A joint team from Tokyo University of Science and partner institutions developed the entropy-feature-eXtended Ginzburg-Landau (eX-GL) model to study maze magnetic domains in rare-earth iron garnet and assess their role in energy loss in electric motors.

The researchers collect inputs from microscopic domain images of a rare-earth iron garnet sample across temperatures to feed the model, aiming to connect microstructure to macroscopic dissipation.

The study seeks to explain magnetic hysteresis and temperature-driven magnetization reversal by linking domain-scale structures to overall energy dissipation through a physics-based, explainable AI framework.

The eX-GL workflow fuses persistent homology to extract topological features from domain images, machine learning to identify key features, and energy landscape analysis to relate microstructures to magnetization-reversal dynamics.

In essence, eX-GL combines topological data analysis, ML feature extraction, and energy-landscape insight to connect microscopic maze domains with magnetization reversal behavior.

Findings show maze domains grow more complex as domain-wall length increases, due to entropy interacting with exchange forces, revealing hidden energy barriers tied to energy loss in magnetic materials.

The study quantifies energy transfer among exchange interactions, demagnetizing effects, and entropy, showing longer walls drive more intricate maze domains through entropy–exchange coupling.

The work was published in Scientific Reports on February 11, 2026, using temperature-varied domain images of a rare-earth iron garnet as inputs.

A novel computational approach using the eX-GL model analyzes maze-domain patterns in soft magnets to understand magnetization reversal and the influence of temperature.

The analysis identifies a dominant feature (PC1) that captures the magnetization-reversal process and maps four major energy barriers that shape reversal dynamics, clarifying how entropy, exchange, and demagnetizing effects drive maze-domain behavior.

The eX-GL framework automates interpretation of complex magnetization processes and offers a generalizable approach that could extend to other systems with similar free-energy landscapes, potentially aiding efforts to reduce iron loss in motors.

The study, published in Scientific Reports, is supported by JSPS KAKENHI and JST-CREST, with additional institutional support from TREMS and collaborating researchers.