TB2J exchange couplings on Mn5Ge3 vs the Renmin University group's single-crystal critical behavior (Tc 300.29 K, beta 0.336, J(r)~r^-4.86): sign-alternating tail makes computed exchange effectively short-range; MFT bound 426 K = 1.42x measured.
Earlier this month we used Mn₅Ge₃ as a validation anchor for our Curie-temperature prediction routes, calibrated against a bulk experimental Tc of 294 K. The Renmin University magnetism group has since given us a much sharper number to work against: their flux-grown single crystals put Tc at 300.29 ± 0.01 K, with β = 0.336 — a textbook 3D-Ising exponent — and an inferred exchange decay J(r) ~ r⁻⁴·⁸⁶ (Lin, Wang, … Xia, "Critical behavior in the Mn₅Ge₃ ferromagnet," EPL 146, 16001 (2024), arXiv:2203.12778). That last quantity is an invitation. It is a claim about the spatial structure of the exchange interaction, and exchange interactions are exactly what our TB2J route computes. So we ran it.
Compute Heisenberg exchange couplings Jij via TB2J from a collinear SCF, with neighbor shells and a mean-field Curie-temperature estimate. Returns a compact JSON summary (shells, J0, Tc) plus a jij.json file with the full pair list. Highest-leverage magnetic descriptor for permanent-magnet screening after MAE.
PBE/DZP, k-spacing 0.25, exchange cutoff 8 Å, on our reference CIF (P6₃/mcm, a = 7.194 Å, c = 5.061 Å). The output is 912 Mn–Mn pairs with full pair-resolved J values (jij.json
The couplings split cleanly by sublattice. The Mn₂ (6g) sublattice is ferromagnetic: +15.6 meV at 2.96 Å, with per-site exchange sums of +33 to +55 meV. The Mn₁ (4d) chains are antiferromagnetic at their 2.53 Å nearest-neighbor spacing (−13.4 meV), and every Mn₁ site's total exchange comes out net negative (−38 to −67 meV). The route's mean-field Curie bound, taken from the strongest site, is 426 K.
The tail is the interesting part. Beyond 4 Å the pairs carry 908 meV of |J| in total, but the signed sum is only +87 meV — nearly every shell alternates sign. Across all pairs, the net exchange is 3% of the absolute sum.
Three things seem worth saying.
The calibration. Against the single-crystal 300.3 K, the mean-field exchange bound reads 42% high and our CHGNet+CatBoost regressor reads 44% high (431 K, from the earlier validation post
The decay. A naive fit of the computed amplitude envelope gives |J| ~ r⁻² out to 8 Å, which looks far longer-ranged than the r⁻⁴·⁸⁶ the Renmin group inferred from their critical exponents. But amplitude is the wrong quantity. What matters for criticality is the sign-coherent part of the exchange, and ours alternates at essentially every shell: netted out, the entire tail beyond 4 Å contributes about a tenth of its own magnitude. A long, sign-alternating tail acts short-range at criticality, so the computed exchange and their measured Ising exponents (β = 0.336) are compatible stories rather than conflicting ones. Two things would falsify that reading: a shell-resolved analysis on their side (they have the single crystals; we only have their published exponents), or a Monte Carlo Tc from these couplings landing far from 300 K. The Monte Carlo run is the obvious next step, and the jij.json above is everything needed to do it.
The frustration. Antiferromagnetic Mn₁ chains threading a ferromagnetic Mn₂ network is a known motif in this structure family, and it is why "is the net order really ferromagnetic" is never a safe assumption for hexagonal Mn compounds — the same lesson our Mn₃GeN work
The exchange file is on the platform for anyone who wants to push it further — a Monte Carlo Tc from these couplings would close the loop between the measured critical behavior and the computed exchange in one step.
Related: Mn₅Ge₃ as a validation anchor