In recent years, the surge in electric vehicle adoption has thrust attention onto the performance of electric motors, particularly their energy conversion efficiency. A persistent challenge lies in a fundamental source of energy loss known as iron loss or magnetic hysteresis loss. This phenomenon occurs due to the cyclic reversal of magnetic fields within the soft magnetic materials composing the motor cores. These materials operate under high-temperature conditions that exacerbate thermal effects, leading to phenomena like partial demagnetization. Such thermal influences introduce complexity to the intrinsic mechanisms governing hysteresis loss, directly impacting motor efficiency and longevity.
At the heart of these magnetic systems are intricate configurations known as magnetic domains—microscale regions where magnetization is uniform internally but varies sharply at their boundaries. Some soft magnetic materials develop distinctive patterns called maze domains, characterized by complex zig-zag arrangements. These domains exhibit highly nonlinear and temperature-sensitive behaviors influencing magnetic response and energy dissipation, posing immense challenges for existing theoretical and computational models. The interplay of thermal fluctuations, metallurgical microstructures, and magnetic energy landscapes complicates detailed analysis, calling for innovative approaches to delineate cause and effect in these systems.
To overcome these analytical barriers, a multidisciplinary research team led by Professor Masato Kotsugi and Dr. Ken Masuzawa at Tokyo University of Science, Japan, has engineered an advanced computational framework titled the entropy-feature-extended Ginzburg-Landau model (eX-GL). This model innovatively integrates concepts from statistical physics, topology, and machine learning to unravel the hidden intricacies underpinning temperature-dependent magnetization reversal phenomena in maze domain structures. Their recent study, published in Scientific Reports, leverages this framework to comprehensively investigate complex magnetic domain behavior in rare-earth iron garnet (RIG), a soft magnetic compound relevant to motor technologies.
At the core of the eX-GL model lies persistent homology, a sophisticated topological data analysis tool adept at extracting inhomogeneous and multi-scale structural features from microscopic domain images. By processing domain images acquired experimentally at varied temperatures, persistent homology translates convoluted spatial patterns of magnetic domains into quantifiable topological summaries. The research team then employs machine learning algorithms to distill essential features from this topological data, synthesizing a digital free-energy landscape that dynamically maps the evolution of magnetic microstructures as temperature varies.
A pivotal breakthrough of this approach is the identification of a principal component, designated PC1, which robustly encapsulates the magnetization reversal mechanism. Correlating PC1 with physically meaningful parameters, the researchers delineated four key energy barriers embedded within the free-energy landscape. These barriers govern magnetic domain dynamics and serve as critical hurdles that magnetic moments must overcome during reversal transitions. Their elucidation provides unprecedented insight into the microscopic origins of hysteresis loss and temperature susceptibility in maze magnetic domains.
Deep causal analyses of these energy barriers revealed intricate energy transfer among fundamental magnetic interactions—exchange coupling, demagnetizing fields, and entropy contributions arising from thermal agitation. Surprisingly, the study underscores the role of entropy in driving complexity within the maze domains, highlighting how increasing domain wall length accentuates domain labyrinthine intricacy. This entropic-exchange interaction coupling redefines traditional views on magnetization dynamics, offering novel explanatory power on how thermal fluctuations modulate domain architectures and hysteresis behavior.
Professor Kotsugi emphasizes that conventional simulation frameworks often oversimplify the rich heterogeneity found in real soft magnetic materials, while experimental observations uncover complexity without clear mechanistic explanations. The eX-GL model bridges this gap, providing a physics-grounded, explainable artificial intelligence framework that mechanistically interprets temperature-dependent magnetization reversal. By mapping intricate domain morphologies onto universal thermodynamic constructs like free energy, this methodology transcends material specifics, hinting at extensibility to a broad range of physical systems exhibiting complex energy landscapes.
Importantly, the free-energy landscape reconstructed by this model serves as a universal metric bridging microscale magnetic structures and macroscale material behavior. This paves the way for future studies to systematically dissect multifaceted energy interactions within magnetic and related condensed matter systems. The entropic feature integration into the classical Landau model represents a significant conceptual advance, furnishing a versatile platform that fuses topological insights and machine learning with well-established physics principles.
The implications of this research extend beyond fundamental physics to practical engineering. By elucidating the detailed energy barriers and reversal processes in maze domains, the study provides critical knowledge that can influence the design and optimization of soft magnetic materials for electric motors and other technologies where minimizing energy loss is paramount. Additionally, the framework orientation towards explainability addresses a key need in scientific AI applications, ensuring interpretable results conducive to experimental validation and material innovation.
Underpinning this advance is a collaborative effort involving Tokyo University of Science, University of Tsukuba, Okayama University, and Kyoto University. This multidisciplinary consortium combined expertise in materials science, computational physics, and advanced data analysis to achieve this breakthrough. Supported by the Japan Society for the Promotion of Science (KAKENHI), JST-CREST, and other funding bodies, the collective endeavor exemplifies the synergy between basic science and applied research driving energy-efficient technological progress.
Professor Masato Kotsugi, a leading figure in solid-state physics and magnetism with over 130 peer-reviewed publications, spearheaded this research. His laboratory’s focus on high-performance materials towards a green energy society aligns with the broader societal imperative to reduce energy loss and promote sustainable technologies. The development of the eX-GL model marks a transformative step toward deciphering the complexity of magnetic domain structures, opening new frontiers in materials informatics and physics-based AI.
This groundbreaking study not only refines fundamental understanding of complex magnetization reversal in soft magnets but also establishes a generalizable, explainable analytical toolset for exploring intricate energy landscapes. By marrying persistent homology, machine learning, and thermodynamic modeling, it sets a precedent for future exploration of multifactorial physical phenomena where conventional approaches face limitations. Ultimately, such innovation will accelerate the development of next-generation materials critical to sustainable energy and advanced electronic applications.
Subject of Research: Not applicable
Article Title: Explainable analysis of the complex maze magnetic domain structure through extension of the Landau free energy model by adding an entropy feature
News Publication Date: 11-Feb-2026
References: DOI: 10.1038/s41598-026-39617-x
Image Credits: Prof. Masato Kotsugi, Tokyo University of Science
Keywords
Physical sciences, Chemistry, Inorganic chemistry, Inorganic compounds, Magnetism, Soft magnetic materials, Magnetic domains, Maze domains, Persistent homology, Machine learning, Free energy landscape, Entropy, Ginzburg-Landau model
Tags: electric motor core material propertiesenergy conversion efficiency in electric vehiclesinnovative approaches to magnetic pattern researchmagnetic energy landscape modelingmagnetic hysteresis loss in electric motorsmaze domain patterns in magnetismmetallurgical microstructure impact on magnetismmicroscopic magnetic domain configurationsnonlinear magnetic behavior analysispartial demagnetization phenomenasoft magnetic materials in high temperaturesthermal effects on magnetic domains
