# Methods and Provenance

This document describes how the magnet-screening dataset in this directory was
produced: the computational pipeline, the exact parameters of every stage, the
data sources, the calibration study that quantifies label accuracy, the quality
flags, and the known limitations. It is the authoritative reference for anyone
using or reviewing the dataset.

## 1. What the dataset is

A screening-scale dataset of computed magnetic properties for uniaxial
(tetragonal, hexagonal, trigonal) inorganic crystals, built for rare-earth-free
permanent-magnet discovery and for training structure→property machine-learning
models. The headline label is the magnetocrystalline anisotropy: the anisotropy
constant K1, the saturation magnetization Ms, the dimensionless magnetic
hardness κ = √(K1 / µ₀Ms²), and the easy-axis direction. Supporting labels
cover thermodynamic stability (energy above the convex hull), Curie
temperature, magnetic moments, and, for compounds that pass the full screen,
a micromagnetic estimate of the achievable energy product (BH)max under a
microstructure parameter sweep.

Final contents (campaign closed 2026-06-30):

| artifact | contents |
|---|---|
| `magnet_screening.parquet` / `.csv` | 3,573 records, 2,242 with MAE labels (2,044 κ-reliable) |
| `screening_records.jsonl` | full per-record pipeline output (all stages, nested) |
| `relaxed_cifs/` + `manifest.jsonl` | 2,787 relaxed structures with atomic coordinates (88% of labeled rows) |
| `calibration.jsonl` | 287 compounds re-computed at high-accuracy DFT settings |
| `calibration_summary.json` | per-band correction factors and uncertainty derived from the above |
| `validation_table.md` | computed vs literature K1 for 11 canonical hard magnets |

## 2. Pipeline

Every record went through the same staged cascade, implemented in
`magnet_discovery/cascade.py` and executed on Modal against property-prediction
routes hosted on the Ouro platform. Stages run cheapest-first so the expensive
anisotropy calculation is only paid for structures that are physical, uniaxial,
and magnetic.

1. **Structure relaxation.** Orb-v3 machine-learned interatomic potential
   (`orb-v3-conservative-inf-mpa`), force convergence fmax = 0.05 eV/Å,
   maximum 200 optimization steps. The relaxed structure (not the input) feeds
   every downstream stage. Structures whose relaxed nearest-neighbour distance
   fell below 1.5 Å were rejected as unphysical.
2. **Symmetry gate.** Only uniaxial crystal systems (tetragonal, hexagonal,
   trigonal/rhombohedral) proceed, since only these support a uniaxial
   easy axis. Space group and crystal system are recorded from the relaxed
   structure.
3. **Stability.** Energy above the convex hull from the platform's e_hull
   route (referenced against the Materials Project hull;
   `include_user_materials=False`). Recorded in meV/atom with a tier label
   (≤50 stable, ≤100 metastable, ≤200 aggressive).
4. **Intrinsic magnetism.** Curie temperature from the platform's Curie route
   (treat as a method-level estimate; such estimates typically run high), and
   magnetization density from the mag_props route, converted to Ms in A/m
   (1 µB/ų = 9.274×10⁶ A/m). Per-element moment breakdowns are recorded
   where available.
5. **Magnetocrystalline anisotropy (the expensive stage).** TB2J magnetic
   Hamiltonian extraction on top of ABACUS density-functional-theory
   calculations with the Dojo-NC-FR fully-relativistic norm-conserving
   pseudopotential set. Production settings: k-point spacing 0.16 Å⁻¹,
   plane-wave cutoff 65 Ry (the route defaults). Outputs K1 (MJ/m³), Ms,
   κ, easy axis, and MAE in meV/atom. Submission is asynchronous with
   polling (a single calculation takes ~8–15 minutes at production settings,
   up to several hours at high-accuracy settings).
6. **Microstructure sweep** (PASS compounds only). A local micromagnetic proxy
   model (`mag_microstructure`) sweeps 7 microstructure parameters (order
   parameter, texture spread, grain size, grain-boundary exchange and
   magnetization, soft-phase fraction, dead-layer thickness) over 2,000
   Latin-hypercube samples (fixed seed 42), reporting the peak (BH)max, peak
   Br, and a robustness score = the share of sampled microstructures that
   clear Hc ≥ 600 kA/m, Br ≥ 0.8 T, (BH)max ≥ 100 kJ/m³, weighted by their
   margin above those thresholds.

Exchange stiffness A (needed by the sweep, not emitted by any route) is a
mean-field estimate A ≈ k_B·Tc / (2·a_eff) with a_eff the effective spacing
between magnetic atoms; it is order-of-magnitude only (FePt comes out ~1.2×10⁻¹¹
J/m vs ~1×10⁻¹¹ literature).

Two gate configurations were used. Discovery mode enforces magnet-viability
floors (Tc ≥ 400 K, Ms ≥ 0.5 MA/m, e_hull ≤ 200 meV/atom, κ > 1, easy axis
along c). Label mode, used for most of the dataset, relaxes those floors
(Tc ≥ 0, Ms ≥ 0.1 MA/m, e_hull ≤ 500 meV/atom) so that the anisotropy label is
captured even for compounds that fail the magnet screen; a REJECT verdict
therefore still carries a valid κ/K1/easy-axis label, and rejects are the
dataset's negative examples.

## 3. Scope: rare-earth-free by construction

The Dojo-NC-FR pseudopotential set contains no lanthanides, actinides, Y, or
Sc, so the anisotropy stage cannot compute rare-earth compounds; every
rare-earth submission fails before the self-consistent-field step. The dataset
is therefore rare-earth-free as a hard constraint, which matches its purpose
(rare-earth-free magnet discovery). Precious-metal compounds (Pt, Pd, Ir, Rh,
Au, …) *are* computable and are included as positive examples of high
anisotropy: 160 of the 2,044 reliable labels contain a precious metal, and
they are identifiable from the composition.

## 4. Data sources

Each record's `source` column tags its origin:

| source | n | description |
|---|---|---|
| `mp_broad` | 2,013 | Materials Project pulls: rare-earth-free uniaxial magnetic compounds, ≤24–30 sites, e_hull ≤ 0.30–0.40 eV/atom, anchored on Fe/Mn/Co/Cr/Ni/V/Ti/Cu/Zn/Nb/Mo. The accessible space under these filters was exhausted (~1,900 screened). |
| `substitution` | 1,101 | Ordered single-element substitutions (e.g. Fe↔Co/Mn/Ni/V, Al→Ga/In, S→Se/Te) applied to already-screened structures; uniaxial-filtered and deduplicated. Off-database compositions forming controlled structure–property series. |
| `template` | 367 | Compositions placed into known hard-magnet prototype structures (L1₀, ThMn₁₂, Fe₂P, D0₁₉, boride, Heusler and related). |
| `ordered` | 57 | Hand-built ordered variants. |
| `generated` | 30 | De-novo structures from the GPSK-300 generative model (low yield; retained for provenance). |
| `doping` | 5 | Solid-solution doping probes. |

Structures relaxed before labeling in all cases; 59 compositions appear more
than once as genuine polymorphs (same formula, different relaxed structure),
distinguishable via the relaxed CIFs.

## 5. Calibration and error model

Most computed-anisotropy datasets omit this analysis; it determines how the
labels should be used.

A stratified subset of 287 compounds (~50–90 per κ band) was re-computed at
high-accuracy settings (k-point spacing 0.16 → 0.10 Å⁻¹ and plane-wave cutoff
65 → 80 Ry) and compared against the production labels
(`calibration.jsonl`). Findings:

The systematic bias is small and κ-dependent. Median κ_hiacc/κ_default per
band: ×1.00 (κ<0.8), ×0.99 (0.8–1.2), ×0.98 (1.2–2), ×0.96 (2–4), ×0.97 (>4).
These per-band medians are applied to the shipped `kappa_corrected` column
(and squared for `K1_corrected_J_per_m3`), replacing the raw values' ~2–4%
overestimate. The benchmark table shows the correction grows for the very
hardest magnets (FePt: −18% in κ), so high-κ values should be treated as upper
estimates.

Per-label scatter is the dominant error term. In the magnet-relevant band
(κ ≥ 0.8, n = 199): interquartile range of the high-accuracy/default ratio is
[0.84, 1.05] (a robust one-sigma of roughly ±16%), 5th–95th percentile
[0.36, 1.48], with 48% of labels within ±10% of their high-accuracy value and
66% within ±25%. Practically: a regression model trained on this dataset
should not be expected to predict κ better than ~±15–20%, and about a third of
individual labels move by more than 25% under a converged re-computation.

The easy-axis label is most reliable exactly where it matters. The meaningful
failure mode is an axis↔plane change (001 vs in-plane; the in-plane directions
100/010 are degenerate in uniaxial cells). The axis↔plane flip rate between
default and high-accuracy settings falls from 19% for soft, ill-defined
compounds (κ < 0.8) to 8% for strongly anisotropic ones (κ 2–4). The
`easy_axis_confidence` column encodes 1 − (per-band flip rate).

Absolute scale: these are density-functional-theory values, and for hard
magnets they exceed room-temperature experiment by roughly 1.5–2×, the
well-documented DFT↔experiment MAE gap (zero-temperature calculation,
exchange-correlation overestimate of orbital anisotropy), not a pipeline
error. See `validation_table.md` for the 11-compound benchmark comparison. The
pipeline reproduces the correct hardness ordering (FePt > CoPt > FePd) and the
correct easy axis for well-defined hard magnets.

## 6. Quality flags

| column | meaning |
|---|---|
| `kappa_reliable` | False when MAE-stage Ms < 0.1 MA/m: κ diverges as Ms→0, so near-compensated ferrimagnets/antiferromagnets produce huge artifact κ values. 198 labels flagged. |
| `k1_outlier` | True when K1_corrected > 20 MJ/m³ or κ_corrected > 8. Extreme single-shot values sit in the calibration tail where the production settings are least trustworthy (the credible hard-magnet ceiling is FePt at ~16 MJ/m³). 165 labels flagged. Flagged values should be recomputed at refined settings before use. |
| `fm_assumption_risk` | The pipeline assumes ferromagnetic alignment. This flag marks compositions where that assumption plausibly overestimates Ms (and hence κ and (BH)max): two or more Mn/Cr atoms per reduced formula, or two or more magnetic atoms together with an anion (superexchange chemistry favours antiferro/ferrimagnetic order). ~50% of rows flagged, consistent with an oxide- and chalcogenide-heavy set. |
| `ms_ordering_risk` | The original, narrower version of the above (≥2 Mn/Cr sites only); retained for compatibility. |
| `easy_axis_confidence` | 1 − per-κ-band axis↔plane flip rate from the calibration study. |
| relax stage `backfilled: True` (in `screening_records.jsonl`) | Structure metadata recovered from the pre-relaxation source CIF rather than the relaxed output (affects lattice constants slightly; space group is usually preserved through relaxation). |

## 7. Relaxed coordinates (graph-model readiness)

`relaxed_cifs/` holds the relaxed structure (P1 CIF with full atomic
coordinates) for every record that retained its relaxation asset: 2,787
unique structures covering 88% of labeled rows. Files are named
`<composition>_<asset-id-prefix>.cif` and `manifest.jsonl` maps composition +
asset id + source to each file. The 12% of labeled rows without coordinates
are early records whose relaxation output was reconstructed after a backend
outage; their lattice parameters and space groups are present in the main
table but their coordinate files were not recoverable.

## 8. Column dictionary (main table)

| column | units | source stage |
|---|---|---|
| `record_id` | stable identifier `mag-NNNNN` | release |
| `mp_id` | Materials Project id of the source structure (null off-database) | provenance |
| `composition` | reduced formula | input |
| `source` | — | provenance tag (§4) |
| `verdict`, `stopped_at` | — | cascade outcome: PASS (cleared all discovery gates), REJECT (failed a gate; label still valid), LABELED (label-mode record), ERROR |
| `structure_family`, `actual_space_group`, `actual_crystal_system` | — | relax |
| `a, b, c, alpha, beta, gamma, volume_A3` | Å, °, ų | relax |
| `n_magnetic_atoms` | count | composition |
| `e_above_hull_meV`, `predicted_stable` | meV/atom | e_hull route |
| `Tc_K` | K | Curie route |
| `Ms_A_per_m` | A/m | MAE stage (TB2J; preferred over the mag_props gate value) |
| `K1_J_per_m3`, `kappa`, `easy_axis`, `mae_meV_per_atom` | J/m³, —, axis, meV/atom | MAE stage, production settings |
| `kappa_corrected`, `K1_corrected_J_per_m3` | —, J/m³ | per-band convergence correction applied (§5) |
| `A_exchange_J_per_m` | J/m | mean-field estimate from Tc (§2) |
| `peak_BHmax_kJ_per_m3`, `peak_Br_T`, `robustness_score`, `pass_fraction` | kJ/m³, T, — | microstructure sweep (PASS rows only) |
| `max_moment_uB`, `fm_alignment` | µB | mag_props |
| flags | — | §6 |

## 9. Known limitations

1. Uniaxial crystal systems only, by construction; no cubic or lower-symmetry
   anisotropy data.
2. Ferromagnetic alignment is assumed throughout; ferrimagnetic and
   antiferromagnetic ground states are not resolved (see `fm_assumption_risk`).
   The two antiferromagnetic benchmarks (CrPt, MnPt) correctly do not present
   as easy-axis ferromagnets, but their K1 magnitudes are spin-orbit anisotropy
   scales, not usable permanent-magnet constants.
3. Labels are single-shot at production DFT settings with the per-label
   uncertainty quantified in §5; treat this as a screening and machine-learning
   dataset, not a reference database.
4. Curie temperatures and exchange stiffness are method-level estimates.
5. Chemistry is Fe/Mn/O-heavy (oxides prominent); Ni-rich uniaxial magnets are
   intrinsically scarce and under-represented.
6. Values are zero-temperature DFT-scale; expect ~1.5–2× experimental K1 for
   hard magnets (§5).

## 10. Reproducibility

The full cascade, gate configurations, calibration runner, and correction
script are in `magnet_discovery/` (`cascade.py`, `run_wave.sh`, `run_calib.sh`,
`apply_calibration.py`). Property routes are hosted on the Ouro platform
(route IDs in `cascade.py`; anisotropy route `1671b2d5-…`, maintained by its
respective owners). The experiment history, including every campaign decision
and mid-course correction, is in `magnet_discovery/EXPERIMENT_LOG.md`.