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

We present a machine learning (ML) guided approach to predict saturation magnetization $({M}_{\mathrm{S}})$ and coercivity $({H}_{\mathrm{C}})$ in Fe-rich soft magnetic alloys, particularly Fe-Si-B systems. ML models trained on experimental data reveal that increasing Si and B content reduces ${M}_{\mathrm{S}}$ from 1.81 T $(\mathrm{DFT}\ensuremath{\approx}2.04 \mathrm{T})$ to $\ensuremath{\approx}1.54$ T $(\mathrm{DFT}\ensuremath{\approx}1.56\phantom{\rule{0.28em}{0ex}}\mathrm{T})$ 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 (2.09 T), Fe-5Si-5B (2.01 T), and Fe-10Si-10B (1.54 T) alloy compositions further supports our findings. These trends are consistent with density functional theory predictions, which link increased electronic disorder and band broadening to lower ${M}_{\mathrm{S}}$ 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 reveal that ${M}_{\mathrm{S}}$ is governed by a nonlinear interplay between Fe content and early transition metal ratios, while ${H}_{\mathrm{C}}$ 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 pseudoquaternary compositional space, which shows comparable magnetic properties to NANOMET $({\mathrm{Fe}}_{84.8}{\mathrm{Si}}_{0.5}{\mathrm{B}}_{9.4}{\mathrm{Cu}}_{0.8}{\mathrm{P}}_{3.5}{\mathrm{C}}_{1})$, FINEMET $({\mathrm{Fe}}_{73.5}{\mathrm{Si}}_{13.5}{\mathrm{B}}_{9}\phantom{\rule{0.16em}{0ex}}{\mathrm{Cu}}_{1}{\mathrm{Nb}}_{3})$, NANOPERM $({\mathrm{Fe}}_{88}{\mathrm{Zr}}_{7}{\mathrm{B}}_{4}{\mathrm{Cu}}_{1})$, and HITPERM $({\mathrm{Fe}}_{44}{\mathrm{Co}}_{44}{\mathrm{Zr}}_{7}{\mathrm{B}}_{4}{\mathrm{Cu}}_{1}$. Our findings demonstrate the potential of the ML framework for accelerated search of high-performance soft magnetic materials.