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Machine learning guided processing, microstructure and coercivity mapping in M type strontium hexaferrite
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DOI：10.1038/s41598-026-55574-x.png)
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Abstract
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M-type hexaferrites are technologically important rare-earth-free permanent magnets in which coercivity (Hc) emerges from a strongly coupled and non-linear interplay between processing conditions, microstructural evolution, and intrinsic magnetic parameters. Here, we develop an experimentally grounded, physics-informed machine-learning framework by studying the multidimensional influence of processing parameters (processing temperature and time), microstructural descriptors (grain size), and intrinsic magnetic properties (saturation magnetization (Ms) and magnetocrystalline anisotropy constant (K1)) on Hc. Multiple machine-learning models were trained and extreme gradient boosting (XGBoost) yielded the highest predictive accuracy (test $${R}^{2}=0.970$$ and train $$R^{2}= 0.953$$). A prediction function using nested for-loops was constructed based on the trained XGBoost model and uniform manifold approximation and projection (UMAP) mapping combined heat map consisting of 5600 points was constructed to analyse experimentally actionable design rules for optimization of Hc as a function of five-dimensional input. High Hc is achieved by maintaining optimal combination of grain size within the single-domain regime (500–700 nm), moderate processing temperatures, limited processing durations to suppress grain coarsening, maximizing K1 (2.5–3 × 106 erg cm−3) and reduced Ms (20–30 emu g−1) to limit demagnetizing effects. These findings suggests that enhancement in Hc requires simultaneous control of processing kinetics, microstructural length scales, and intrinsic magnetic parameters, rather than isolated optimization of any single variable. The extracted trends are consistent with established micromagnetic principles, demonstrating that machine learning trained on experimental data can capture physically meaningful processing-structure-property correlations.
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