Accelerated discovery and design of Fe-Co-Zr magnets with tunable magnetic anisotropy through machine learning and parallel computing

Rare earth (RE)--free permanent magnets, as alternative substitutes for RE-containing magnets for sustainable energy technologies and modern electronics, have attracted considerable interest. We performed a comprehensive search for new hard magnetic materials in the ternary Fe-Co-Zr space by leveraging a scalable, machine learning--assisted materials discovery framework running on GPU-enabled exascale computing resources. This framework integrates a crystal graph convolutional neural network (CGCNN) machine learning (ML) method with first-principles calculations to efficiently navigate the vast composition-structure space. The efficiency and accuracy of the ML approach enable us to reveal 9 new thermodynamically stable ternary Fe-Co-Zr compounds and 81 promising low-energy metastable phases with their formation energies within 0.1 eV/atom above the convex hull. The predicted compounds span a wide range of crystal symmetries and magnetic behaviors, providing a rich platform for tuning functional properties. Based on the analysis of site-specific magnetic properties, we show that the ${\mathrm{Fe}}_{6}{\mathrm{Co}}_{17}{\mathrm{Zr}}_{6}$ compound obtained from our ML discovery can be further optimized by chemical doping. Chemical substitutions lead to a ternary ${\mathrm{Fe}}_{5}{\mathrm{Co}}_{18}{\mathrm{Zr}}_{6}$ phase with a strong anisotropy of ${\mathrm{K}}_{1}=1.1\phantom{\rule{0.16em}{0ex}}\mathrm{MJ}\text{/}{\mathrm{m}}^{3}$ and a stable quaternary magnetic ${\mathrm{Fe}}_{5}{\mathrm{Co}}_{16}{\mathrm{Zr}}_{6}{\mathrm{Mn}}_{4}$ compound.