Benchmark Validation: computed vs literature K1
Comparison of our computed magnetocrystalline anisotropy (TB2J/ABACUS, Dojo-NC-FR) for
canonical hard magnets against published experimental and DFT K1. Production =
kspacing 0.16 / ecutwfc 65; refined = kspacing 0.10 / ecutwfc 80 (all rows recomputed
July 2026; raw values in benchmark_hiacc.json). Fe3Pt failed at the relaxation stage
on the rerun and has no refined value.
| Compound | phase | easy (prod → refined) | K1 prod | K1 refined | K1 lit (exp, RT) | K1 lit (DFT) | note |
|---|---|---|---|---|---|---|---|
| FePt | L1₀ | 001 → 001 ✓ | 15.9 | 10.6 | ~6.6 | 7–11 | refined lands in the DFT range |
| FeCoPt₂ | L1₀-der. | 001 → 001 | 20.5 | 10.0 | — | ~10–20 (DFT) | halves under refinement, like FePt |
| CoPt | L1₀ | 001 ✓ → 100 ✗ | 8.9 | 2.5 | ~4.9 | 5–8 | the exception: refined run flips against experiment |
| FePd | L1₀ | 010 ✗ → 001 ✓ | 1.5 | 1.8 | ~1.8 | 2–3 | refinement corrects the axis and matches experiment |
| Fe₂B | CuAl₂ | 001 → plane ✓ | 1.4 | 0.56 | −0.8 (easy-plane) | ≈0, near boundary | refined matches experiment; the earlier version of this table misread the experimental sign |
| Co₂B | CuAl₂ | — → plane ✓ | — | 0.42 | easy-plane | — | matches experiment |
| CoPt₃ | L1₂ | 001 → 001 | 2.6 | 4.5 | — | — | no firm literature anchor |
| FePd₃ | L1₂ | 001 → 001 | 1.1 | 1.3 | — | — | — |
| CrPt | — | 010 → 100 | 10.4 | 17.7 | AFM | — | antiferromagnet; non-001 at both settings |
| MnPt | — | 100 → 100 | 6.7 | 8.4 | AFM | — | antiferromagnet; non-001 at both settings |
Key validation findings
Our values are DFT-scale. The refined hard-magnet values land inside the published DFT ranges (FePt 10.6, FeCoPt₂ 10.0) but remain above room-temperature experiment (FePt ~6.6), the well-documented gap between zero-temperature density-functional anisotropy and measurement. Users should treat these as DFT-level upper estimates.
The convergence overestimate is κ-dependent and largest at the hard end. FePt drops ×0.67 and FeCoPt₂ ×0.49 in K1 under refinement, far more than the ~2% stratified-average bias. The per-band correction covers the bulk of the dataset; for κ > 3 the refined values are the ones to trust.
Refinement corrects the marginal easy-axis errors. FePd moves from in-plane to the known 001 axis with K1 = 1.8 MJ/m³, matching experiment, and Fe₂B moves from 001 to the easy plane, matching its measured K1 of −0.8 MJ/m³ at room temperature. Co₂B likewise comes out easy-plane, in agreement with experiment. The Fe₂B result also anchors the dataset's boride story in the literature: the parent compound is easy-plane, and hardening it requires substitution, the role Mn plays in Fe₁₅MnB₈ as Co does in (Fe,Co)₂B alloys.
CoPt is the exception. The refined run flips it to in-plane with K1 = 2.5 MJ/m³, against the known 001 easy axis. Single calculations carry the per-label variance of the calibration study at either setting, and near-boundary compositions can flip in either direction.
The antiferromagnet controls (CrPt, MnPt) do not present as easy-axis ferromagnets at either setting. Their large anisotropy energies are spin–orbit scales, not usable permanent-magnet constants.
Takeaway for the dataset
The pipeline reproduces the correct hardness ordering (FePt > CoPt > FePd) and, at refined settings, the correct easy axis for four of five well-characterized benchmarks, at DFT-scale magnitudes. The refined column confirms the calibration study's error model: small average bias, large per-label scatter, and axis flips concentrated near the easy-axis/easy-plane boundary. The labels ship as a screening and machine-learning dataset with a documented κ-dependent correction and a quantified noise floor.