Quantification of the Coercivity Factor in Soft Magnetic Materials at Different Frequencies Using Topological Data Analysis

The kinetics of magnetic domain structure in soft magnetic materials is crucial for the understanding of their functional properties, such as coercivity and loss. We have developed a high-speed and real-time magnetic domain measurement system based on the magnetic-optical Kerr effect (MOKE) microscope. High-speed evolution of domain structures of yttrium iron garnet (YIG) thin film under ac magnetic field and its frequency-dependent hysteresis curves were measured by the system. Subsequently, we combined persistent homology (PH) with principal component analysis (PCA), a dimensionality reduction method, to extract topological information on domain structure and analyze the complex magnetization process. We successfully extracted physically meaningful features of the frequency-dependent magnetic domain structures. As a result, using the machine-learning outputted features, the coercivity contributing factors of the magnetization reversal process were visualized onto domain structures. We also found that the occurrence of the coercivity factors increases along excitation magnetic field frequency, indicating the increase of loss. These findings provide new insight into the relationship between coercivity and magnetic domain structure dynamics.