The search for next-generation electronic materials often starts with studying the Fermi surface, which serves as a map of a material's electronic structure. Its shape varies with crystal structure, composition, and electronic band arrangement, directly impacting properties such as carrier density, magnetic behavior, and spin polarization. This makes it a crucial tool for understanding and engineering new materials.
The Fermi surface of a material is determined experimentally using techniques such as angle-resolved photoemission spectroscopy (ARPES). However, interpreting ARPES data requires specialized expertise, and the measurements themselves are often susceptible to noise. As experiments produce larger amounts of data, carefully reviewing every image by hand becomes time-consuming and inefficient.
To address this challenge, a team from Tokyo University of Science (TUS), Nagoya University, and Kyoto Institute of Technology in Japan developed a machine learning approach to analyze Fermi surface images of a material called Co2MnGaxGe1-x. This material belongs to a family known as Heusler alloys and is of particular interest for spintronics, a field that uses the spin of electrons—rather than only their charge—to process information. The alloy is also known for exhibiting the anomalous Nernst effect, in which a voltage is generated from a temperature difference in a magnetic material. Both phenomena are closely related to special features called nodal lines that appear on the material's Fermi surface.
The team at TUS included Professor Masato Kotsugi, former Master's student Daichi Ishikawa, and Kentaro Fuku. "The study contributes to a growing movement that harnesses artificial intelligence (AI) to reveal patterns in materials that might otherwise remain hidden," says Prof. Kotsugi. The study will be published in the journal Scientific Reports on April 27, 2026.
The researchers used a technique called principal component analysis (PCA). PCA is a type of unsupervised machine learning that simplifies complex data while keeping the most important patterns. Even though Fermi surfaces can have detailed and complicated shapes, the range of compositions studied in this alloy is relatively narrow, making PCA well-suited for identifying systematic trends.
The researchers began with computer simulations based on density functional theory to calculate the electronic structure of the material at different compositions. From these calculations, the team generated images of the Fermi surface. They also calculated spin polarization, a key property that describes the imbalance between electrons with different spin directions. The Fermi surface images were converted into one-dimensional vectors and analyzed using PCA to identify similarities and differences among compositions.
The method successfully identified the exact compositions where significant changes in the Fermi surface topology occur. In particular, near a gallium concentration of about 0.94 to 0.95, sudden "jumps" in the simplified PCA representation corresponded to the emergence of nodal lines and extrema and inflection points in spin polarization.
Importantly, the method remained effective even when the images were intentionally blurred or strong noise was added to simulate real experimental conditions, mimicking ARPES data, and the approach continued to successfully identify compositions associated with variations in spin polarization and nodal lines.
The findings show that this machine learning approach can quickly highlight important changes in a material's Fermi surface. Such tools could help scientists screen large datasets more efficiently and accelerate the development of materials with desirable electronic properties. Moreover, its ability to detect outliers through differential analysis in PCA space could be extended to screen other material candidates, including strongly correlated materials with flat bands and Weyl or Dirac semimetals with multiple nodal features, enabling researchers to identify promising material candidates for diverse applications.
"AI will be able to analyze all kinds of materials, from spintronics to topological materials and superconductivity," says Prof. Kotsugi.
Reference
DOI: https://doi.org/10.1038/s41598-026-39115-0
About The Tokyo University of Science
Tokyo University of Science (TUS) is a well-known and respected university, and the largest science-specialized private research university in Japan, with four campuses in central Tokyo and its suburbs and in Hokkaido. Established in 1881, the university has continually contributed to Japan's development in science through inculcating the love for science in researchers, technicians, and educators.
With a mission of "Creating science and technology for the harmonious development of nature, human beings, and society," TUS has undertaken a wide range of research from basic to applied science. TUS has embraced a multidisciplinary approach to research and undertaken intensive study in some of today's most vital fields. TUS is a meritocracy where the best in science is recognized and nurtured. It is the only private university in Japan that has produced a Nobel Prize winner and the only private university in Asia to produce Nobel Prize winners within the natural sciences field.
Website: https://www.tus.ac.jp/en/mediarelations/
About Professor Masato Kotsugi from Tokyo University of Science
Professor Masato Kotsugi graduated from Sophia University, Japan, in 1996 and subsequently received his Ph.D. from the Graduate School of Engineering Science at Osaka University, Japan, in 2001. He joined Tokyo University of Science in 2015 as a lecturer and is now a Professor at the Faculty of Advanced Engineering, Department of Materials Science and Technology. Prof. Kotsugi and his students conduct cutting-edge research on high-performance materials to create a green energy society. He has published over 130 peer-reviewed papers and is currently interested in solid-state physics, magnetism, synchrotron radiation, and materials informatics.
