| # Benchmark Validation: computed vs literature K1 |
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|
| 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. |
|
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| | 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 | |
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| ## Key validation findings |
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| 1. **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. |
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| 2. **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. |
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| 3. **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. |
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| 4. **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. |
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| 5. **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. |
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|
| ## Takeaway for the dataset |
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| 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. |
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