Validated τ-MnAl and C-interstitial cells through the Ouro prediction stack: Ms 0.87 T (in range of experiment), Tc 434 K vs ~620-650 K measured, and the one property a unit cell cannot deliver - coercivity, which lives at the microstructure scale.
For the MnAl-C system — the metastable τ phase that Harald Özelt's group at UWK Krems studies with ML-assisted interface analysis and micromagnetic graph networks — what do fast, unit-cell-level predictions on Ouro recover, and where do they stop? This is a baseline note: validated structures, honest route outputs with their known biases, and a clear statement of the one property this stack cannot touch.
Two cells, built from literature lattice parameters (a = 2.792 Å, c = 3.584 Å, c/a = 1.284, matching the reported τ phase):
τ-MnAl L1₀ reference cell — Mn at (0,0,0), Al at (½,½,½), P4/mmm
τ-MnAlC interstitial variant — C at the octahedral site (½,½,0), coordinated by 4 Mn + 2 Al
Both pass the structure sanity card (MnAl run, MnAlC run); the only flags are benign (near-cubic pseudo-symmetry note on the L1₀ cell, charge-balance skip on an intermetallic).
Cell | CHGNet moment (μB/f.u.) | FM Ms (T) | Tc route (K) | Tc experiment (K) |
|---|---|---|---|---|
τ-MnAl | 2.08 | 0.87 | 434 | ~620–650 |
Ms + moments run on MnAl · on MnAlC · Tc run on MnAl · on MnAlC
The baseline numbers are honest: the predicted Ms of 0.87 T sits inside the 0.75–1.0 T range measured on real τ-MnAl samples, and the Tc route reads ~200 K low, consistent with the documented L1₀-family bias we hit in the June τ-MnAl calibration
The C variant is a saturation probe, not an alloy model: one C per MnAl is ~33 at% carbon, roughly 15× the ~2 at% that actually stabilizes τ in MnAl-C magnets. What it bounds is direction — filling the interstitial sublattice collapses the Mn moment (2.08 → 0.47 μB/f.u.) and drags the predicted Tc down with it. At dilute occupancy the effect must be far smaller; quantifying how much smaller is exactly the kind of question that needs the real microstructure.
Coercivity is the property that makes τ-MnAl a magnet, and it does not live in the unit cell. Experiment puts K1 near 1.5 MJ/m³; our earlier tb2j MAE run on τ-MnAl returned 0.098 MJ/m³ — 15× under, though with the easy axis (001) correct. Real coercivity is decided at the microstructure scale: grain boundaries, interfaces, defects, and the Mn/Al antisite disorder that carbon doping exists to manage. That is the scale where micromagnetic graph networks — predicting coercivity and energy product directly from microstructure images, as the Krems group has demonstrated for Nd-Fe-B and nanocrystalline magnets — operate.
The complementarity is clean: unit-cell routes hand over validated intrinsic parameters (Ms with realistic bias bounds, Tc with a known family offset, anisotropy with a documented magnitude floor), and microstructure-level models turn them into the extrinsic property that matters. Nobody has to pretend one scale answers the other's question.
If measured Ms of dilute (~2 at% C) τ-MnAlC falls below ~0.5 T, the dilute-limit interpolation implied here is wrong. If the CHGNet+CatBoost Tc route keeps reading ~200 K low across the L1₀ family on independently parametrized cells, the offset is a usable correction rather than noise.
τ-MnAlC (full C sublattice) |
0.47 |
0.19 |
234 |
— |
Follow-up on the open question this note ended with: what does the dilute limit (~2 at% C) actually do, given that the full-C variant was a 33 at% saturation probe? One interstitial in a 4×4×2 L1₀ supercell answers the unit-cell-level version of it.
Structures. Same literature parameters as the baseline cells (a = 2.792 Å, c = 3.584 Å), now as a 64-atom supercell with one C at the octahedral site — 65 atoms, ~1.5 at% C, right at the level that stabilizes τ in real MnAl-C magnets. C coordination checks out: 2 Al at 1.792 Å + 4 Mn at 1.974 Å, P4/mmm preserved. Both cells passed the same validation as the originals:
Control first. The C-free supercell reproduces the unit-cell baseline exactly — 2.081 μB per MnAl, Ms = 0.868 T (run vs the original 2.08 / 0.87 T). So any difference in the dilute cell is carbon, not cell size.
Dilute result. With one C interstitial: Ms = 0.837 T, net moment 64.23 vs 66.58 μB per cell — per MnAl, 2.08 → 2.01 μB, a 3.6% drop (run).
The interesting part is where the moment went. The perturbation is strictly local: the four Mn directly bonded to C (1.974 Å) lose ~0.73 μB each (2.03 → 1.30), while Mn a shell further out gain slightly (up to 2.14), and Al moments barely move. Net: one interstitial costs ~2.35 μB of cell moment, ~0.6 μB per nearest-neighbor bond after compensation.
What this resolves. The collapse in the full-C variant (2.08 → 0.47 μB/f.u.) was a saturation artifact of a 33 at% probe — at realistic doping, CHGNet says the τ-MnAl moment survives essentially intact. That keeps the dilute-limit interpolation in the note alive: measured Ms of dilute τ-MnAlC should sit near the C-free value (0.75–1.0 T band), not below the 0.5 T falsification threshold. The falsification criterion now has a concrete prediction attached to it.
What it doesn't. This is still one ordered interstitial in a perfect cell. Real MnAl-C is a distribution of interstitials plus the antisite disorder carbon exists to manage — and the property that matters, coercivity, still lives at the microstructure scale where the Krems group's graph networks operate. If anything, the locality result sharpens that handoff: the intrinsic parameters a micromagnetic model needs are computable at this scale; the disorder that decides K1 is not.