Superstrength permanent magnets with iron-based superconductors by data- and researcher-driven process design

Iron-based high-temperature superconductors (IBSs), with their high superconducting transition temperature (Tc ~ 60 K) and topological characteristics, show promise in various applications, including topological quantum computation, next-generation superstrength permanent magnets, and superconducting electronics. IBSs outperform Nb-based superconductors at higher temperatures and stronger magnetic fields, offering scalability advantages over cuprate superconductors. Their high upper critical field (Hc2 > 50 T) makes them suitable for enhancing particle accelerators, MRI scanners, and MAGLEV trains. However, anisotropic superconducting pairing and short coherence lengths impact grain boundary transport. While IBSs exhibit a robust critical current density (Jc ~ 104–5 A/cm²), exceeding that of cuprate superconductors, it's significantly lower than single crystals and thin films. Although progress has been made in modeling polycrystalline materials and evaluating grain boundary characteristics, the interplay between microstructures and chemical compositions remains complex. Machine learning has been applied to materials science for modeling Tc and optimizing properties; however, its application to synthesis, particularly process informatics using large databases, is limited. This study focuses on optimizing the critical current properties of polycrystalline (Ba,K)Fe2As2 using Bayesian optimization, integrating data-driven and researcher-driven approaches.

The literature review highlights the significant potential of iron-based high-temperature superconductors (IBSs) for next-generation applications, particularly in high-field magnets. Previous research has established the superior properties of IBSs compared to Nb-based superconductors, emphasizing their higher operating temperatures and stronger magnetic fields. The challenges associated with the anisotropic nature of superconductivity in IBSs and the impact of grain boundaries on supercurrent transport have been discussed extensively. Studies exploring the critical misorientation angle and critical current density in different IBS phases have been referenced, showcasing the inherent complexities of these materials. Furthermore, the literature review touches upon the existing approaches for enhancing critical current properties, including methods for growing larger grains and those focused on generating smaller grains. However, a gap in the literature is identified regarding the use of comprehensive data-driven approaches and machine learning techniques in optimizing the synthesis process of IBS-based magnets.

This study employed a collaborative framework integrating Bayesian optimization, a machine-learning approach, with researcher-driven process design. The process began by defining a three-dimensional search space of process parameters (ramping rate, maximum temperature, and dwell time) governing the spark plasma sintering process for (Ba0.6K0.4)Fe2As2 precursor powder. Researchers initially conducted a researcher-driven optimization, providing initial data and a general framework. This data was then input into a customized Bayesian optimization software, BOXVIA, which predicted synthesis conditions for superior properties (data-driven loop). Researchers synthesized samples, performed measurements (Jc at 3T), and updated the database. This iterative process continued until optimal parameters were identified. Two bulk samples (Bulk1 and Bulk2) were fabricated using parameters from the data-driven and researcher-driven approaches, respectively, for comparison. The critical current density (Jc) was measured as a function of magnetic field at 5 K. Nanostructural analysis (STEM, ADF-STEM, elemental mapping) was performed to understand the microstructural differences and their correlation with Jc. Permanent magnet properties, including trapped field and temperature dependence, and hysteresis loops were measured.

The data-driven approach (Bulk1) resulted in a higher Jc at 3 T, while the researcher-driven approach (Bulk2) yielded the highest Jc at zero field. Both approaches showed improvements in Jc compared to previous results. Bulk1 exhibited a bimodal grain size distribution with small grains and dense intragranular defects, while Bulk2 showed fine-grained crystals. The nanostructural analysis revealed the presence of planar defects within the grains in both samples, with an average spacing exceeding the superconducting coherence length. The maximum trapped field recorded was 2.83 T at the center of a stacked pair of Bulk1 samples, which is 2.7 times higher than the previous record for iron-based superconducting magnets. This high trapped field was accompanied by excellent magnetic field stability exceeding 0.1 ppm/h for a 1.5 T permanent magnet. The study suggests a novel 'third' pathway for enhancing critical current properties in IBSs, characterized by a bimodal grain size profile with small grains and high-density intragranular defects.

The findings demonstrate the successful integration of data-driven and researcher-driven approaches for optimizing the synthesis process of IBS permanent magnets. The superior performance of the magnet prepared with the data-driven approach highlights the potential of machine learning in uncovering optimal processing parameters that may not be intuitively obvious to researchers. The observed bimodal grain size distribution and high density of intragranular defects contribute to the enhanced flux pinning, leading to the improved critical current density and high trapped field. This study provides a new strategy for the design and fabrication of high-performance IBS permanent magnets, paving the way for future advancements in various applications.

This study successfully demonstrated a novel approach for fabricating high-performance iron-based superconducting permanent magnets by combining data-driven and researcher-driven process design. The resulting magnet showed a significantly enhanced trapped field and excellent stability. The findings highlight the potential of machine learning in materials discovery and optimization, particularly in complex systems like IBS superconductors. Future research could focus on exploring the underlying mechanisms governing the formation of the bimodal grain size distribution and further optimizing the synthesis process to achieve even higher performance.

The study focused on a specific iron-based superconductor, (Ba,K)Fe2As2, and the findings might not be directly transferable to other IBS compositions. The sample size was relatively small, limiting the generalizability of the results. A more comprehensive understanding of the interplay between microstructure, defects, and superconducting properties is still needed. Future work should investigate scaling up the synthesis process for practical applications and exploring other IBS systems.