data/METHODS.md

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.