The explosive growth of electric vehicles has intensified the search for ways to make electric motors more energy efficient. One major challenge is iron loss, also called magnetic hysteresis loss, which occurs when magnetic fields inside the motor repeatedly reverse direction. This process wastes energy as heat within the motor core, which is made from soft magnetic materials. Because electric motors often operate at high temperatures, thermal effects can also partially demagnetize these materials, making the energy loss problem even more complicated.
A key factor behind these effects is the behavior of magnetic domains, which are tiny magnetic regions inside materials. The arrangement and structure of these domains strongly affect how magnetic materials respond to heat and how much energy they lose during operation.
Complex Magnetic Maze Domains
Some soft magnetic materials contain highly intricate magnetic structures called maze domains, named for their zig-zag, labyrinth-like appearance. These maze domains can change abruptly as temperatures rise or fall, influencing how energy is lost in the material. However, scientists have struggled to fully understand these structures because many interacting factors are involved, including the material’s microscopic structure, thermal effects, and energy stability.
To better understand this behavior, researchers led by Professor Masato Kotsugi and Dr. Ken Masuzawa from the Department of Material Science and Technology at Tokyo University of Science (TUS), Japan, worked with collaborators from the University of Tsukuba, Okayama University, and Kyoto University to develop a new model called the entropy-feature-eXtended Ginzburg-Landau (eX-GL) model. The team used this approach to study the energy landscape of maze domains in a rare-earth iron garnet (RIG).
“Conventional simulations oversimplify real materials, while experiments reveal complexity without a clear way to quantify cause and effect,” explains Prof. Kotsugi. “Our physics-based explainable artificial intelligence framework addresses these limitations and is designed to mechanistically explain temperature-dependent magnetization reversal process.”
Their findings were published in the journal Scientific Reports.
AI and Physics Reveal Hidden Magnetic Behavior
To explore how temperature affects magnetization removal in maze domains, the researchers captured microscopic images of the magnetic domains in the RIG sample at different temperatures. These images were then analyzed using the eX-GL model.
The first stage of the model uses persistent homology (PH), a sophisticated mathematical method that identifies topological features within data. This allowed the team to detect uneven structural characteristics in the magnetic domain images. Next, machine learning-based pattern recognition was used to determine the most important features from the PH data, producing a digital free-energy landscape that tracks how magnetic microstructures evolve as energy changes. Finally, mathematical analysis linked these microscopic domain structures to the larger magnetization reversal process.
Using this method, the researchers identified a dominant feature known as PC1, which successfully captured the magnetization reversal process. By connecting PC1 with physical properties, the team visualized four major energy barriers that strongly influence magnetization reversal dynamics.
Hidden Energy Barriers Inside Magnetic Materials
A detailed analysis of these barriers and the related microstructures revealed how different forms of energy affect magnetization reversal. The researchers measured energy transfer involving exchange interactions, demagnetizing effects, and entropy.
They also discovered that maze domains grow more complex as the length of domain walls increases. This increasing complexity is driven by interactions between entropy and exchange forces. These results helped clarify the physical mechanisms behind maze-domain reversal behavior.
“Our eX-GL approach effectively automates the interpretation of complex magnetization reversal process and enables identification of hidden mechanisms, difficult to discern using conventional methods,” says Prof. Kotsugi. “In addition, since free energy is a universal thermodynamic metric, our model can be extended to other systems with similar characteristics.”
Overall, the study not only sheds light on the mechanics of maze domains, but also introduces a broader strategy for investigating complex energy landscapes in magnetic systems and other related physical materials.
This research was supported by a Japan Society for the Promotion of Science (KAKENHI) Grant-in-Aid for Scientific Research (A) (21H04656). Additional support came from JST-CREST (Grant No. JPMJCR21O1). C. Mitsumata received support from the Tsukuba Research Center for Energy Materials Science (TREMS) at the University of Tsukuba.