Rare-earth-free permanent magnets ("gap magnets")
Identify rare-earth-free compounds with enough magnetization, magnetocrystalline anisotropy and Curie temperature to fill the performance gap between ferrites and Nd-Fe-B magnets.
Cite
@misc{cairn-rare-earth-free-permanent-magnets,
title = {Rare-earth-free permanent magnets ("gap magnets")},
author = {{Cairn Commons contributors}},
howpublished = {\url{https://cairn-commons.com/problems/rare-earth-free-permanent-magnets}},
year = {2026},
note = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-11-12}
} Also: CITATION.cff · Atom feed of results
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What a result looks like: C-16, a newcomer working with an AI model found C(85,24,3) ≤ 76 (previous best 77), and a computer verified it within minutes. A documented dead end counts too.
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Current state
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The problem
High-performance permanent magnets rely on rare earths (Nd-Fe-B, Sm-Co). The open question is whether a rare-earth-free compound can combine high saturation magnetization, large uniaxial magnetocrystalline anisotropy and a high Curie temperature — intrinsic prerequisites for a useful magnet — and then whether it can be made coercive.
Known status. Nd2Fe14B was discovered independently at General Motors (Croat) and Sumitomo (Sagawa) in 1982 and announced in 1984. Coey (Engineering 2020) puts the gap at about 48 kJ/m3 for ferrites versus 515 kJ/m3 for the best rare-earth magnets, and notes that no commercially viable "gap magnet" has emerged despite decades of work. High-throughput DFT screens continue: Jami, Bhagat & Bhattacharya (arXiv:2507.01849, 2025) filtered about 8,372 binary rare-earth-free Materials Project compounds by magnetization (> 0.5 T), anisotropy (> 0.5 MJ/m3), Curie temperature (> 1200 K) and stability to 56 candidates, highlighting tetragonal ZnFe and Fe8N.
What counts as progress
- Reproducible screens with fully published workflows (functional, U values, spin-orbit settings, k-point convergence for anisotropy energies) and complete ranked candidate lists.
- Benchmarks of computed anisotropy and Curie temperatures against known magnets, quantifying the typical error of each method.
- Machine-learning surrogates for anisotropy or Curie temperature evaluated on held-out chemistries.
- Documented negative results: a candidate eliminated because it is dynamically or thermodynamically unstable, or because anisotropy collapses at finite temperature.
How it is checked. A reviewer re-runs selected calculations, checks convergence of the anisotropy energy (which is small and sensitive), confirms the database snapshot and filters, and compares against published benchmarks for known compounds.