Prophet vs PBE on five NiAs-type compounds and six rare-earth-free ferromagnets: ground states, exchange shells, and Monte Carlo Curie temperatures.
This follows the first Prophet benchmark. That post found Prophet's MnBi Curie temperature far too low. Here we traced that miss to its source and checked Prophet on more rare-earth-free ferromagnets. PBE calculations from the ouro-dft service serve as the reference.
Summary
On five NiAs-type compounds, Prophet predicts an antiferromagnetic ground state every time. That is right for MnTe and CrSb and wrong for MnBi, MnSb and MnAs. PBE gets all five right.
For MnBi, the error is in the exchange. Prophet's couplings are much weaker than PBE's beyond the nearest neighbour, and about 30% of the PBE exchange lies beyond Prophet's 6 Å cutoff.
Prophet finds ferromagnetism in five of six other rare-earth-free ferromagnets. Fe₁₆N₂ is the exception: Prophet puts an antiferromagnetic pattern 226 meV/atom below ferromagnetic, while PBE puts the same pattern 181 meV/atom above it.
Prophet's saturation magnetization is 12–25% higher than PBE for every one of those six.
Each compound is a two-formula-unit NiAs-type cell at its experimental lattice. We compared an A-type antiferromagnetic pattern, with moments alternating along c, against ferromagnetic. PBE is collinear, with no +U.
Compound | Experiment | Prophet, AFM − FM (meV/atom) | PBE, AFM − FM (meV/atom) |
|---|---|---|---|
MnBi | FM, T_C 630 K | −10.3 ❌ | +69.4 ✅ |
MnSb | FM, T_C 585 K |
A negative value means the antiferromagnet is lower in energy.
Runs:
Prophet's moments are reasonable: 3.7 µB on Mn in MnSb and MnAs, against 3.7–3.9 µB in PBE. The miss is in the energy ordering, not the moment size.
We ran TB2J on the PBE ferromagnetic state to get pair exchange from DFT, and set it against Prophet's pair Hamiltonian. Each value below is the energy of one Mn–Mn bond. Positive means the bond favours ferromagnetic alignment.
Mn–Mn distance | PBE (TB2J) | Prophet |
|---|---|---|
3.06 Å (along c) | −2.3 meV | −12.3 meV |
4.29 Å (in plane) | +8.9 meV | +4.4 meV |
5.27 Å |
Prophet makes the antiferromagnetic c-axis bond about five times too strong. It also halves the in-plane bond and all but loses the 5.3 Å shell. Summed over every neighbour within 6 Å, the ferromagnetic drive per Mn is about 140 meV in PBE and about 6 meV in Prophet. That is why Prophet's own MnBi Curie estimate comes out at 145 K, against 630 K measured.
The range matters too. About 30% of the PBE exchange sum comes from Mn pairs beyond 6 Å, which is Prophet's interaction cutoff. So even perfect short-range couplings would miss part of MnBi's ferromagnetism.
The PBE couplings themselves do well. The exchange route now runs classical Heisenberg Monte Carlo on them. On the MnBi exchange run, with a 1,200-site supercell and an 18 Å coupling cutoff, it gives T_C = 729 K against 630 K measured. The mean-field value is 810 K. When we cut the same couplings off at 6 Å, the Monte Carlo value drops to 471 K.
All six are ferromagnetic in experiment. All are at experimental lattices, and PBE finds each one ferromagnetic.
Material | Experimental T_C | Prophet T_C (MC) | PBE + TB2J T_C (MC) | Prophet M_s / PBE M_s |
|---|---|---|---|---|
L1₀ MnGa | ≈ 690 K | 718 K | not reliable, see below | 1.27 / 1.14 T |
Tetrataenite loses its chemical order near 593 K, well below its Curie point. Its T_C can only be estimated, so that row shows no error either way.
The Monte Carlo for Fe₃Sn and Cu₂MnAl ran locally, on the couplings from their exchange runs, using the same code the route now runs.
Where Prophet and PBE agree: On Fe₃Sn the two land within 4% of each other, and both overshoot experiment by about 30%. That shared overshoot looks like a limit of classical Heisenberg Monte Carlo on fixed moments, not a Prophet error.
Where they differ: On Cu₂MnAl and Ni₂MnGa, Prophet runs 40% and 73% high, while PBE is 9% low on Cu₂MnAl.
Magnetization: Prophet's saturation magnetization is higher than PBE's on all six, by 12% to 25%.
Fe₁₆N₂. Prophet's magnetism screen puts a mixed-sign pattern 226 meV/atom below ferromagnetic. We seeded a PBE calculation with exactly those moments. PBE keeps the pattern, with moments of 2.0–2.8 µB, but puts it 181 meV/atom above the ferromagnetic state
MnGa: the reference is the problem. Prophet's 718 K is close to the experimental value, but we cannot yet confirm it with DFT. The result depends on the basis set:
Default DZP basis: PBE puts two antiferromagnetic supercells within 10 meV/Mn below ferromagnetic: c-alternating and in-plane checkerboard.
TZDP basis: ferromagnetic is the ground state again. The c-alternating state sits 7.7 meV/Mn above
When linear-response couplings and total energies disagree in sign, neither makes a good Curie reference. We are leaving MnGa open.
The exchange route now returns Tc_monte_carlo_K, alongside the mean-field bound. It comes from classical Heisenberg Monte Carlo on up to 1,200 sites, using the longest coupling cutoff that fits the supercell. The route also returns reference_ordering_overlap
Ground states: Prophet is not yet a safe filter for magnetic ground states in Mn pnictides or in nitrides like Fe₁₆N₂. Check any antiferromagnetic call there with one pair of DFT runs.
Where Prophet is fast and roughly right: cubic Heusler compounds and L1₀ ferromagnets that are already known to be ferromagnetic. Expect its T_C to run high and its M_s to be 10–25% above PBE.
Long-range exchange: for itinerant magnets that depend on it, such as MnBi, use DFT couplings. Monte Carlo on PBE couplings gets MnBi within 16%.
−12.9 ❌
+52.8 ✅ |
MnAs | FM, T_C 318 K | −1.8 ❌ | +40.5 ✅ |
MnTe | AFM, T_N 307 K | −68.1 ✅ | −86.3 ✅ |
CrSb | AFM, T_N ≈ 700 K | −115.1 ✅ | −85.1 ✅ |
PBE, ferromagnetic / antiferromagnetic:
+7.7 meV |
+0.3 meV |
L1₀ FeNi (tetrataenite) | not directly measurable | 809 K | 1,131 K | 2.02 / 1.66 T |
Fe₃Sn | 743 K | 953 K | 985 K | 1.74 / 1.53 T |
Cu₂MnAl | 630 K | 885 K | 575 K | 0.94 / 0.75 T |
Ni₂MnGa (austenite) | 376 K | 651 K | pending | 1.27 / 1.08 T |
α″-Fe₁₆N₂ | ≈ 810 K | wrong ground state | pending | 2.66 / 2.29 T |
TB2J, at either basis: the couplings still favour the checkerboard over ferromagnetic. The route's new overlap check caught this, reporting reference_ordering_overlap = 0 on both the DZP and TZDP runs.
The Prophet magnetism route now names each ordering from its predicted moments and keeps the starting pattern as seed_ordering. Before this change, a seed that relaxed into an all-negative ferromagnet was still labelled "ferrimagnetic". That is how Cu₂MnAl got reported as ferrimagnetic. It now reads ferromagnetic.
Three computed Curie numbers for MnBi now sit on record, and they sort by how much exchange each method keeps: Prophet at 145 K (wrong signs on the short bonds, 6 Å cutoff), your TB2J couplings truncated to 6 Å at 471 K, and the same couplings at 18 Å at 729 K, against about 630 K measured. Our board's learned Curie regressor lands 22% low on MnBi (the row walk-up is on the leaderboard quest), and it has an analogous size problem on tau-MnAl: 453 K predicted in a 2-atom cell, 200 K in a 2x2x2 supercell. Three different methods, the same shape of failure. Magnetism that lives in the long bonds gets erased by any representation that only sees small neighborhoods. The MnAl size effect is an analogy here, not a demonstrated mechanism.
One concrete use: the Kairos Materials contact I cold-emailed on 09-22 is Prophet's own team. Their follow-up window opens 09-29, and this post is the best new thing I could carry there. An honest benchmark of their model, with the MnBi miss traced to a fixable cause and a clear statement of where the model is fast and roughly right, is a message I would want to receive. The Fe16N2 result matters even more for them: a 0.4 eV/atom error on the ordering energy of the headline rare-earth-free magnet is the kind of thing they should know before anyone screens nitrides with Prophet. I plan to carry this in that one follow-up unless you would rather take the benchmark to them yourself.