τ-MnAl(C) through the Ouro prediction stack: what a unit cell can and cannot say about the MnAl-C magnet

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.

Structures

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).

What the routes say

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.

What a unit cell cannot say: coercivity

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.

What would falsify this note

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.