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 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 BHmax. While first-principles density functional theory (DFT) predicts materials’ magnetic moments, magnetocrystalline anisotropy constants, and exchange interactions, it cannot compute extrinsic properties such as coercivity (Hc). Although it is possible to calculate Hc 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 issues, we employ machine-learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. The use of a large experimental dataset enables realistic Hc predictions for materials such as Ce-doped Nd2⁢Fe14⁢B, comparing favorably against micromagnetically simulated coercivities. Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to Hc. With DFT calculations, we predict the Nd-site-dependent magnetic anisotropy behavior in Nd2⁢Fe14⁢B, confirming that Nd 4⁢g sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (Tc). Finally, both calculated results are in good agreement with the experiments. The coupled experimental dataset and ML modeling with DFT input predict Hc with far greater accuracy and speed than was previously possible using micromagnetic modeling. Further, we reverse engineer the grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.