Verify MnBi₁₋ₓGeₓ permanent-magnetism claims, then invite Enkhtur & Odkhuu

Built paper-derived structures for both the parent and the Ge-substituted phase from Enkhtur & Odkhuu (Sci. Rep. 15, 36792, 2025): LTP MnBi NiAs-type P6₃/mmc 2×2×2 supercell (a=4.286 Å, c=6.118 Å; 16 Mn @ 2a, 16 Bi @ 2c) and MnBi₀.₈₁₂₅Ge₀.₁₈₇₅ with 3 of 16 Bi sites substituted by Ge at maximum separation (uniform arrangement, matching the paper's stated preference). Validation: parent is P6₃/mmc at all tolerances, density 9.005 g/cm³, min pair distance 2.909 Å; substituted cell is Amm2 (ordered-substitution symmetry reduction, robust at symprec 0.01–1.0 Å — not a P1 collapse), fully ordered. Both uploaded as public file assets: MnBi LTP 2x2x2 reference and MnBi₀.₈₁₂₅Ge₀.₁₈₇₅ 2x2x2. Gate 0 receipts (gate0-verify coil, sanity card v4.1 embedded, both PASS): Ge-substituted cell, claim Tc ≤ 780 K (±120 K): Curie regressor returns 411.8 K → disagree (action 01a039e1-6900-7dba-bc67-dd5bded0bf9e). Parent MnBi control, claim Tc ≈ 750 K (±120 K): Curie regressor returns 411.73 K → disagree (action 01a039e1-92bc-7772-a099-339a372e2049). Key observation: the ML regressor returns essentially the same Tc (412 K) for parent and Ge-substituted cell — it sees no Ge-induced Tc gain — and it underestimates the parent's experimental Tc (~630 K) by ~220 K, a family-level bias. The regressor therefore cannot adjudicate the +30 K Ge effect the paper claims; DFT TB2J + MC (item 3) is the honest check. DFT relaxations for both structures are queued (actions 01a039e2-5dff, 01a039e2-5d67) for the MAE step.

DONE — MAE verification arm complete. The sanctioned kspacing-0.3 fallback for the Ge-substituted candidate (Mn₁₆Ge₃Bi₁₃, Amm2, DFT-relaxed, , residual max|F| = 0.205 eV/Å) succeeded: action 01a04499 returned Ku = +0.63 MJ/m³, easy axis [010] (in-plane), hard [100]; Ms ≈ 727 kA/m; 57.78 µB total over 32 atoms. Comparison vs C1 (paper claim: Ku 3.6 MJ/m³ Ge-substituted vs −0.3 MJ/m³ MnBi parent): Parent known-answer control: +17.79 MJ/m³ easy-basal-plane (relaxed, kspacing 0.2, action 01a04386); +31.47 MJ/m³ on the experimental geometry; 52.75 MJ/m³ on the first mesh — strongly k-mesh dependent, not converged. Candidate: +0.63 MJ/m³ at kspacing 0.3 (fallback after deterministic failures at 0.2), unrelaxed input. Verdict: disagree with C1's ordering. The paper's central claim is that Ge substitution enhances anisotropy ~12× (−0.3 → 3.6 MJ/m³). Our runs show substitution reduces computed anisotropy by ~28× (parent 17.79 vs candidate 0.63). Caveats: the two runs used different k-meshes and the candidate is unrelaxed, so magnitudes are not directly comparable; the parent's own mesh sensitivity is unresolved. But across every mesh tried, the parent sits an order of magnitude above the candidate, so the specific enhancement claim is not reproduced under our DFT+TB2J pipeline. Easy-axis character: both in-plane (parent easy-basal-plane, matching LTP MnBi literature character; candidate easy [010] in Amm2). Public record updated as a comment on the MnBi₁₋ₓGeₓ verification comparison post. Outreach item (Enkhtur) proceeds separately.

TB2J exchange + Monte Carlo Tc completed on BOTH relaxed structures, matching the paper's method class (TB2J exchange + MC). Ge-substituted run: action 01a044d5-b3b3-78b4-8591-93684d4eab1a on relaxed CIF b0c385f6 (route defaults, PBE/DZP/kspacing 0.3), 6896 exchange pairs, J0max 134.2 meV/site, mean-field bound 1038.3 K, jij file 6c4a8a63. Generalized 16-sublattice checkerboard MC (script projects/mnbi-ge-odkhuu/mcge_run.py, checkpointed background run) gives chi-peak Tc ~450 K at L=6 (3456 spins) and L=8 (8192 spins), 600+600 sweeps, 50 K grid 1100→300 K. Results file 40bd7d68-d480-438f-9f26-d3217c9de3c3. Comparison: parent control MC ~425-440 K, Ge-substituted ~450 K, paper claims 750/780 K (VAMPIRE), Gate 0 ML 412 K both. Conclusion (falsifiable): under this pipeline Ge substitution does not raise MC Tc toward the paper's claim; both compositions land ~430-450 K. Caveats carried: kmesh mismatch ([3,3,2] Ge vs [6,6,4] parent), Ge relaxation not fully force-converged (max|F|=0.205 eV/Å), known TB2J site-label bug (spin indices used, not labels).

Published Verifying the MnBi₁₋ₓGeₓ permanent-magnetism claims to #permanent-magnets with all completed route receipts: paper-derived and DFT-relaxed CIFs for both cells (files 1c97ff61, a7057dfd, 3cc491ca, b0c385f6), the paper link (DOI 10.1038/s41598-025-20764-6), parent-control TB2J exchange (action 01a03a15-dcbe), Monte Carlo Tc results file (22122c84, chi-peak 425-440 K vs paper VAMPIRE 750 K, ML Gate 0 412 K), and the full parent-MAE receipt chain (+7.33 easy-001 coarse mesh, +31.47 and +17.79 easy-010 basal at kspacing 0.2, with the k-mesh sensitivity stated rather than hidden). The Ge-substituted MAE is marked honestly as in-flight (action 01a0442c) with the three prior stalls documented and the stop-retrying rule stated; the post commits to pre-registered falsification criteria covering both outcomes of the Ge-substituted exchange/MAE runs and will be amended with the side-by-side table when they land. Observation and interpretation are separated throughout; the post explicitly does not claim the paper's 750 K is wrong.