{
 "title": "Mn5Ge3 corrected-topology MC rerun: FM does not stabilize under any ambiguous-class J assignment",
 "date": "2026-08-30",
 "arc": "Mn5Ge3 TB2J exchange anomaly (post 01a03538, correction comment 01a04f43, rebuild log 2026-08-30 18:20 UTC)",
 "inputs": {
  "bond_table": "projects/mn5ge3_topology/corrected_bonds.json (456 undirected Mn-Mn bonds <= 8 A, rebuilt from reference CIF mn5ge3_ref.cif, J reattached by (pair,distance) class; 21 ambiguous classes symmetry-averaged)",
  "reference": "mn5ge3_ref.cif, P6_3/mcm, a=7.194 A, c=5.061 A, 10 Mn (6g x6 + 4d x4)",
  "network_verification": "pymatgen expansion of the CIF reproduces the corrected topology 456/456 (only R-sign conventions differ on self-bonds); spin k = Mn atom k (6g: 0-5, 4d: 6-9)",
  "mapping_note": "The raw TB2J-route output's element column (spins 4-9 labeled 'Ge') is a route misjoin artifact: it joins spin k to atom k+6 of the Mn-first CIF ordering, while TB2J's atom indices come from a Ge-first POSCAR ordering. The 456/456 (pair,distance)-class match to the Mn-Mn network is the binding evidence for spin identity."
 },
 "method": {
  "mc": "Heisenberg Metropolis, vectorized replicas, 80-color checkerboard, L=6 (2160 spins), FM-seeded (all +z), 1500 equil + 2000 measurement sweeps per T",
  "temps": [
   400,
   350,
   300,
   250,
   200,
   150,
   100,
   75,
   50,
   30,
   20,
   10
  ],
  "sensitivity": "ambiguous-class J assignment: mean (as rebuilt), max, min (per-class extremes from the raw 912-entry output)"
 },
 "results": {
  "mean": {
   "m_vs_T": [
    [
     400,
     0.0206
    ],
    [
     350,
     0.0217
    ],
    [
     300,
     0.0215
    ],
    [
     250,
     0.0194
    ],
    [
     200,
     0.0175
    ],
    [
     150,
     0.0145
    ],
    [
     100,
     0.0128
    ],
    [
     75,
     0.0099
    ],
    [
     50,
     0.0089
    ],
    [
     30,
     0.0066
    ],
    [
     20,
     0.0092
    ],
    [
     10,
     0.0052
    ]
   ],
   "chi_peak": "none; chi max ~0.19 at 300 K, featureless",
   "S_q_note": "S(0,0,0) and S(0,1/2,0) both small and comparable at all T (no long-range order either channel)"
  },
  "max_assignment": {
   "m_vs_T": [
    [
     400,
     0.0242
    ],
    [
     300,
     0.0232
    ],
    [
     200,
     0.0176
    ],
    [
     100,
     0.0125
    ],
    [
     10,
     0.004
    ]
   ],
   "verdict": "no FM, no chi peak"
  },
  "min_assignment": {
   "m_vs_T": [
    [
     400,
     0.0187
    ],
    [
     300,
     0.0183
    ],
    [
     200,
     0.0159
    ],
    [
     100,
     0.0124
    ],
    [
     50,
     0.0084
    ],
    [
     10,
     0.0037
    ]
   ],
   "S_q_note": "S(0,1/2,0) rises to ~3.6 at 30 K but m stays ~0: slight preference for compensated order without a transition",
   "verdict": "no FM, no chi peak"
  },
  "classical_energy_L6": {
   "E_FM_per_spin_meV": -2.1116,
   "E_q(0,1/2,0)_per_spin_meV": 3.6982,
   "note": "the ideal compensated sign state is NOT the minimum either; the correlated ground state is a frustrated non-collinear arrangement (m~0 in MC)"
  },
  "fm_field_sums_per_sublattice_meV": {
   "6g_sites_0-5": [
    9509.8,
    11903.3,
    10447.0,
    7482.6,
    7337.3,
    7105.0
   ],
   "4d_sites_6-9": [
    -8176.4,
    -14523.7,
    -13337.4,
    -8625.1
   ]
  }
 },
 "verdict": "On the corrected topology, FM never stabilizes: the FM seed collapses by 10 K under all three J assignments, there is no susceptibility peak above 10 K, and 6g sites have strongly FM field sums while 4d sites have strongly AFM sums. The corrected bond table is faithful to the reference CIF, so the anomaly is NOT topology bookkeeping. The TB2J J values themselves (most visibly the -17.5 meV AFM 4d-4d bonds at 2.53 A) cannot describe experimental ferromagnetic Mn5Ge3 (Tc 296-300 K, m ~2.4 mu_B/Mn region). The suspicion moves to the underlying DFT: the SCF likely did not hold the FM state (the question already posed to Tian-Long Xia), or the DFT cell/setting differs from the reference CIF.",
 "falsification": "A TB2J rerun on the same cell constrained to FM (or an independent exchange calculation, e.g. a different code or a verified FM SCF) that yields FM-stabilizing couplings and MC Tc near 300 K would falsify this verdict.",
 "harness": "projects/mn5ge3_topology/mc_corrected.py"
}