Magnet-Anisotropy-Screening

Will Bryan, Matt Moderwell · ghost-projects · July 2026

Magnetocrystalline anisotropy is central to permanent magnet performance, yet this value is one of the scarcest labels in public materials science datasets. Computing the anisotropy constant \(K_1\) requires relativistic density functional theory that costs orders of magnitude more than a standard relaxation. We built a screening dataset of 3,573 uniaxial rare-earth-free crystals, 2,242 of them carrying a computed anisotropy label, each with a relaxed structure, stability, a Curie estimate, and a quantified per-label error model.

Labels

Each labeled row carries \(K_1\), the saturation magnetization \(M_s\), the easy-axis direction, and the dimensionless hardness

$$\kappa \;=\; \sqrt{K_1 / \mu_0 M_s^2}$$

\(\kappa > 1\) is the commonly accepted bar for a permanent magnet. The anisotropy stage runs TB2J magnetic-interaction extraction over ABACUS density-functional calculations with fully relativistic pseudopotentials, at a 0.16 Å⁻¹ k-spacing and 65 Ry cutoff. The pseudopotential set contains no lanthanides, so rare-earth compounds are absent by construction.

Error model

Screening settings trade accuracy for throughput, and we measured exactly how much. A stratified 287-compound subset was recomputed at tightened settings (0.10 Å⁻¹ and 80 Ry, six to ten times the runtime per compound), and comparing the two values per compound separates the error into a bias and a scatter. The bias is small and shipped as a correction with per-band medians of 0 to 4%, applied in the kappa_corrected column. The scatter is not small with an interquartile range of roughly ±16% in the magnet-relevant bands, and only 48% of labels within ±10% of their high-accuracy value.

no correction, ×1.01.31.00.8flip 19%< 0.8flip 14%0.8–1.2flip 14%1.2–2flip 8%2–4flip 16%> 4κ band · box = per-label IQR, red tick = median correction, flip = axis↔plane raterefined / production κ

Models trained on this data should not be expected to regress \(\kappa\) better than roughly ±15 to 20%. Below that, a validation score measures label noise, not model skill.

Landscape

Every reliable label on the hardness-magnetization plane, filterable by anion class:

0.10.31310300.51.01.52.0corrected magnetic hardness κ (log scale)Mₛ (MA/m)κ = 1NdFeB-class ceiling, Mₛ ≈ 1.13 MA/mFePtMn₂SbTeHfGaFe₄Fe₇MnB₄

2,044 reliable labels · median κ = 1.22 · 59% at κ > 1

The upper-right corner, compounds simultaneously hard and strong enough for an NdFeB-class energy product, is nearly empty. Iron-rich intermetallics crowd the strong-but-soft left edge, and the hard right side belongs to dilute-moment oxides, chalcogenides, and halides. Precious-metal compounds (160 of the reliable labels) supply the high-anisotropy positive examples.

Candidates

A manufactured magnet is a polycrystal, so intrinsic numbers alone overstate a candidate. For every compound that clears the gates, a micromagnetic proxy sweeps 2,000 sampled microstructures (chemical order, texture, grain size, boundary chemistry, soft-phase fraction, dead layers) and records how much of processing space still makes a working magnet. Here we’re looking for coercivity ≥ 600 kA/m, remanence ≥ 0.8 T, \((BH)_{max}\) ≥ 100 kJ/m³.

robustness: margin-weighted share of 2,000 microstructures clearing all magnet thresholdsFePtL1₀ precious reference · peak 372 kJ/m³0.91Mn₂SbTelayered pnictide-chalcogenide · peak 195 kJ/m³0.71HfGaFe₄trigonal A-Fe · peak 198 kJ/m³0.10ZrGaFe₄trigonal A-Fe · peak 211 kJ/m³0.05Mn₂Gehexagonal · peak 393 kJ/m³0.01Fe₇MnB₄(Fe,Mn)₂B boride · peak 404 kJ/m³0.01Fe₁₅MnB₈(Fe,Mn)₂B boride · peak 423 kJ/m³<0.01
Ball-and-stick unit cells of Mn2SbTe, HfGaFe4, and (Fe,Mn)2B, the three leading rare-earth-free candidate families surfaced by the screen.

Mn₂SbTe is the most robust rare-earth-free lead, clearing the thresholds across 71% of sampled microstructures, though it carries the FM-assumption flag and a modest 438 K Curie point. The (Fe,Mn)₂B borides occupy the opposite property trade-off with NdFeB-class energy-product ceilings (404 and 423 kJ/m³) and processing windows so narrow they demand near-perfect texture. The HfGaFe₄ family sits between, with both the A site and the anion open to substitution.

Benchmark

We ran canonical hard magnets through the same pipeline and compared against literature (\(K_1\) in MJ/m³):

compoundeasy axisproductionrefinedexperimentDFT literature
FePt (L1₀)001 ✓15.910.6~6.67–11
CoPt (L1₀)001 ✓8.92.5~4.95–8
FePd (L1₀)001 ✓ (refined)1.51.8~1.82–3
Fe₂Beasy-plane ✓ (refined)1.40.6−0.8≈0, near boundary

The pipeline recovers the correct hardness ordering (FePt > CoPt > FePd), and refinement moves the hardest values into published DFT ranges while staying above room-temperature experiment, the well-documented 1.5 to 2× gap for zero-temperature density-functional anisotropy. Refinement also corrects both marginal easy-axis calls: FePd flips to the known 001 axis and Fe₂B flips to its measured easy plane.

Usage

Known failure modes ship as per-row flags; rows are retained and the filtering threshold is left to the user:

flagrowsmeaning
kappa_reliable = False198κ diverges as \(M_s \to 0\); near-compensated ferrimagnets produce artifact hardness values
k1_outlier = True165\(K_1\) beyond the credible hard-magnet ceiling; recompute at refined settings before use
fm_assumption_risk = True1,773ferromagnetic alignment plausibly overestimates \(M_s\), κ, and the energy product
easy_axis_confidenceallone minus the per-band axis↔plane flip rate

Limitations

  • Uniaxial only. Tetragonal, hexagonal, and trigonal systems. Cubic systems were avoided as these structures seldom yield permanent magnet performance.
  • Ferromagnetic alignment is assumed. True ground-state orderings are flagged, and over half the dataset carries the risk flag.

The dataset (v1.0) ships under CC-BY-4.0: the main table in Parquet and CSV, complete per-record pipeline output, 2,787 relaxed structures with a record-linked manifest, the 287-pair calibration tier, and a parameter-level methods document. The property-calculation routes are hosted on Ouro at https://ouro.foundation.