Weighted ranking of the RE-free permanent magnet campaign candidates

Weighted ranking of the RE-free permanent magnet campaign candidates · Posts on Ouro

Every structure in the rare-earth-free magnet campaign that made it through first-principles DFT (ABACUS + TB2J, production fidelity where available: ecutwfc 65, kspacing 0.16, mp smearing) characterization, ranked by a single transparent score.

Design goal

A permanent magnet has to hold coercivity, which means it has to be uniaxial ([001] easy axis) and stable at room temperature. Beyond that gate, the scoring is built so a high-hardness, low-Ms magnet is not destroyed by its low Ms — hardness (κ) is valuable on its own, independent of energy product, for applications where coercivity or thermal stability matters more than raw output.

Sub-scores (each 0–1)

Property	Transform	Rationale
Uniaxiality	1.0 if easy axis [001], else 0.15	Make-or-break for coercivity
Hardness (κ)	min(κ / 1.0, 1.0)	Saturates at ideal-hard (κ≥1) so a low-Ms hard magnet gets full credit without needing huge Ms
Ms	min(Ms / 1.30, 1.0)	NdFeB ≈ 1.28 MA/m = excellent; capped so it can't dominate
Tc	clamp((Tc − 293) / (600 − 293))	Hard room-temperature floor — 0 below 293 K (not a viable RT magnet), full marks at 600 K (NdFeB-class thermal headroom)
Stability (e_hull)	max(0, 1 − e_hull / 0.30)	On-hull = 1, 300 meV/atom = 0

Weights

Uniaxiality 0.28, Hardness 0.26, Tc 0.20, Ms 0.13, Stability 0.13 (sum 1.0)

Uniaxiality and hardness dominate; Ms is deliberately capped at 13% so it can't rescue a soft or easy-plane structure, and can't erase a hard structure's score just because its moment is modest. The Tc weight (20%) enforces room-temperature viability as a first-class requirement, not an afterthought.

Full ranking

#	Candidate	Easy axis	κ	Ms (MA/m)	Tc (K)	e_hull (eV/atom)	uni

Reading the list

#1 — Fe2B Cmcm is the campaign winner on all-round balance: uniaxial, semi-hard (κ 0.88), NdFeB-class Ms, hot Tc (648 K), near-hull (85 meV/atom). Discovered by GGen generative search; a genuinely novel structure not in Materials Project, structurally related to the AlFe2B2 layered-iron-boride (MAB phase) family. Dynamically stable (0 imaginary phonon modes) and confirmed at production DFT fidelity.

#2 — Fe2B P4/mmm scores well on every live property but its 374 meV/atom metastability zeroes the stability term — a mechanism proof for a strain/substitution route, not a standalone bulk phase.

#3 — Zr2CrFe3 is the demonstration case for the scoring design: it has the lowest Ms in the set (0.33 MA/m) yet still ranks third, because κ saturates at ideal-hard (3.69, full credit) and it's uniaxial. Ms is capped at 13% weight, so the low moment costs only ~0.10 of total score — hardness is not erased by weak Ms. Caveat: Tc is 275 K, below room temperature, scoring zero on the Tc gate — this is a cryogenic/sub-ambient hard magnet, not a room-temperature one.

#4–5 (Fe3B, Fe2B I4/mcm) are the highest-Ms, highest-Tc, most stable structures in the whole campaign — but both are easy-plane and can't hold coercivity standalone. They're the natural soft-phase partners for exchange-coupled nanocomposites with a hard phase like Fe2B Cmcm.

#6–7 are easy-plane with either modest Ms/Tc (Fe3CuAs2) or a hot κ that can't be used because the axis is wrong and Tc is sub-room-temperature (CrSn3).

Screened and disqualified (excluded from ranking — Ms far below usable threshold)

Ten additional candidates were screened via GGen generation + Orb relaxation + DFT-moments/Curie/e_hull, gated at Ms ≥ 1.0 MA/m, Tc ≥ 400 K, e_hull < 0.20 eV/atom before spending production MAE compute. None cleared the gate:

ZrMn3, CrNi3, AlCr3Fe3As2 — all antiferromagnetic/ferrimagnetic, Ms 6–30× below the usable floor, despite strong collaborator synthesizability scores. Same Cr/Mn superexchange-cancellation mechanism that pins Zr2CrFe3's Ms.
TiNbFe4 — correctly ferromagnetic (no competing antiferromagnetic sublattice), perfectly on-hull, but the moment itself is weak (0.17 MA/m) — likely itinerant-magnetism dilution from Ti/Nb d-electron hybridization, a distinct failure mode from cancellation.
MgMn2Co2S6 — reverted to antiferromagnetic despite the sulfide (not oxide) bonding; Mn dominates the ordering.

Takeaway: synthesizability score and magnetic ordering are largely orthogonal. A high synthesizability rank says nothing about whether a structure will actually order ferromagnetically with a usable moment.

Every structure screened across the campaign (77 rows, all phases)

The ranking above uses only the 7 structures that received full production-fidelity MAE. This is the complete record — every polymorph, strain point, GGen variant, and synthesizability candidate touched across all five phases, at whatever fidelity it was actually characterized at (coarse kspacing 0.25 screening vs. production kspacing 0.16 MAE). Blank cells mean that property wasn't computed at that stage (screen-phase rows don't get κ/K1 since MAE wasn't run; the strain rows are held, unrelaxed geometries so their absolute values are indicative, not final).

Full raw CSV: https://ouro.foundation/files/will/re-free-magnet-campaign-full-master-table-77-rows

plaintext

| Phase | Label | Fidelity | Easy axis | K1 (MJ/m³) | κ | Ms (MA/m) | Tc (K) | e_hull (eV/at) | Order | Note |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 baseline | Fe2B | coarse (k0.25) | 100 | 0.465 | 0.434 | 1.401 | 695 |  | FM |  |
| 0 baseline | Fe3CuAs2 | coarse (k0.25) | 100 | 0.726 | 0.866 | 0.878 | 458 |  | FM |  |
| 0 baseline | Zr2CrFe3 | coarse (k0.25) | 001 | 3.168 | 4.806 | 0.330 | 275 |  | AFM/ferri |  |
| 0 baseline | CrSn3 | coarse (k0.25) | 010 | 0.489 | 1.597 | 0.391 | 194 |  | FM |  |
| 0 baseline | MnSn2 | coarse (k0.25) |  |  |  | 0.395 | 336 |  | FM |  |
| 1a polymorph | Zr2CrFe3 P6_3/mmc | coarse | 001 | 3.279 | 4.842 | 0.334 | 281 |  | AFM/ferri | mp-aaacreig |
| 1a polymorph | Zr2CrFe3 Amm2 | coarse | 010 | 0.623 | 1.490 | 0.472 | 306 |  | AFM/ferri | mp-aaacreke |
| 1a polymorph | Fe2B I4/mcm | coarse | 100 | 0.643 | 0.508 | 1.408 | 760 |  | FM | mp-aaaaacvr |
| 1a polymorph | Fe2B P4/mmm | coarse | 001 | 1.189 | 0.754 | 1.291 | 741 |  | FM | mp-aaabgjiy |
| 1b strain | Fe2B c/a=0.9 | coarse | 010 | 0.735 | 0.532 | 1.437 | 668 |  |  | held strain, not relaxed |
| 1b strain | Fe2B c/a=0.95 | coarse | 010 | 2.171 | 0.926 | 1.420 | 706 |  |  | held strain, not relaxed |
| 1b strain | Fe2B c/a=1.0 | coarse | 100 | 0.643 | 0.508 | 1.408 | 760 |  |  | held strain, not relaxed |
| 1b strain | Fe2B c/a=1.05 | coarse | 010 | 2.061 | 0.913 | 1.403 | 714 |  |  | held strain, not relaxed |
| 1b strain | Fe2B c/a=1.1 | coarse | 100 | 1.655 | 0.822 | 1.396 | 701 |  |  | held strain, not relaxed |
| 1b strain | Fe3CuAs2 c/a=0.9 | coarse | 001 | 0.268 | 0.552 | 0.835 | 467 |  |  | held strain, not relaxed |
| 1b strain | Fe3CuAs2 c/a=0.95 | coarse | 010 | 0.144 | 0.394 | 0.861 | 470 |  |  | held strain, not relaxed |
| 1b strain | Fe3CuAs2 c/a=1.0 | coarse | 100 | 0.726 | 0.866 | 0.878 | 458 |  |  | held strain, not relaxed |
| 1b strain | Fe3CuAs2 c/a=1.05 | coarse | 010 | 0.960 | 0.990 | 0.883 | 442 |  |  | held strain, not relaxed |
| 1b strain | Fe3CuAs2 c/a=1.1 | coarse | 100 | 1.142 | 1.074 | 0.888 | 449 |  |  | held strain, not relaxed |
| 1b strain | Zr2CrFe3 c/a=0.9 | coarse | 010 | 0.955 | 2.754 | 0.316 | 263 |  |  | held strain, not relaxed |
| 1b strain | Zr2CrFe3 c/a=0.95 | coarse | 001 | 1.030 | 2.757 | 0.328 | 265 |  |  | held strain, not relaxed |
| 1b strain | Zr2CrFe3 c/a=1.0 | coarse | 001 | 3.279 | 4.842 | 0.334 | 281 |  |  | held strain, not relaxed |
| 1b strain | Zr2CrFe3 c/a=1.05 | coarse | 001 | 2.891 | 4.481 | 0.339 | 290 |  |  | held strain, not relaxed |
| 1b strain | Zr2CrFe3 c/a=1.1 | coarse |  |  |  |  | 301 |  |  | held strain, not relaxed |
| 2 GGen | Fe2B sg123->I4/mmm | coarse | 010 | 0.452 | 1.447 | 0.414 | 629 |  | FM |  |
| 2 GGen | Fe2B sg129->Cmcm | coarse | 001 | 2.424 | 0.973 | 1.428 | 648 |  | FM |  |
| 2 GGen | Fe2B sg139->nan | coarse |  |  |  |  |  |  |  |  |
| 2 GGen | Fe2B sg140->I4/mmm | coarse | 010 | 0.782 | 1.895 | 0.416 | 627 |  | FM |  |
| 2 GGen | Zr2CrFe3 sg123->Pmm2 | coarse |  |  |  |  | 266 |  |  |  |
| 2 GGen | Zr2CrFe3 sg129->P2_12_12 | coarse |  |  |  |  | 229 |  | AFM/ferri |  |
| 2 GGen | Zr2CrFe3 sg139->C2/m | coarse | 100 | 1.354 | 3.050 | 0.340 | 227 |  | AFM/ferri |  |
| 2 GGen | Zr2CrFe3 sg140->Pmc2_1 | coarse | 010 | 0.771 | 2.740 | 0.286 | 234 |  | AFM/ferri |  |
| 2 GGen | Fe3CuAs2 sg123->P4mm | coarse | 010 | 0.609 | 0.980 | 0.710 | 363 |  | FM |  |
| 2 GGen | Fe3CuAs2 sg129->P4mm | coarse | 010 | 0.600 | 0.971 | 0.711 | 356 |  | FM |  |
| 2 GGen | Fe3CuAs2 sg139->P1 | coarse | 001 | 0.629 | 0.935 | 0.757 | 466 |  | FM |  |
| 2 GGen | Fe3CuAs2 sg140->P4mm | coarse | 100 | 0.592 | 0.965 | 0.711 | 356 |  | FM |  |
| prod MAE resweep | Fe2B_ca0.95 | PRODUCTION (k0.16) | 100 | 1.066 | 0.649 | 1.419 |  |  |  | success |
| prod MAE resweep | Fe2B_ca1.05 | PRODUCTION (k0.16) | 100 | 1.857 | 0.867 | 1.403 |  |  |  | success |
| prod MAE resweep | Fe3CuAs2_ca1.1 | PRODUCTION (k0.16) | 100 | 0.929 | 0.969 | 0.887 |  |  |  | success |
| prod MAE resweep | Fe2B_mp-aaabgjiy | PRODUCTION (k0.16) | 001 | 0.664 | 0.564 | 1.290 |  |  |  | success |
| prod MAE resweep | Zr2CrFe3_mp-aaacreig | PRODUCTION (k0.16) |  |  |  |  |  |  |  | error |
| prod MAE resweep | Zr2CrFe3_mp-aaacreke | PRODUCTION (k0.16) |  |  |  |  |  |  |  | timed-out |
| prod MAE resweep | Fe3CuAs2_sg123 | PRODUCTION (k0.16) | 100 | 0.771 | 1.102 | 0.711 |  |  |  | success |
| prod MAE resweep | Fe3CuAs2_sg139 | PRODUCTION (k0.16) |  |  |  |  |  |  |  | error |
| prod MAE resweep | Fe2B_sg140 | PRODUCTION (k0.16) | 010 | 0.639 | 1.751 | 0.407 |  |  |  | success |
| prod MAE resweep | Zr2CrFe3_sg139 | PRODUCTION (k0.16) | 100 | 1.061 | 2.700 | 0.340 |  |  |  | success |
| prod MAE resweep | top5_Fe2B | PRODUCTION (k0.16) | 100 | 0.787 | 0.565 | 1.400 |  |  |  | success |
| prod MAE resweep | top5_Fe3CuAs2 | PRODUCTION (k0.16) |  |  |  |  |  |  |  | error |
| prod MAE resweep | top5_Zr2CrFe3 | PRODUCTION (k0.16) | 001 | 1.857 | 3.687 | 0.330 |  |  |  | success |
| prod MAE resweep | top5_CrSn3 | PRODUCTION (k0.16) | 100 | 0.555 | 1.712 | 0.388 |  |  |  | success |
| prod MAE resweep | top5_MnSn2 | PRODUCTION (k0.16) |  |  |  |  |  |  |  | error |
| 3 Fe-enrich screen | Zr2Fe3_tmpl | screen (coarse) |  |  |  | 0.446 | 339 | 0.3716 | FM | hold |
| 3 Fe-enrich screen | Zr2Fe4_tmpl | screen (coarse) |  |  |  | 0.711 | 427 | 0.0114 | FM | hold |
| 3 Fe-enrich screen | Zr2Fe3_g194 | screen (coarse) |  |  |  | 0.254 | 289 | 0.1076 | FM | hold |
| 3 Fe-enrich screen | Zr2Fe5_g139 | screen (coarse) |  |  |  | 0.439 | 483 | 0.2059 | FM | hold |
| 3 Fe-enrich screen | ZrFe3_g194 | screen (coarse) |  |  |  | 0.253 | 532 | 0.1718 | FM | hold |
| 3 Fe-enrich screen | LiFe6As5_g139 | screen (coarse) |  |  |  | 0.331 | 310 | 0.1256 | FM | hold |
| 3 Fe-enrich screen | LiFe6As5_g194 | screen (coarse) |  |  |  |  | 305 | 0.1793 |  | hold |
| 3 Fe-enrich screen | LiFe7As5_g139 | screen (coarse) |  |  |  | 0.705 | 316 | 0.1783 | FM | hold |
| 3 Fe-enrich screen | Zr2Fe3Si_g194 | screen (coarse) |  |  |  | 0.231 | 271 | 0.0131 | FM | hold |
| 3 Fe-enrich screen | Zr2Fe3Si_g139 | screen (coarse) |  |  |  | 0.456 | 252 | 0.1304 | FM | hold |
| 3 Fe-enrich screen | Zr2Fe4Si_g139 | screen (coarse) |  |  |  | 0.333 | 328 | 0.2275 | FM | hold |
| 3 Fe-enrich screen | Fe3B_g140 | screen (coarse) |  |  |  | 1.538 | 781 | 0.0082 | FM | PASS |
| 3 Fe-enrich screen | Fe3B_g62 | screen (coarse) |  |  |  | 1.538 | 782 | 0.0082 | FM | PASS |
| 3 Fe-enrich screen | Fe4CuAs2_g129 | screen (coarse) |  |  |  | 0.939 | 556 | 0.1163 | FM | hold |
| 3 Fe-enrich MAE | Fe3B_g140 | PRODUCTION* |  |  |  |  |  |  |  | error |
| 3 Fe-enrich MAE | Fe3B_g62 | PRODUCTION* | 100 | 1.048 | 0.593 | 1.540 |  |  |  | success |
| 4 synth screen | ZrMn3_g194 | screen (coarse) |  |  |  |  | 389 | 0.2078 |  | hold |
| 4 synth screen | ZrMn3_g139 | screen (coarse) |  |  |  | 0.063 | 277 | 0.2553 | AFM/ferri | hold |
| 4 synth screen | AlCr3Fe3As2_g139 | screen (coarse) |  |  |  |  | 275 | 0.2085 |  | hold |
| 4 synth screen | AlCr3Fe3As2_g123 | screen (coarse) |  |  |  | 0.037 | 282 | 0.1428 | AFM/ferri | hold |
| 4 synth screen | CrNi3_g221 | screen (coarse) |  |  |  | 0.165 | 333 | 0.0000 | AFM/ferri | hold |
| 4 synth screen | CrNi3_g139 | screen (coarse) |  |  |  | 0.165 | 333 | 0.0000 | AFM/ferri | hold |
| 5 synth screen | TiNbFe4_g194 | screen (coarse) |  |  |  | 0.172 | 350 | 0.0000 | FM | hold |
| 5 synth screen | TiNbFe4_g139 | screen (coarse) |  |  |  | 0.172 | 350 | 0.0000 | FM | hold |
| 5 synth screen | MgMn2CoS3x2_g12 | screen (coarse) |  |  |  | 0.208 | 194 | 0.1636 | AFM/ferri | hold |
| 5 synth screen | MgMn2CoS3x2_g225 | screen (coarse) |  |  |  | 0.107 | 213 | 0.2336 | AFM/ferri | hold |

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