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Published by NationalInstitute for Materials Science in partnershipwith Taylor & Francis GroupView supplementary material Published online: 20 Sep 2024.Submit your article to this journal Article views: 100View related articles View Crossmark datahttps://www.tandfonline.com/action/journalInformation?journalCode=tstm20https://www.tandfonline.com/journals/tstm20?src=pdfhttps://www.tandfonline.com/action/showCitFormats?doi=10.1080/27660400.2024.2403966https://doi.org/10.1080/27660400.2024.2403966https://www.tandfonline.com/doi/suppl/10.1080/27660400.2024.2403966https://www.tandfonline.com/doi/suppl/10.1080/27660400.2024.2403966https://www.tandfonline.com/action/authorSubmission?journalCode=tstm20&show=instructions&src=pdfhttps://www.tandfonline.com/action/authorSubmission?journalCode=tstm20&show=instructions&src=pdfhttps://www.tandfonline.com/doi/mlt/10.1080/27660400.2024.2403966?src=pdfhttps://www.tandfonline.com/doi/mlt/10.1080/27660400.2024.2403966?src=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1080/27660400.2024.2403966&domain=pdf&date_stamp=20 Sep 2024http://crossmark.crossref.org/dialog/?doi=10.1080/27660400.2024.2403966&domain=pdf&date_stamp=20 Sep 2024Autonomous search for half-metallic materials with B2 structureYuma Iwasaki a, Ryo Toyama b, Takahiro Yamazaki c, Yasuhiko Igarashi d, Masato Kotsugi c and Yuya Sakuraba baCenter for Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS), Tsukuba, Japan; bResearch Center for Magnetic and Spintronic Materials (CMSM), National Institute for Materials Science (NIMS), Tsukuba, Japan; cDepartment of Materials Science and Technology, Tokyo University of Science, Tokyo, Japan; dGraduate School of System and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, JapanABSTRACTExploring vast material spaces efficiently is challenging in materials science. Autonomous methods for material search – integrating machine learning and ab initio calculations – have emerged as powerful alternatives to traditional approaches, which are often time-consuming and limited in scope. Although these autonomous methods have been applied to various material systems, the extensive material space of B2 structured materials for half-metallicity remains largely unexplored. Herein, we introduce a simulation-based autonomous search approach to identify B2 structured alloys exhibiting high spin polarization of sp conduction electrons (Psp), sp minority spin band gap (Gsp), and Curie temperature (Tc). The proposed method explores the material space of disordered quaternary B2 magnetic alloys using the Korringa – Kohn – Rostoker coherent potential approximation and Bayesian optimization. Over a continuous search of approximately 100 days, the system identified Co1.0Mn0.7Al0.3 as a promising candidate, demonstrating high values of Psp, Gsp, and Tc. Although additional experimental and theoretical validation is necessary, this study demonstrates the potential of autonomous material search methods to expedite material discovery and enhance material property optimization.NOVELTY STATEMENTAutonomous search methods identify a promising B2 structured alloy, Co1.0Mn0.7Al0.3, with high spin polarization, minority spin band gap, and Curie temperature, showcasing a significant leap in efficient material discovery.ARTICLE HISTORY Received 24 July 2024 Revised 2 September 2024 Accepted 9 September 2024 KEYWORDS Half-metal; machine learning; ab initio calculations; Bayesian optimizationIntroductionThe scope of material spaces has recently expanded. Traditionally, humans have systematically explored these vast material spaces through iterative cycles of material synthesis, property measurement, and analysis. However, this traditional approach is time- consuming and inadequate for comprehensively exploring recently expanded material spaces. To overcome these limitations, researchers have integrated machine learning into automated material search methodologies. These approaches can be broadly categorized into two primary technologies: autonomous search based on robotics and material simulations. In the robotics approach, robots automate tasks such as material synthesis and property measurement. Subsequently, machine learning CONTACT Yuma Iwasaki IWASAKI.Yuma@nims.go.jp Center for Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS), Tsukuba, JapanSupplemental data for this article can be accessed online at https://doi.org/10.1080/27660400.2024.2403966SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS: METHODS 2024, VOL. 4, NO. 1, 2403966 https://doi.org/10.1080/27660400.2024.2403966© 2024 The Author(s). Published by National Institute for Materials Science in partnership with Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.http://orcid.org/0000-0002-7117-277Xhttp://orcid.org/0000-0002-7398-5803http://orcid.org/0000-0003-0738-9373http://orcid.org/0000-0003-1042-6657http://orcid.org/0000-0002-4841-1808http://orcid.org/0000-0003-4618-9550https://doi.org/10.1080/27660400.2024.2403966http://www.tandfonline.comhttps://crossmark.crossref.org/dialog/?doi=10.1080/27660400.2024.2403966&domain=pdf&date_stamp=2024-09-20analyzes the collected data to suggest materials and optimal process conditions for subsequent synthesis cycles. This closed-loop system – driven by robotic synthesis and measurement – enables autonomous material searches. With the development of numerous autonomous material search robots, robotic searching has emerged as a highly effective method in material development [1–12]. In the second approach, simulations – such as ab initio calculations – are used to obtain material property data. Subsequently, machine learning analyzes the data to guide future material design related to structure and composition. This iterative process forms a closed loop, enabling autonomous exploration of material spaces in a computer environment, offering convenience, versatility, and widespread adoption [13–20]. Herein, we describe simulation-based autonomous methods for exploring half-metallic materials with a B2 structure. Half-metallic materials are characterized by possessing a metallic spin band and a semiconducting spin band [21], which have been extensively investigated for applications in tunnel magnetoresistance (TMR) [22–25], giant magnetoresistance (GMR) [26–29], and other spintronic devices [30–32]. Heusler alloys are a promising category for half-metallic applications, often adopting L21 (X2YZ) or C1b (XYZ) structures composed of three different elements: X, Y, and Z. Owing to their multielemental nature and disordered phases, the material search space for Heusler alloys is extensive, making simulation-based autonomous methods highly effective for exploration [14,19,33].However, Heusler alloys present significant challenges in synthesis owing to their complex four- sublattice structures, often resulting in poor properties or synthesis failures despite promising predictions from machine learning and ab initio calculations. The high synthesis temperatures required for Heusler alloys are a bottleneck for practical device applications. In contrast, the B2 structure is simpler, featuring only two sublattices, and can be viewed as a disordered form of the L21 structure, making it more feasible to synthesize at lower temperatures. In fact, half-metallicity in B2- structured materials such as Co2(MnFe)Ge, Co2MnGe, Co2MnSi, and Co2(CrFe)Al has been studied from experimental and theoretical perspectives [34–40]. Therefore, suggesting material compositions with potential half-metallicity in the B2 structure through autonomous material search methods is promising for successful synthesis and practical application.MethodsThe material space was defined as quaternary B2 materials with two sublattices: A site composed of two disordered elements (A1 and A2), and B site composed of two disordered elements (B1 and B2). The composition at each site was incremented by 10 atomic percent (at%). Therefore, the composition formula for the materials under exploration is expressed as where A, B, a, and b are defined as and The elements A1 and A2 predominantly occupy the X site in L21 structures (X2YZ), whereas B1 and B2 typically reside at the Y or Z sites [41]. To reduce the number of candidate materials, the exploration was intentionally limited to materials containing Fe, Co, or Ni, which are major magnetic elements at room temperature. This approach narrowed the scope to approximately 4.4 million potential material configurations in the specified material space. The challenge of performing ab initio calculations for all candidates was alleviated using sequential calculations guided by machine learning, which efficiently navigated the material space.The autonomous search simultaneously maximizes three indicators. The first indicator is sp spin polarization (Psp). Typically, spin polarization is defined as the difference in the density of states (DOS) between up- and down-spin electrons at the Fermi level. Higher spin polarization values are linked to increased magnetoresistance (MR) ratios in TMR and GMR devices. However, studies have demonstrated that the MR ratio is more influenced by the spin polarization of conduction electrons (sp) than the total electron (spd) spin polarization [24,33,36,42]. Sci. Technol. Adv. Mater. Meth. 4 (2024) 2 Y. IWASAKI et al.where n"sp EFð Þ and n#sp EFð Þ are the DOS of up- and down-spin electrons at the Fermi level, respectively.The second indicator is the sp minority spin band gap (Gsp). When Psp is high and approaches 1.0, the DOS of sp minority spin electrons at the Fermi level is nearly zero, indicating the existence of an sp minority spin band gap. A larger Gsp indicates that half- metallicity remains stable even at room temperature, preventing the formation of electronic states in the sp minority spin band gap.The third indicator is Curie temperature (Tc), which is the temperature at which a magnetic material transitions from a magnetic to a nonmagnetic state. A higher Tc indicates more stable magnetic properties, which is critical for spintronic device applications.The methodology for autonomous material search is depicted in Figure 1. It includes sequential ab initio calculations and machine learning. The ab initio phase calculates Psp, Gsp, and Tc based on compositions recommended by the machine learning phase. Data accumulated from these calculations guide the composition choices for subsequent ab initio calculations.The ab initio calculations used Green’s function- based density functional theory using the Korringa – Kohn – Rostoker coherent potential approximation (KKR – CPA) method, implemented in AkaiKKR software [43]. CPA allows accurate simulations of alloy systems, particularly for multielement disordered phases [44–47]. Psp and Gsp were determined from the DOS, whereas Tc was calculated using the following equation: where Efmg and Elmd are the total energies of the ferromagnetic and local moment disorder states, respectively [48], kB is the Boltzmann constant, and c is the concentration of magnetic atoms. The lattice constants were optimized to minimize the total energy. Further details of the ab initio calculations are provided in the Supplementary Materials (S1).The machine learning phase used Bayesian optimization [49] and an autoencoder [50] to identify material compositions for subsequent KKR – CPA calculations based on accumulated Tc data. The material space (descriptors) was designed based on a previous report [19]. A composition vector and Magpie descriptor vector [51] were compressed into a 30-dimensional latent vector representing the unexplored material space. Additional details are provided in the Supplementary Materials (S2). This phase integrated KKR – CPA with multiobjective Bayesian optimization, using Psp, Gsp, and Tc as objective variables and the latent vectors generated by the autoencoder as explanatory variables in the Gaussian-process regression model. The upper confidence bound (UCB) was calculated as an acquisition function for each material [52]. The candidate material with the highest Pareto hypervolume, based on the UCB value and training data (observed Psp, Gsp, and Tc), was selected for subsequent KKR – CPA calculations. This iterative approach facilitated autonomous exploration for materials exhibiting high Psp, Gsp, and Tc. Further details are provided in the Supplementary Materials (S3).Results and DiscussionThe developed autonomous search system operated continuously for approximately 100 days. Figure 2(a) depicts a three-dimensional plot of the explored Figure 1. Overview of an autonomous material search system; the ab initio calculation phase computes sp spin polarization (Psp), sp minority spin band gap (Gsp), and Curie temperature (Tc) using crystal structure and composition data determined in the machine learning phase; the machine learning phase generates compositional information for subsequent ab initio calculations (KKR – CPA = korringa – Kohn – Rostoker coherent potential approximation). This method is based on previous research [19].Sci. Technol. Adv. Mater. Meth. 4 (2024) 3 Y. IWASAKI et al.materials, illustrating their Psp, Gsp, and Tc characteristics. For clarity, Figures 2(b–d) show two- dimensional plots of Psp vs. Gsp, Psp vs. Tc, and Gsp vs. Tc. Materials with low Psp typically lack a minority spin band gap, resulting in a Gsp value of zero. Although some materials showed potential for very high Curie temperatures (Tc >1,000 K), these data points are speculative because the stability of the B2 structure at such high temperatures is uncertain.Despite adopting the B2 structure, several new alloys with high Psp, Gsp, and Tc were proposed. One such alloy is B2-Co1.0Mn0.7Al0.3 shown by red arrows in Figure 2(a–d). A well-known half-metallic material composed of Co, Mn, and Al is the full-Heusler alloy L21-Co2.0Mn1.0Al1.0, which demonstrates high magnetic moments, spin polarization, and Curie temperatures, making it highly promising for applications in TMR and GMR devices [53]. However, the synthesis of L21-Co2.0Mn1.0Al1.0 is challenging, often resulting in the formation of B2-Co2.0Mn1.0Al1.0 instead, attributed to the low order/disorder transition temperature [54–56].The proposed B2-Co1.0Mn0.7Al0.3 alloy is predictably more promising than L21-Co2.0Mn1.0Al1.0 and B2- Co2.0Mn1.0Al1.0. Figures 3(a–c) depict the crystal structures of B2-Co1.0Mn0.7Al0.3, B2-Co2.0Mn1.0Al1.0, and L21-Co2.0Mn1.0Al1.0, respectively. These figures, generated using VESTA software [57], show Co in yellow, Mn in red, and Al in blue, with disorder observed in the Mn and Al sites for B2-Co1.0Mn0.7 Al0.3 and B2-Co2.0Mn1.0Al1.0. Figures 3(d–f) display the total DOS, encompassing all spd orbitals, for B2- Co1.0Mn0.7Al0.3, B2-Co2.0Mn1.0Al1.0, and L21-Co2.0 Mn1.0Al1.0 and indicating high spin polarization across all materials. Figures 3(g–i) depict the DOS specifically for conduction electron sp orbitals, crucial for GMR and TMR devices. All materials exhibit pronounced sp spin polarization and minority spin band gap-like features, with B2-Co1.0Mn0.7Al0.3 displaying a particularly sharp minority spin band gap edge.Table 1 presents the magnetic moment (M), lattice constant (a), sp spin polarization (Psp), sp minority spin band gap (Gsp), Curie temperature (Tc), and formation energy (ΔEf) for B2-Co1.0Mn0.7Al0.3, B2-Co2.0 Figure 2. Results of the autonomous search for materials with high sp spin polarization (Psp), sp minority spin band gap (Gsp), and Curie temperature (Tc); (a) three-dimensional plot of the materials explored by the system, illustrating their Psp, Gsp, and Tc; (b) two- dimensional plot of Psp vs. Gsp; (c) two-dimensional plot of Psp vs. Tc; (d) two-dimensional plot of Gsp vs. Tc. Red arrows show B2- Co1.0Mn0.7Al0.3.Sci. Technol. Adv. Mater. Meth. 4 (2024) 4 Y. IWASAKI et al.Mn1.0Al1.0, and L21-Co2.0Mn1.0Al1.0. These values were calculated using the KKR – CPA method used in the autonomous search, with detailed calculation conditions provided in Supplementary Materials (S1). The Psp, Gsp, and Tc values for the newly proposed B2- Co1.0Mn0.7Al0.3 surpass those of the well-known B2- Co2.0Mn1.0Al1.0 and L21-Co2.0Mn1.0Al1.0, highlighting the effectiveness of the autonomous search system in identifying promising new materials.The newly proposed B2-Co1.0Mn0.7Al0.3 (B2-Co2.0 Mn1.4Al0.6) can be regarded as a significantly different material from L21-Co2.0Mn1.0Al1.0 in terms of the stoichiometric composition as its composition is rich in Mn and poor in Al and perfect disorder between Mn and Al atoms. Note that, in previous experimental and theoretical studies, a lot of effort has been made to enhance spin polarization by controlling compositions deviating from the stoichiometric composition of an ideal L21 structure. For instance, materials with compositions deviating from L21 structures in the Co2 MnSi, Co2Mn(Ge,Ga), and Co2(Mn,Fe)Si systems have been investigated [42,58,59]. The MR ratio in TMR and GMR devices is improved by relatively reducing the Co composition ratio from the stoichiometric one, which is reflected in the reduction in the number of Co anti-sites, a major cause of reduced spin polarization. However, B2-Co1.0Mn0.7Al0.3 proposed by our autonomous material search is considered a new single material with high spin polarization originating from a mechanism different from the suppression of Co anti-sites in the previously studied Co- poor L21 structure as the proposed material has the B2 Figure 3. Density of states (DOS) of B2-Co1.0Mn0.7Al0.3, B2-Co2.0Mn1.0Al1.0, and L21-Co2.0Mn1.0Al1.0; (a) crystal structure of B2-Co1.0 Mn0.7Al0.3; (b) crystal structure of B2-Co2.0Mn1.0Al1.0; (c) crystal structure of L21-Co2.0Mn1.0Al1.0; (d) total (spd) electron DOS of B2- Co1.0Mn0.7Al0.3; (e) total (spd) electron DOS of B2-Co2.0Mn1.0Al1.0; (f) total (spd) electron DOS of L21-Co2.0Mn1.0Al1.0; (g) conduction (sp) electron DOS of B2-Co1.0Mn0.7Al0.3; (h) conduction (sp) electron DOS of B2-Co2.0Mn1.0Al1.0; (i) conduction (sp) electron DOS of L21-Co2.0Mn1.0Al1.0.Table 1. Magnetic moment (M), lattice constant (a), sp spin polarization (Psp), sp minority spin band gap (Gsp), Curie temperature (Tc), and formation energy (ΔEf) for B2-Co1.0Mn0.7Al0.3, B2-Co2.0Mn1.0Al1.0, and L21-Co2.0Mn1.0Al1.0 calculated by KKR – CPA.M (μB) a (Å) Psp Gsp (eV) Tc (K) ΔEf (eV/cell)B2-Co1.0Mn0.7Al0.3 1.41 2.801 0.913 0.563 620.732 −0.74856B2-Co1.0Mn0.5Al0.5 1.023 2.806 0.906 0.344 411.337 −1.34266L21-Co2.0Mn1.0Al1.0 1.03 5.619 0.744 0.313 587.613 −2.68496Sci. Technol. Adv. Mater. Meth. 4 (2024) 5 Y. IWASAKI et al.structure and stoichiometric Co composition ratio. The fact that it has a disordered B2 structure, which is easier to synthesize than L21, adds practical value.Machine learning analysis, particularly white-box approaches, may help deduce material mechanisms in the future. Although extracting valuable insights from data accumulated through the autonomous material search may be challenging due to significant data bias, supplementing the database with high- throughput ab initio calculations and experiments can eventually provide new data-driven insights into the material mechanisms.Herein, we successfully used autonomous exploration methods to propose new B2 alloys with high Psp, Gsp, and Tc. However, these newly proposed alloy materials are speculative predictions derived from ab initio calculations, and the accuracy of Psp, Gsp, and Tc predictions has not been verified. Moreover, the stability of the disordered B2 structure formed by the elements in these alloys is uncertain. Notably, a negative formation energy does not necessarily guarantee synthesizability, necessitating further experimental and theoretical investigations of the proposed alloy materials.ConclusionsA simulation-based autonomous material search method is highly effective in exploring the extensive alloy space of quaternary B2 materials, focusing on achieving high sp spin polarization (Psp), sp minority spin band gap (Gsp), and Curie temperature (Tc). By integrating machine learning and ab initio calculations, this system efficiently navigates the complex material landscape, ultimately proposing the new material Co1.0Mn0.7Al0.3 with exceptional Psp, Gsp, and Tc values. This autonomous search approach demonstrates versatility and adaptability across various material systems and properties, serving as a powerful tool capable of accelerating advancements in material discovery.AcknowledgementsWe thank K. Masuda and K. Sodeyama at the National Institute for Materials Science. This study was supported by JST-CREST Grant JPMJCR21O1.Disclosure statementNo potential conflict of interest was reported by the authors.FundingThis study was supported by JST-CREST under Grant [JPMJCR21O1]; Core Research for Evolutional Science and Technology [JPMJCR21O1].ORCIDYuma Iwasaki http://orcid.org/0000-0002-7117-277XRyo Toyama http://orcid.org/0000-0002-7398-5803Takahiro Yamazaki http://orcid.org/0000-0003-0738- 9373Yasuhiko Igarashi http://orcid.org/0000-0003-1042-6657Masato Kotsugi http://orcid.org/0000-0002-4841-1808Yuya Sakuraba http://orcid.org/0000-0003-4618-9550Data availability statementThe data supporting the results of this research are available from the corresponding author upon reasonable request.References[1] Coley CW, Thomas DA, Lummiss JA, et al. A robotic platform for flow synthesis of organic compounds informed by AI planning. Science. 2019;365(6453): eaax1566. doi: 10.1126/science.aax1566 [2] Burger B, Maffettone PM, Gusev VV, et al. 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