Machine learning-accelerated discovery of iron cobalt phosphides as rare-earth-free magnets

The discovery of rare-earth-free permanent magnets has been a goal of scientists for decades. The absence of rare-earth elements will alleviate a pressing concern about the availability of rare-earth elements used in permanent magnets. These magnets are crucial for applications such as wind turbines, electric cars, and memory devices. Rare-earth magnets are special owing to a large magnetic anisotropy energy (${K}_{1}$). In contrast, iron cobalt phosphides hold promise since doping P into cubic FeCo can induce anisotropy, leading to a large coercivity, without introducing rare-earth elements. We present a comprehensive search over the Fe-Co-P ternary space for magnets, utilizing recently developed adaptive machine learning feedback to efficiently screen over 850 000 structures. We focus on machine learning acceleration as a paradigm for materials design. Further adaptive genetic algorithm searches and first-principles calculations aid in the identification of 16 new structures below the known convex hull. Five of them possess high magnetic polarization (${J}_{s}\phantom{\rule{4pt}{0ex}}>$ 1 T). The structures with desirable magnetic properties center on ${(\mathrm{Fe},\mathrm{Co})}_{2}\mathrm{P}$. This supports conventional wisdom, which focuses on the mixture of the two known end compounds: ${\mathrm{Fe}}_{2}\mathrm{P}$ and ${\mathrm{Co}}_{2}\mathrm{P}$. Our work provides guidance for synthesis. We find ${\mathrm{Fe}}_{7}{\mathrm{CoP}}_{4}$ shows the most promise (${J}_{s}=1.03\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ and ${K}_{1}=0.83\phantom{\rule{0.16em}{0ex}}\mathrm{MJ}/{\mathrm{m}}^{3}$).