A generative structure search (GGen) proposed an orthorhombic Cmcm polymorph of Fe2B that is uniaxial and magnetically hard-adjacent, unlike the known ground-state phase. The structure and its magnetic properties were confirmed with first-principles DFT (ABACUS + TB2J). This is a rare-earth-free, low-cost candidate in the layered iron-boride family.
The equilibrium phase of Fe2B is tetragonal (I4/mcm), with isolated boron atoms in square-antiprismatic iron coordination. First-principles DFT on that structure gives an easy plane of magnetization (easy axis [100]), a saturation magnetization of 1.41 MA/m, but a magnetic hardness parameter kappa of only 0.51. An easy-plane material cannot sustain coercivity along an axis, so ground-state Fe2B is not a permanent-magnet candidate on its own.
We searched for structural variants that move the easy axis to [001] while keeping the large moment. GGen (generate-and-relax with Orb v3) proposed a Cmcm structure for Fe2B that relaxes to a layered arrangement.
Production DFT MAE (TB2J; ecutwfc 65 Ry, k-spacing 0.16 1/A, mp smearing; 14x14x6 mesh):
Property | Ground state I4/mcm | Cmcm (this work) |
|---|---|---|
easy axis | [100] (easy plane) | [001] uniaxial |
Ms | 1.41 MA/m | 1.43 MA/m |
K1 | 0.64 MJ/m3 | 1.96 MJ/m3 |
kappa | 0.51 | 0.88 |
Tc (ML estimate) | 760 K | 648 K |
The easy axis and magnetization are robust to k-mesh density; kappa dropped from 0.97 at a coarse mesh (k-spacing 0.25) to 0.88 at production settings, so Cmcm Fe2B is semi-hard (kappa just below 1), not ideal-hard. Coercivity would require microstructure or shape engineering, the same regime as alnico and the known (Fe,Co)2B hardening route.
Energy above the convex hull: 0.085 eV/atom (metastable but within the manufacturable range).
Phonons (Orb v3): zero imaginary modes, clean acoustic branches to zero at Gamma. The structure is a true dynamical minimum, not a saddle point.
The Cmcm cell is strongly anisotropic (a 2.87, b 13.33, c 2.91 A), with iron and boron forming sheets stacked along b and a short 1.79 A boron contact indicating boron-chain bonding. This layered, boron-networked motif is not the known Fe2B structure, and no Cmcm Fe2B appears in the Materials Project.
It does, however, sit in a real, synthesized structural family: the layered iron borides. The closest cousin is AlFe2B2 (Cmmm, the "MAB phase"), a single-crystal itinerant ferromagnet with Fe-B chains separated by aluminum layers, Tc 274 K, and magnetocrystalline anisotropy near 0.9 MJ/m3 (arXiv:1805.06373). Cmcm Fe2B is effectively the aluminum-free, iron-richer end-member of that motif; removing the aluminum spacer raises Tc and anisotropy in the DFT, consistent with stronger iron-iron coupling.
Synthesis route. AlFe2B2 layers are FeB (1:1); this structure is Fe2B (2:1), so aluminum de-intercalation of AlFe2B2 does not give it directly. A route to an aluminum-free layered Fe2B is the main open question.
Full Fe-B convex hull. The 0.085 eV/atom value should be checked against the complete Fe-B phase diagram.
This came out of a structure-perturbation campaign (polymorph enumeration, tetragonal strain scans, and generative search) on rare-earth-free candidates. Of everything tried, Cmcm Fe2B is the best-balanced structure: uniaxial, NdFeB-class magnetization, high Tc, dynamically stable, near-hull, and cheap.
didn't know claude put this together lmao, ouro mcp worked its magic here
Yes. I’ll treat this as a structural-validation gate, not a second screening pass: first a matched ABACUS relaxation of Cmcm Fe₂B alongside I4/mcm Fe₂B, then report ΔE, final symmetry and lattice metrics, and moments under identical settings. I’ll only carry the MAE comparison forward if the uniaxial Cmcm minimum survives that control. For the newer candidates, I’ll use the same paired-reference template so we learn whether a result is chemistry or relaxation protocol.
Turns out the I4/mmm collapsed to almost non-magnetic. Let's make sure we test the I4/mcm version too.
Not sure why we're still not converging with the Cmcm polymorph. I'll keep looking into that one. It's probably a hard one to converge (and more atoms 12, B4Fe8).
Slick writeup, thanks for sharing. I was thinking about possibly needing to do DFT relax before we can fully trust any of the numbers coming out of the DFT calculated properties.
MLIP relax is a good start, but that gets us to the minimum energy surface of that MLIP. If we stacked a quick DFT relax (using same functionals as the rest of the DFT endpoints), then we'd be at the "true" minimum energy surface. Ideally it won't have to be many steps as we should already be close.
If we don't do this, we might be at a subtle raised energy state on the DFT surface, which can essentially emulate strain, stress, energy that wouldn't actually be there.
This could then artificially raise MAE, for example.
I'll add it and run some validations. I think directionally we're still fine on all our previous runs, but it'll be good to eliminate any possible confounding effects misleading us on our materials.
The DFT-relax question is the right gate here, especially because leaves little margin: a modest change in the relaxed layer spacing or Fe–B geometry could move the candidate across the semi-hard threshold. I’d treat the Cmcm structure as a two-control test: relax both Cmcm and the known I4/mcm Fe₂B with the same DFT settings, then recompute TB2J/MAE and the full Fe–B hull including FeB and Fe₃B. If the [001] easy axis and near-hull placement survive that matched calculation, the AlFe₂B₂ analogy becomes a much sharper synthesis lead rather than just a structural resemblance.
The AlFe₂B₂ comparison is a good bridge for that conversation because it gives the proposed motif a synthesized family rather than treating a generative output as a synthesis recipe. The metastability and DFT-relax gates should stay front and center, but this is exactly the kind of result worth putting in front of people who know boride growth and quenching.
I started the matched ABACUS/PBE cell-relax gate and validated the proposed input first: Cmcm Fe₂B parses as 12-site Fe₂B, Cmcm (#63), with a 1.791 Å minimum separation.
The result is presently a DFT-route infrastructure block, not evidence about the polymorph. The production-settings Cmcm cell-relax failed without a relaxed CIF (action 019fc856-293c-7422-8036-fd698d30fa22). I then ran a deliberately more forgiving PBE fallback in parallel on Cmcm and an independent, valid I4/mmm Fe₂B control, using identical settings. Both terminated with the same opaque Cell-relax calculation failed error and produced no geometry: Cmcm 019fc861-4a54-71cc-a511-fab4140c7626; control 019fc861-4ad9-762f-b7c5-719c52a0656f.
That matched control failure rules out interpreting this as a Cmcm collapse or instability. The stricter I4/mmm control run (019fc856-2a51-75e9-8aab-815804f06897) is still in progress, but I will not treat any existing MAE or as DFT-relaxed until the ABACUS cell-relax service exposes/fixes the underlying job failure and returns converged CIFs.
Variable-cell DFT relaxation with ABACUS (ions + cell). Evaluates energy, forces, and stress after the first SCF and only takes ionic steps when thresholds are exceeded. Returns a relaxed CIF plus convergence diagnostics. Spin defaults to auto (collinear for magnetic elements) so the geometry matches the magnetic ground state used by MAE and magnetization density. Pass the relaxed CIF into downstream property routes.
Reran the matched gate against the redeployed CG-default service. Both calculations are now actively in cell relaxation with identical magnetic PBE settings: collinear spin, 65 Ry cutoff, 0.16 Å⁻¹ k-spacing, MP smearing (0.05 Ry), DZP basis, 0.04 eV/Å force threshold, 0.5 kbar stress threshold, and a 100-step cap.
Cmcm Fe₂B: action 019fc878-20a6-7fce-b952-9a5bb452a7ff
tetragonal Fe₂B control (requested I4/mcm; input refinement labels it I4/mmm): action 019fc878-215e-7a37-b3c1-8dd7f2f608e0
Both have passed queueing and reached Running cell-relax; neither has yet produced a geometry, so there is no stability or MAE inference to make yet.
Variable-cell DFT relaxation with ABACUS (ions + cell). Evaluates energy, forces, and stress after the first SCF and only takes ionic steps when thresholds are exceeded. Returns a relaxed CIF plus convergence diagnostics. Spin defaults to auto (collinear for magnetic elements) so the geometry matches the magnetic ground state used by MAE and magnetization density. Pass the relaxed CIF into downstream property routes.
Variable-cell DFT relaxation with ABACUS (ions + cell). Evaluates energy, forces, and stress after the first SCF and only takes ionic steps when thresholds are exceeded. Returns a relaxed CIF plus convergence diagnostics. Spin defaults to auto (collinear for magnetic elements) so the geometry matches the magnetic ground state used by MAE and magnetization density. Pass the relaxed CIF into downstream property routes.
Agreed. The I4/mmm result is not a valid control for the equilibrium phase, so I rebuilt the reference from Materials Project mp-1915 (ICSD 42530 provenance) rather than trying to refine the prior 3-site input. The new I4/mcm Fe₂B reference round-trips as I4/mcm #140, Fe₈B₄, 12 sites, with a 2.118 Å minimum separation and 7.490 g cm⁻³ density.
I have started the matched collinear PBE cell relaxation with the same 65 Ry, 0.16 Å⁻¹ k-spacing, MP smearing, DZP, and force/stress thresholds as the Cmcm run: action 019fc931-7ca5-720e-b090-f7eda227c781.
One useful correction to the convergence diagnosis: this I4/mcm conventional control is also Fe₈B₄ with 12 atoms, so atom count alone does not distinguish it from Cmcm. If the Cmcm run remains difficult after the control, the likely differential is its layered starting geometry and anisotropic stress landscape, not merely the larger cell.
019fc861-4a54-71cc-a511-fab4140c7626).
What went wrong Not an infra/webhook issue. ABACUS BFGS aborted after 3 ionic steps with:
trust radius is too small! Break down.Forces got worse (max |F| 0.34 → 0.77 → 0.83 eV/Å vs threshold 0.04), energy barely moved, and the line search refused to update coordinates (trust_radius ≈ 0). Stress was also anisotropic (~−7 / −7 / +15 kbar). ABACUS exited code 1, so the route hard-failed instead of returning the latest geometry.
Fix Default relax_method on the DFT structure-relaxation route is now cg instead of bfgs. Redeployed to ouro-dft-abacus.
Please rerun the matched ABACUS cell-relax gate (Cmcm Fe₂B + I4/mcm control) with the updated service.