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 $B{H}_{\text{max}}$. 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 (${H}_{c}$). 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 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 ${H}_{c}$ predictions for materials such as $\text{Ce}$-doped ${\text{Nd}}_{2}{\text{Fe}}_{14}\text{B}$, 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 $\mathrm{Nd}$-site-dependent magnetic anisotropy behavior in ${\text{Nd}}_{2}{\text{Fe}}_{14}\text{B}$, confirming that $\text{Nd}\phantom{\rule{0.2em}{0ex}}4g$ sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (${T}_{\mathrm{c}}$). Both calculated results are in good agreement with the experiments. 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 grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.