study J local c of RE123 samples with different ΔS mix to clarify the effect of high configurational entropy of mixing to J c characteristics. Then, seven samples having different ΔS mix and almost comparable OP were selected for this study (highlighted with a square in figure 1b). As well, high enough T c and bulk nature of superconductivity of the sample was confirmed through M-T measurements as displayed in the electronic supplementary material, figure S1 after oxygenation. These indicating that the samples were oxygenated enough, and OP are high enough and not a critical parameter to consider for J global c and J local c . According to the number of RE elements, examined samples are labelled RE-1-RE-7 (table 1).

Results and discussion
Through EDX analyses for cube-shaped samples (see electronic supplementary material, figure S1), we confirmed that the actual composition of the examined samples is comparable to the nominal value, as summarized in table 1. Figure 2a shows powder XRD patterns for all the samples (RE-1-RE-7). All the peaks could be indexed with the orthorhombic RE123 model with a space group of Pmmm (#47). As displayed in figure 2b, no peak broadening was observed among seven samples, indicating that the increase in ΔS mix does not affect crystallinity of the polycrystalline RE123 samples. The major peaks shifted according to the average ionic radius at the RE site. The shift of peaks from RE-2 to RE-7 is originated from the systematic increase of RE element with smaller ionic radius such as Sm, Eu, Dy, Ho, Yb and Lu. As mentioned earlier, however, in the RE123 system, OP is the essential parameter for superconducting properties rather than lattice constants. We, therefore, estimated lattice constants, a and b, using the Rietveld refinements. The typical refinement result with a reliability factor, R wp = 5.8%, for RE-5 is shown in figure 2c, which shows that the orthorhombic   /(a + b)). In this study, we examined J local c for samples surrounded by an orange square in the (b). Because of low SVF estimated from temperature dependence of susceptibility, one RE-2 sample containing Y and Sm was excluded in this study. Some of the J global c data have already been published in [27].
royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211874 model can nicely reproduce the XRD patterns even for a HEA-type sample with five different RE. The estimated lattice constants and the calculated OP are summarized in the electronic supplementary material, table S1. To perform remanent magnetization (m R ) measurements, powders with similar diameter are prepared and observed by SEM. As shown in figure 3, the diameter of the powders was almost homogeneous, and the estimation of the average diameter was successful using ImageJ software. The estimated average diameter of powders for RE-1-RE-7 is summarized in table 2. Figure 4 shows the results of the m R measurements at T = 2.0, 4.2, 10.0, 20.0 K plotted in a form of dm R /dlogH m as a function of maximum applied field (H m ). Basically, we observed two peaks in the plots; the first peak observed at lower fields is originating from J Having compared the OP parameter for RE-1, RE-4 and RE-5, we found that OP for those samples is almost the same. Therefore, the oxygen amount would be comparable in those samples. Therefore, the improvement of J local c by the increase in ΔS mix observed between RE-1, RE-4 and RE-5 would be originating from local structural modification by the disordered RE site and chemical bonds near the RE site. In BiS 2 -based RE(O,F)BiS 2 superconductors, local structure modification in the conducting BiS 2 layers by the increase in ΔS mix was observed [35]. Therefore, we expect that structural modulation was generated

Conclusion
Here, we reported the improvement of J local c in REBa 2 Cu 3 O 7-d by the increase in ΔS mix at the RE site. Polycrystalline RE123 samples with different ΔS mix were synthesized by solid-state reaction. Through  Figure 3. Powder characterization. (a-g) SEM images of REBa 2 Cu 3 O 7-δ powders (upper panels) and diameter analyses (lower panels) for all the samples, RE-1-RE-7. SEM images were analysed using ImageJ software in [33]. was observed for RE-4 and RE-5 with a higher ΔS mix as compared with that for RE-1, RE-2, and RE-3 with zero or low entropy of mixing at the RE site. Although the results of the current work showed the merit of high-entropy alloying at lower temperatures only, there should be optimal conditions on constituent RE element, mixing ratio and ΔS mix , which will achieve higher J local c at higher temperatures as well. If the trial was achieved, the HEA concept can be applied to all RE123 practical materials to additionally improve their critical current properties.
Ethics. Since our work is related to inorganic materials research, it is not relevant to our work. Data accessibility. The datasets supporting this article have been uploaded as part of the electronic supplementary material [36].
Authors' contributions. A.Y.: conceptualization, investigation, resources, visualization, writing-original draft and writing-review and editing; Y.S.: data curation and investigation; Y.M.: supervision and writing-review and editing.
All authors gave final approval for publication and agreed to be held accountable for the work performed therein.   royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 9: 211874