Accurate Machine Learning Predictions of Coercivity in High-Performance Permanent Magnets

Increased demand for high-performance permanent magnets in the electric vehicle and wind turbine industries has prompted the search for cost-effective alternatives.Discovering new magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge to researchers because of issues with the global supply of rare-earth elements, material stability, and a low maximum magnetic energy product BH$_{max}$.While first-principle density functional theory (DFT) predicts materials' magnetic moments, magneto-crystalline anisotropy constants, and exchange interactions, it cannot compute coercivity ($H_c$).Although it is possible to calculate $H_c$ theoretically with micromagnetic simulations, the predicted value is larger than the experiment by almost an order of magnitude, due to the Brown paradox.To circumvent these, we employ machine learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling.The use of a large dataset enables realistic $H_c$ predictions for materials such as Ce-doped Nd$_2$Fe$_{14}$B, comparing favorably against micromagnetically simulated coercivities.Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to $H_c$. With DFT calculations, we predict the Nd-site dependent magnetic anisotropy behavior in Nd$_2$Fe$_{14}$B, confirming that Nd $4g$-sites mainly contribute to uniaxial magneto-crystalline anisotropy, and also calculate Curie temperature (T$_{C}$).Both calculated results are in good agreement with experiment.The coupled experimental dataset and ML modeling with DFT input predict $H_c$ with far greater accuracy and speed than was previously possible using micromagnetic modeling.Further, we reverse-engineer the inter-grain exchange coupling with micromagnetic simulations by employing the ML predictions.