Magnetic hysteresis loss or iron loss is an important magnetic property that determines the efficiency of electric motors and is therefore critical for electric vehicles. It occurs when the magnetic field within the motor core, made up of soft magnetic materials, is repeatedly reversed due to the changing flow of current in the windings. This reversal forces tiny magnetic regions called magnetic domains to repeatedly change their magnetization direction. This change is, however, not perfectly efficient and results in energy loss. In fact, iron loss accounts for approximately 30% of the total energy loss in motors, leading to the emission of carbon dioxide, which represents a pressing environmental concern.

Despite over half a century of research, the origin of iron loss in soft magnetic materials remains elusive. The energy spent during magnetization reversal in these materials depends on complex changes in magnetic domain structures. These have mainly been interpreted visually, and the underlying mechanisms have been discussed only qualitatively. Researchers believe that investigating the correlation between energy loss and the microstructure of magnetic domains is a promising direction. However, most current physical models for analyzing magnetization reversal are designed for homogeneous systems, while practical soft magnetic materials like nonoriented electrical steel (NOES) are heterogeneous, making their analysis difficult.

Now, in a breakthrough, a research team led by Professor Masato Kotsugi from the Department of Material Science and Technology at Tokyo University of Science (TUS), Japan, along with Mr. Michiki Taniwaki, also from TUS, has developed a new approach utilizing the extended-Ginzburg-Landau (ex-GL) framework. This method successfully traces the origin of iron loss to the magnetic domain structure. Prof. Kotsugi explains, "The Ginzburg-Landau (GL) free energy was a useful concept for analyzing the magnetization reversal in a homogeneous system. Recent progress in data science has enabled the ex-GL model, which can be used to analyze heterogeneous systems. In this study, we paired the ex-GL framework with interpretable machine learning for automated analysis of complex magnetization reversal in NOES." Their study was published in the journal Scientific Reports on July 15, 2025.

The team first quantified the complexity of magnetic domains from microstructure images of NOES using persistent homology (PH), a mathematical tool for multiscale analysis of topological features in data. Next, they applied principal component analysis (PCA), a statistical technique, to extract the essential features hidden in the complex PH data. Two features emerged, namely PC1, representing magnetization, and PC2, representing magnetic domain walls.

Using these features, the team then constructed an extended energy landscape using the ex-GL framework, which mapped the changes in the magnetic domain structure with energy as a graph with each point corresponding to a magnetic domain image. The team then performed a comprehensive correlation analysis between the features and physical parameters using this graph, uncovering physically meaningful features that explain energy loss during magnetization reversal.

Their analysis revealed the presence of promoting and resisting factors in the magnetization reversal process. Interestingly, both factors were found in the same locations, mainly near grain boundaries, which are interfaces between different crystals in a crystalline material. This suggests competition between these factors. "The competition between the promoting and resisting factors automatically identifies the location of magnetic domain wall pinning, a key phenomenon responsible for energy loss in soft magnetic materials," notes Prof. Kotsugi. "In locations with only resisting factors, segmented magnetic domains were found to be the main contributors to energy loss."

The significance of this method lies on the automated, precise, data-driven insights into both the mechanism and location of energy loss.

"Our approach enabled us to extract information that would otherwise have been difficult to obtain with only visual inspection," remarks Prof. Kotsugi.

This research paves the way in realizing the United Nations sustainable development goals-affordable and clean energy, industrialization, innovation and infrastructure, and combating climate change. In summary, this study presents an innovative data-driven approach for identifying the origin and addressing energy loss in soft magnetic materials, leading to more efficient, greener electric cars, paving the way towards a sustainable future.

Image title: Proposed extended Ginzburg-Landau (GL) framework for automated analysis of magnetization reversal in nonoriented electrical steel (NOES)
Image caption: The proposed approach automatically identifies the origin of energy loss in NOES, offering information that is difficult to discern using visual inspection. This approach offers a new method for designing efficient soft magnetic materials.
Image credit: Professor Masato Kotsugi from Tokyo University of Science, Japan
License type: Original content
Usage restrictions: Cannot be reused without permission.

Image title: Identification of magnetization reversal process in nonoriented electrical steel based on the data-driven model
Image caption: Scientists identify the complex interplay of promoting and resisting factors that occurs between microscopic magnetic domains and macroscopic magnetic hysteresis using the feature extended Ginzburg-Landau free energy model.
Image credit: Professor Masato Kotsugi from Tokyo University of Science, Japan
Image Source Link: https://doi.org/10.1038/s41598-025-00357-z
License type: CC BY-NC-ND 4.0
Usage restrictions: Credit must be given to the creator. Only noncommercial uses of the work are permitted. No derivatives or adaptations of the work are permitted.

Image title: Extended Ginzburg-Landau free energy model illustrating magnetization reversal process in data space
Image caption: Scientists utilized principal component analysis to extract essential features from the persistent homology concept.
Image credit: Professor Masato Kotsugi from Tokyo University of Science, Japan
Image Source Link: https://doi.org/10.1038/s41598-025-00357-z
License type: CC BY-NC-ND 4.0
Usage restrictions: Credit must be given to the creator. Only noncommercial uses of the work are permitted. No derivatives or adaptations of the work are permitted.

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.