Magnetic hysteresis loss, often referred to as iron loss, plays a crucial role in determining the efficiency of electric motors, which are vital components of electric vehicles. This phenomenon occurs when the magnetic field within the motor core, composed of soft magnetic materials, is repeatedly reversed due to the fluctuating current in the windings. This reversal causes tiny magnetic regions, known as magnetic domains, to change their magnetization direction, albeit inefficiently, leading to energy loss. Notably, iron loss accounts for approximately 30% of the total energy loss in motors, contributing significantly to carbon dioxide emissions and posing a pressing environmental challenge.
Despite over 50 years of research, the precise origins of iron loss in soft magnetic materials have remained elusive. The energy expended during magnetization reversal in these materials is linked to complex changes in magnetic domain structures, which have primarily been interpreted visually, with underlying mechanisms discussed only qualitatively. Researchers suggest that exploring the correlation between energy loss and the microstructure of magnetic domains could be a promising avenue. However, most existing physical models for analyzing magnetization reversal are tailored for homogeneous systems, whereas practical soft magnetic materials like nonoriented electrical steel (NOES) are heterogeneous, complicating their analysis.
Innovative Approach by Tokyo University of Science
In a groundbreaking development, 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 devised a novel approach utilizing the extended-Ginzburg–Landau (ex-GL) framework. This method successfully traces the origin of iron loss to the magnetic domain structure. Professor 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.”
Their study was published in the journal Scientific Reports on July 15, 2025.
The team initially 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. Subsequently, they applied principal component analysis (PCA), a statistical technique, to extract essential features hidden in the complex PH data. Two features emerged: PC1, representing magnetization, and PC2, representing magnetic domain walls.
Mapping the Energy Landscape
Utilizing these features, the team constructed an extended energy landscape using the ex-GL framework, mapping changes in the magnetic domain structure with energy as a graph where each point corresponds to a magnetic domain image. A comprehensive correlation analysis between the features and physical parameters using this graph uncovered physically meaningful features explaining energy loss during magnetization reversal.
The analysis revealed the presence of promoting and resisting factors in the magnetization reversal process. Interestingly, both factors were found in the same locations, primarily near grain boundaries, which are interfaces between different crystals in a crystalline material. This suggests a competition between these factors. Professor Kotsugi notes,
“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.”
In locations with only resisting factors, segmented magnetic domains were identified as the main contributors to energy loss.
Implications for Sustainable Development
The significance of this method lies in its 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 Professor Kotsugi. This research paves the way for 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, and paving the way towards a sustainable future.
