Interpretable machine learning-guided design of Fe-based soft magnetic alloys

Abstract

We present a machine-learning guided approach to predict saturation magnetization (MS) and coercivity (HC) in Fe-rich soft magnetic alloys, particularly Fe-Si-B systems. ML models trained on experimental data reveals that increasing Si and B content reduces MS from 1.81T (DFT~2.04 T) to ~1.54 T (DFT~1.56T) in Fe-Si-B, which is attributed to decreased magnetic density and structural modifications. Experimental validation of ML predicted magnetic saturation on Fe-1Si-1B (2.09T), Fe-5Si-5B (2.01T) and Fe-10Si-10B (1.54T) alloy compositions further support our findings. These trends are consistent with density functional theory (DFT) predictions, which link increased electronic disorder and band broadening to lower MS values. Experimental validation on selected alloys confirms the predictive accuracy of the ML model, with good agreement across compositions. Beyond predictive accuracy, detailed uncertainty quantification and model interpretability including through feature importance and partial dependence analysis reveals that MS is governed by a nonlinear interplay between Fe content, early transition metal ratios, and annealing temperature, while HC is more sensitive to processing conditions such as ribbon thickness and thermal treatment windows. The ML framework was further applied to Fe-Si-B/Cr/Cu/Zr/Nb alloys in a pseudo-quaternary compositional space, which shows comparable magnetic properties to NANOMET (Fe84.8Si0.5B9.4Cu0.8 P3.5C1), FINEMET (Fe73.5Si13.5B9 Cu1Nb3), NANOPERM (Fe88Zr7B4Cu1), and HITPERM (Fe44Co44Zr7B4Cu1. Our fundings demonstrate the potential of ML framework for accelerated search of high-performance, Co- and Ni-free, soft magnetic materials.