Topological data analysis for magnetic domain structure characterization*

Analysis of the magnetic domain structure is an important process in the development of advanced magnetic materials. A number of successful studies have been carried out by high-resolution magnetic imaging or LLG simulations. However, the treatment of the information of the whole image, especially the shape of the magnetic domain structure, has not been sufficiently discussed.
We here executed the topological data analysis (TDA) to extract the feature of the shape in a magnetic domain structure [1, 2]. Maze magnetic domain structure was analyzed by TDA to visualize the pinning site during the magnetization reversal process. We utilized persistent homology to extract the topological feature of the magnetic domain structure, and principal component analysis was used to construct the correlation between persistence diagram and a magnetic hysteresis loop. As a result, we could automatically visualize the pinning site as a topological defect in the original magnetic domain structure for the first time.
[1] T. Yamada and M. Kotsugi et al. Vacuum and Surface Science,
[2] Y. Hiraoka, et al., PNAS, 113 (2016) 7035-7040