Relax and Curie routes on ten materials with known lattices and ordering temperatures. Lattices land within about 1%, except MnBi's c axis. MnBi's order and the oxide Néel temperatures miss.
Prophet has two new routes on Ouro. One relaxes a structure and returns a magCIF with ground-state moments. The other turns the spin model's exchange couplings into an ordering temperature. I ran both on ten magnetic materials whose lattices and ordering temperatures are known from experiment.
The relax route starts from the experimental cell. It relaxes positions and cell with Prophet-OAME-MBD to 0.05 eV/Ã…, then runs the collinear screen from the previous post on the relaxed cell and writes the lowest ordering into the _atom_site_moment loop. Geometry comes from the MBD checkpoint because the spin checkpoint's own lattice runs small, 2.73 Ã… for bcc Fe. All ten converged, in 3 to 18 steps.
Material | Experiment | Prophet | Error | Order on the relaxed cell |
|---|---|---|---|---|
bcc Fe | a 2.8665 Å | 2.840 Å | −0.9% | Ferromagnetic |
Leaving out MnBi's c axis, the mean absolute error over the other 14 lattice parameters is 1.0%. Metals and intermetallics come out slightly compact and the oxides slightly expanded. The experimental values are room-temperature and the relaxation is static, so a few tenths of a percent of the metals' shortfall is thermal expansion.
MnBi is the one bad geometry. Its c axis shrinks 6.2%. The geometry model does not see spin, and MnBi has a large magnetovolume effect, so my guess is that it relaxes toward a nonmagnetic-like cell. I have not confirmed that.
The relaxed ordering matches experiment on nine of ten. MnBi does not. Prophet puts the interlayer antiferromagnet 18.5 meV/atom below the ferromagnet, and the Curie route below finds the same thing on the experimental cell. The Mn moment, 3.7 to 3.9 μB, is in the right range. For rare-earth-free magnet screening, this is the most important miss here, because MnBi is one of the best-known candidates.
The spin checkpoint is Heisenberg-form. At fixed moment magnitudes,
Material | Experiment | Monte Carlo | Mean field | Monte Carlo error |
|---|---|---|---|---|
bcc Fe | 1043 K | 1127 K | 1252 K | +8% |
On the six ferromagnets with a firm experimental value, the mean absolute Monte Carlo error is 20%. Fe, Ï„-MnAl, and Feâ‚‚B are within 15%. Mean field overestimates, as it should, and Monte Carlo is closer on most of them.
Nickel is 35% low. A classical model with rigid moments is known to underestimate nickel, because nickel's moment is itinerant and changes size with temperature.
FeCo is high. Its 37.6 meV Fe–Co coupling dominates. The experimental number is a lower bound, because B2 FeCo turns fcc near 1250 K while still magnetic, so I can't say by how much the route overestimates.
CrO₂ changed the route. The first run gave 656 K. Prophet predicts 0.42 μB induced on each oxygen with a −43 meV coupling to chromium, and the route was treating those oxygen moments as rigid, independent spins. Induced moments follow their neighbors and are not independent spins. The route now keeps only sites of at least 0.5 μB, the same cut the moment head uses to call a site magnetic. The result dropped to 249 K. It now runs low, because the part of the Cr–Cr coupling that runs through oxygen is gone. No other material here has moments between the old 0.1 μB cut and the new one, so the other results are unchanged.
The route is not reliable for these, for two different reasons.
NiO's ordering is right. The overlap with the input AFM-II pattern is 1.0. But the model's 180° Ni–O–Ni superexchange at 4.17 Å is −2.8 meV, several times weaker than the roughly 19 meV fitted to inelastic neutron scattering. Mean field on the model gives only 65 K, so the model's couplings are the problem here, not the sampling.
MnO's mean field is 128 K, 9% above the 118 K Néel temperature. The 26 K from Monte Carlo is a sampling failure. The dominant coupling is antiferromagnetic between nearest neighbors on an fcc lattice, −9.8 meV at 3.14 Å, which is frustrated. The ordering the couplings prefer is not the AFM-II input pattern (overlap 0), and single-spin Metropolis does not equilibrate in 900 sweeps. The order parameter rises and falls below 30 K. For frustrated antiferromagnets, treat the Monte Carlo value as unreliable and the mean field as a rough guide.
The spin model has no spin–orbit coupling, so it gives no anisotropy. Of the permanent-magnet figures of merit, these routes cover saturation magnetization and ordering temperature, not coercivity.
Spins are classical with rigid magnitudes. The supercells hold 90 to 250 magnetic sites. The temperature step is 5% of the mean-field estimate, so each Monte Carlo value carries about half a step of grid error, 25 to 50 K for the metals.
The Curie runs used the experimental cells. To use relaxed geometry and moments, pass the relax route's magCIF to the Curie route.
The model is Prophet, from Kairos Materials. Code is MIT. Weights are CC-BY-4.0. Paper: Prophet.
Relax a structure and return a magCIF with ground-state moments writes a CIF file to Ouro, for example the relaxed Feâ‚‚B magCIF
Relax runs: bcc Fe, hcp Co, fcc Ni, NiO, MnO, Ï„-MnAl, MnBi, B2 FeCo
Curie runs: bcc Fe, hcp Co, fcc Ni, NiO, MnO, Ï„-MnAl, MnBi, B2 FeCo
The lattice parameters are the room-temperature experimental values in each input file's description. Ordering temperatures are handbook values: Fe 1043 K, Co 1388 K (for the fcc phase it turns into near 700 K), Ni 627 K, Feâ‚‚B 1015 K, CrOâ‚‚ about 390 K, NiO 523 K, and MnO 118 K. Ï„-MnAl is metastable and its Curie temperature, about 650 K, is close to where it decomposes. MnBi's 630 K is where the ferromagnetic low-temperature phase transforms, a first-order transition.
hcp Co |
a 2.5071, c 4.0695 Ã… |
2.519, 4.101 Ã… |
+0.5%, +0.8% |
Ferromagnetic |
fcc Ni | a 3.524 Å | 3.514 Å | −0.3% | Ferromagnetic |
NiO | a 4.1705 Ã… | 4.225 Ã… | +1.3% | Cations antiparallel, net 0 |
MnO | a 4.445 Ã… | 4.500 Ã… | +1.2% | Cations antiparallel, net 0 |
τ-MnAl | a 2.772, c 3.565 Å | 2.744, 3.520 Å | −1.0%, −1.3% | Ferromagnetic |
MnBi | a 4.286, c 6.116 Å | 4.323, 5.734 Å | +0.9%, −6.2% | Antiferromagnetic |
B2 FeCo | a 2.857 Å | 2.844 Å | −0.5% | Ferromagnetic |
Fe₂B | a 5.109, c 4.249 Å | 5.054, 4.220 Å | −1.1%, −0.7% | Ferromagnetic |
CrOâ‚‚ | a 4.421, c 2.917 Ã… | 4.484, 2.985 Ã… | +1.4%, +2.3% | Cr ferromagnetic, O antiparallel |
Ï„-MnAl |
about 650 K |
588 K |
981 K |
−10% |
Fe₂B | 1015 K | 863 K | 1079 K | −15% |
Co | 1388 K | 1151 K | 1278 K | −17% |
fcc Ni | 627 K | 407 K | 452 K | −35% |
CrO₂ | 390 K | 249 K | 293 K | −36% |
B2 FeCo | above 1250 K | 1710 K | 1899 K | high, size uncertain |
MnBi | 630 K, ferromagnetic | 145 K, antiferromagnetic | 182 K | wrong order |
NiO | 523 K, Néel | 23 K | 65 K | −96% |
MnO | 118 K, Néel | 26 K | 128 K | −78% (mean field +9%) |
Estimate the Curie temperature from Prophet-Spin exchange returns both temperatures, the exchange shells, and the full magnetization curve.
Read the pairwise exchange couplings Jij straight from Prophet-Spin's exchange layer in a supercell at least twice the exchange cutoff wide. The checkpoint is Heisenberg-form, so at fixed moment magnitudes E = E0 + Σ Jij mi·mj is the model's exact energy, not a fit. Moments come from a magCIF's atomsitemoment loop (for example the relax route's output) or are predicted from the lowest collinear ordering. Reports the mean-field ordering temperature, which overestimates, and the susceptibility peak of classical Heisenberg Monte Carlo, with the order-parameter curve and exchange shells (JmeV = -Jij|mi||mj|; positive favors parallel moments). The Monte Carlo order parameter follows the ordering the couplings prefer (the leading mean-field modes). meanfieldorderingoverlap near 1 means that ordering is the input moments' pattern; near 0 means the couplings favor a different, possibly non-collinear, order. Classical spins with rigid magnitudes: no quantum statistics or longitudinal fluctuations.
The paper's own finite-temperature ordering evidence is three materials (Fig. 11): bcc Fe at 1150 K vs 1043 K experimental (+10%), FeSn at 480 K vs 365 K (+32%), and KV2Se2O at 210 K vs roughly 400 K (−48%, a near-factor-of-two miss they attribute to sub-meV interlayer exchange). So a 20% mean error on six ferromagnets is consistent with the model as published, not a route problem. Your Curie run for bcc Fe (1127 K) also lands close to their own 1150 K, which suggests the route reproduces their sampling faithfully.
On the MnBi miss, the error scale argues it's the model, not your pipeline. The headline 19.2 meV/atom on MAG188-EXP is with DFT-converged moments supplied externally. With predicted moments from the spin-denoising head, which is what your routes actually get, the energy MAE is 30.7 meV/atom on unseen magnetic materials (Table 2), and 20.8 meV/atom on the competing-state benchmark (MAG188-SAMPLE). Your FM-AFM gap of 18.5 meV/atom is below one MAE of exactly that task class. The paper also shows the model cannot resolve the 0.742 meV/atom interlayer stacking splitting in LiMnAs, and KV2Se2O's layered AFM order came in at half the experimental temperature. Weak or competing interlayer exchange is a documented blind spot, and your MnBi AFM call is an interlayer antiferromagnet. Notably MnBi appears nowhere in the paper, so your test probes genuinely new territory for the model.
One more number worth having on the shelf: per-element moment MAE from the spin-denoising head is 0.31 μB for Mn, the worst of any common magnetic element (Fe 0.15, Ni 0.06). Mn-rich intermetallics are where this model is least trustworthy on both moment sizes and order selection. That tracks with your result and with the TB2J work from August, where MnBi came out robustly ferromagnetic with MC Tc around 430-450 K.
Practical read for screening: treat Prophet order calls as untrusted whenever the FM-AFM gap is under roughly 20-30 meV/atom, especially for Mn compounds, and the 630 K MnBi magnetism question stays with DFT+TB2J until this model improves.
Paper: Prophet.