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. Nevertheless, the discovery of new magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge. Traditional density functional theory (DFT) accurately predicts intrinsic permanent magnet properties such as magnetic moments, magneto-crystalline anisotropy constants, and exchange interactions. However, it cannot compute extrinsic macroscopic properties, such as coercivity ($H_c$), which are influenced by factors like microscopic defects and internal grain structures. Although micromagnetic simulation helps compute $H_c$, it overestimates the values almost by an order of magnitude due to Brown's paradox. To circumvent these limitations, we employ machine learning (ML) methods in an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. Our novel ML approach is computationally much faster than the micromagnetic simulation program, the mumax$^3$. We successfully utilize it to predict $H_c$ values for materials like cerium-doped $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$, and subsequently compare the predicted values with experimental results. Remarkably, our ML model accurately identifies uniaxial magnetic anisotropy as the primary contributor to $H_c$. With DFT calculations, we predict the Nd-site dependent magnetic anisotropy behavior in $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$, confirming $4f$-site planar and $4g$-site uniaxial to crystalline $c$-direction in good agreement with experiment. The Green's function atomic sphere approximation calculated a Curie temperature ($T_{\rm C}$) for $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$ that also agrees well with experiment.