Machine Learning for Relating Structure and Coercivity of Permanent Magnets

Abstract

Micromagnetic simulations are typically limited to a few micrometers only. Computing larger systems, especially with the requirement to calculate bulk magnetic properties, are not possible with conventional methods. The advances in the field of machine learning in combination with reduced order models are boosting the size limitations to a new level. Here we propose two strategies to relate the microstructure of permanent magnets with local coercivities of spatially confined areas and further on the superposing of all local field values. In a first approach we create an artificial model of an ideally structured large-grained Nd2Fe14B hard magnetic cube composed of 1000 grains [1]. Switching fields are calculated close to the boundary of the grains, and without pinning sites within the grains, nucleation is instantly switching the grain. We apply the Embedded Stoner–Wohlfarth (ESW) method, which places small ferromagnetic particles close to the grain surface, where the critical field is computed including long-range interactions of uniformly magnetized grains. Due to the reduced order model, much larger magnets, with respect to both grain size and number of grains, can be computed compared to conventional micromagnetic simulations. The simulation data is fed to a machine learning model, more specific a random forest classifier, to identify the most prominent microstructural attributes as well as to find weak spots in the magnet. Machine learning analysis shows that increasing the local coercivity near the top and bottom edges of the bulk sample helps to improve the magnet's properties. In a second approach we create simulation models directly from Electron Backscatter Diffraction (EBSD) data [2]. An automated meshing routine scans the microstructure and creates finite element meshes for interesting sections of the EBSD map. Local switching events are computed and fed into a machine learning model to again find weak spots in the microstructure. In contrast to the work of Blank [3] we calculate macroscopic properties of the permanent magnet by switching field distributions of real microstructures, which are obtained by the trained machine learning model. A full hysteresis curve of the bulk material can be calculated by the local switching fields, exchange coupling between and stray fields of the surrounding grains. Collective reversal starts from neighboring grains with high degree of misalignment. Acknowledgment: The authors gratefully acknowledge the financial support of the Christian Doppler Research Association, the Federal Ministry of Digital and Economic Affairs of the Republic of Austria, the Austrian Science Fund (FWF), Project: I 3288-N36 and the German Research Foundation (DFG), Project: 326646134. [1] Exl, L., et al. "Magnetic microstructure machine learning analysis." Journal of Physics:Materials 2.1 (2018): 014001. [2] Gusenbauer, M., et al. "Extracting local nucleation fields in permanent magnets using machine learning." npj Computational Materials 6.1 (2020): 1-10. [3] Blank, R. "Microscopic model for the demagnetization curve of nucleation type magnets SmCo5 and Nd2Fe14B." Journal of magnetism and magnetic materials 83.1-3 (1990): 192-194.