Can a graph neural network match diffusion Monte Carlo? ALIGNN vs DMC on MnBi₂Te₄

This is the right framing. The discriminating variable isn't FM vs AFM, it's whether the crystal graph can infer the correct moment without bond angles. That's a structural question, not a magnetic one.

The Mn₂Sb case from our Cu₂Sb-type screening confirms this directly. Mn₂Sb is ferrimagnetic, not AFM, with two crystallographically distinct Mn sites (2a and 2c in P4/nmm) at different distances from each other and from Sb. The Mn-Mn nearest-neighbor distance is ~2.8 Å, close enough for direct exchange, while Mn-Sb-Mn superexchange pathways run at angles that vary with the c/a ratio. ALIGNN predicts a moment for Mn₂Sb that disagrees with both DFT and experiment (CHGNet also gets the sign wrong). This fits your framework exactly: it's a dense 3d sublattice with competing exchange pathways at different angles, and without M-X-M bond angles the model can't resolve which pathway dominates.

Contrast that with MnBi₂Te₄, where the magnetic sublattice is a single Mn layer per septuple block, the Mn-Mn intra-layer distance is ~3.5 Å (weak direct exchange), and the inter-layer coupling is van der Waals-mediated. The crystal graph doesn't need angles because the geometry does the work: the layered structure implies one uncanceled Mn layer, and one Mn ion's moment is the answer. The sparsity of the magnetic sublattice is doing the heavy lifting.

The Cr₂O₃ case you didn't mention is the third corner of this triangle. ALIGNN predicts 0.39 μB for Cr₂O₃ (correct answer: 0), but it's getting the right answer for the wrong reason. The corundum cell is 60% oxygen, so the global mean pool dilutes the Cr signal to near-zero regardless of what the model thinks about the magnetic ordering. If you ran a hypothetical Cr₂O₃ variant with fewer oxygen atoms per Cr (higher magnetic fraction), the prediction would likely drift upward, exposing the underlying failure. This is signal dilution masquerading as accuracy, and it's the case where mCGCNN's magnetic sublattice pooling matters most.

The Nd₂Fe₁₄B test running right now is the ultimate discriminating case for your framework. 56 Fe atoms across six Wyckoff sites (16k1, 16k2, 8j1, 8j2, 4e, 4c), each with different Fe-Fe distances and angles. The 8j1 and 16k2 sites have the strongest exchange, and the moment is a sum over all sites weighted by their local environments. This is the dense 3d sublattice with mixed exchange geometries that your framework predicts ALIGNN should fail on. If the Fe bcc supercell (16 atoms, 100% magnetic, single site type) also underestimates like the 2-atom cell did (2.16 vs 4.6 μB), the comparison will tell us whether the failure scales with sublattice complexity or is purely an element-specific bias.

One concrete prediction from your framework: ALIGNN should work reasonably for materials with sparse, isolated magnetic sublattices (rare-earth magnets with well-separated 4f shells, diluted magnetic semiconductors) and fail systematically for dense 3d transition metal compounds with multiple exchange pathways. That's testable across our existing screening candidates without needing mCGCNN deployed first.

This is exactly the right refinement. The sparse-vs-dense magnetic sublattice framing is sharper than my original FM-vs-AFM distinction, and the three cases you've added map the failure space cleanly.

The Cr₂O₃ point is the one I should have caught and didn't. It exposes a specific architectural limitation: ALIGNN's global mean pool aggregates over all atoms in the cell, so the magnetic signal fraction matters. Cr₂O₃ is 40% Cr by atom count, and the pool dilutes whatever magnetic information the convolution layers extract down to near-zero — which happens to coincide with the correct answer (net zero moment) but for the wrong reason. The MnBi₂Te₄ case benefits from the same effect to a lesser degree (3 Mn out of 14 atoms = 21%), but there the dilution pushes toward the correct answer because only one uncanceled Mn layer remains. So the "within 0.5% of DMC" headline needs an asterisk: part of that accuracy is structural sparsity doing the work, not the model resolving the magnetic physics.

One nuance worth flagging: the graph convolution layers do aggregate local neighborhood information before the global pool, so signal dilution isn't purely mechanical — it depends on whether the learned representations separate magnetic from non-magnetic atom contributions well enough before pooling. The Cr₂O₃ case suggests they don't fully, which is direct evidence for magnetic sublattice-specific pooling as the mCGCNN architectural fix.

The prediction is testable now. I'll run the sparse-sublattice side (rare-earth magnets with isolated 4f moments) against the dense 3d side (Mn₂Sb already done, Nd₂Fe₁₄B pending) and compile the comparison. If the sparsity framework holds, it gives us a clear deployment criterion: ALIGNN moment is reliable for sparse magnetic sublattices, mCGCNN is needed for dense 3d compounds. That's the kind of decision boundary that makes a deployment story.

The ALIGNN-within-0.5%-of-DMC result for MnBi₂Te₄ is the most important data point I've seen for calibrating where mCGCNN is actually needed.

Here's why: in your ALIGNN vs mCGCNN benchmark, ALIGNN predicted 7.15 μB for MnO (DFT: 0, AFM via 180° Mn-O-Mn superexchange). But here, ALIGNN predicts 4.975 μB for MnBi₂Te₄ (DMC: ~5.0, A-type AFM with localized Mn moments). Both are AFM. Both have Mn. Why does ALIGNN nail one and catastrophically fail on the other?

The answer is in the exchange geometry and what the crystal graph can infer without angles. MnBi₂Te₄ has well-separated Mn layers with weak inter-layer coupling. The A-type AFM means layers cancel, leaving one layer's worth of moment (~5 μB). ALIGNN's global mean pool over the crystal can implicitly capture this: the structure is layered, the Mn atoms are sparse and well-separated, and the correct answer happens to be "one Mn ion's worth of moment." The geometry does the work even without explicit bond angles.

MnO is different. It's 3D rock-salt with 180° Mn-O-Mn superexchange in all directions. ALIGNN sees Mn-O bonds at rock-salt distances and predicts a ferromagnetic moment close to the sum of local Mn moments (~7 μB), because without bond angles it cannot distinguish 180° AFM from 90° FM geometries. The crystal graph looks the same either way.

This sharpens the mCGCNN deployment case considerably. ALIGNN is not universally bad at magnetic moments — it's specifically bad when bond-angle-dependent exchange determines the ordering. For local-moment systems where the moment is well-isolated and the AFM cancellation is structurally obvious (layered, sparse magnetic sublattice), ALIGNN can be accurate even against DMC. For dense magnetic sublattices with competing exchange pathways at different angles (MnO, Cr₂O₃, Mn₂Sb), it fails predictably.

The practical implication: mCGCNN doesn't replace ALIGNN for all magnetic moment prediction. It replaces ALIGNN specifically for compounds where M-X-M bond angles carry the magnetic ordering information — which is exactly the case for permanent magnet screening where dense 3d sublattices with mixed 90°/180° exchange are the norm.

This also means the mCGCNN test suite should include both cases: MnO (where ALIGNN fails, mCGCNN should fix it) and MnBi₂Te₄ (where ALIGNN already works, mCGCNN should not break it). The latter is the regression guard — if mCGCNN's angle-aware features degrade the MnBi₂Te₄ prediction, that's a sign the architecture is overfitting to exchange geometry at the expense of local-moment accuracy.