Three Curie temperature estimates against 39 measured magnets: the best scorer is recalling its training set

Ouro has three ways to get a Curie temperature from a CIF. Prophet's Curie route returns two: a mean-field value and a Monte Carlo value, both solved from the model's own exchange couplings. The CHGNet route returns one, from a CatBoost regressor on CHGNet features. I ran all three on 39 magnets with measured Curie temperatures: 16 rare-earth-free, 7 rare-earth, and 16 containing gadolinium. Four more structures with no Curie temperature serve as controls.

The short version: neither model is a Curie temperature predictor you can trust on a new compound. The CHGNet route scores best, but it was trained on 36 of the 39 test compounds, so it is mostly recalling them. Prophet is off by about 230 K on average and fails in specific, repeatable ways on gadolinium.

Scores

Every row, with its CIF and both runs:

Checking the structures

A Curie temperature for the wrong polymorph is worthless, so every CIF was checked before any model ran. Each one had to match the measured crystal on formula, space group, and Wyckoff sites, with lattice constants within 3% of measured values. Files tagged with a Materials Project ID were also matched against a fresh pull of that entry. All 43 passed.

Twenty structures are the files from the earlier Prophet benchmark

The Materials Project cells for Gd and GdCo₅ have a c axis 2 to 3% off the measured one. I ran both again at measured lattice constants. No prediction moved by more than 11 K, so lattice error is not what drives the results below.

The CHGNet route is recalling its training set

The route returns 1043.1 K for bcc Fe. The measured value is 1043 K. That is not a prediction. The model's training table holds 6,847 rows covering 3,284 formulas, with Curie temperatures collected from the literature, and the deployed model was fit to all of them with nothing held out. Almost every well-known magnet is in it.

To see what the model does on a compound it has not seen, I retrained it with the same settings, leaving out every row for one formula at a time. That is the "held out" column. The retrained model on the full table reproduces the route to within 0.1 K, so the comparison is like for like.

• bcc Fe drops from 1043 K to 695 K, hcp Co from 1375 K to 1076 K, and B2 FeCo from 1159 K to 947 K.

• Across the 39 magnets the error rises from 100 K to 167 K, and the model reads 144 K low on average.

• The rare-earth compounds barely move, but for a weak reason. Hold out Sm₂Fe₁₇ and the table still contains NdSmFe₁₇, at 370 K. The model is reading the answer off a sibling.

• Three Gd compounds were never in the table: GdFe₃ comes out at 560 K against 728 K measured, Gd₂Co₇ at 290 K against 775 K, and GdIr₂ at 64 K against 88 K.

Cross-validating the whole table gives the same picture. With random rows held out the error is 78 K. With whole formulas held out it is 106 K, and 154 K for materials that order above 300 K. Always guessing the table's mean gives 235 K.

The model also has no way to say "not a magnet". Its training table contains only materials that order, so it returns 291 K for copper, 150 K for aluminum, and 164 K for silicon. And each formula's Curie temperature was copied onto every polymorph of that formula, so fcc iron gets 1025 K, the bcc value.

Rare-earth-free magnets

Prophet gets the iron-rich ferromagnets roughly right. Its mean-field value lands within 10% on Fe₂B, Fe₃Si, Fe₃C, Fe₅SiB₂, hcp Co, and Co₂MnSi, and its Monte Carlo value does on bcc Fe, α″-Fe₁₆N₂, and τ-MnAl. The two numbers differ by a steady factor: Monte Carlo is typically about 0.8 of mean field. Neither is better overall. Mean field runs high and Monte Carlo runs low.

The misses are large:

• MnBi and MnSb come out antiferromagnetic, at 145 K and 174 K. Both are ferromagnets near 600 K. This is the NiAs-type problem from an earlier post

Rare-earth magnets

Prophet gives Nd, Sm, and Y no moment, as the rare-earth post

The CHGNet route looks excellent here, within 8% on all seven. All seven are in its training table along with their substituted variants.

Gadolinium, with iron or cobalt

Prophet gives Gd about 6.8 μB, close to the right size, and then points it the wrong way. In every one of these compounds it puts Gd parallel to the iron or cobalt. In the real materials Gd is antiparallel, and they are ferrimagnets. The Curie temperature that comes out is the 3d sublattice's, with the same pattern as above: cobalt compounds low, Gd₂Fe₁₇ twice too high, and GdFe₂, GdFe₃, and Gd₂Fe₁₄B within 10% on the Monte Carlo value.

Gd₂Co₇ is the clearest unseen case for CHGNet: 290 K against 775 K measured. Prophet's mean-field value is 764 K.

Gadolinium on its own

These are the compounds where gadolinium is the only source of magnetism, or nearly so. Prophet has almost no Gd–Gd exchange. hcp Gd comes out antiferromagnetic at 11 K, GdAl₂ antiferromagnetic at 8 K, and GdZn at 14 K. The measured values are 293 K, 170 K, and 270 K. GdN goes the other way, 450 K against about 65 K. Prophet's errors in this group run opposite to the measured ordering: the compounds that order highest get the lowest numbers.

The CHGNet route is closer here, with a 57 K average error, and holding the compounds out only raises that to 72 K. It still returns 113 K for GdNi₅, which orders at 32 K.

What to use these for

• Prophet, either value: a rough Curie temperature for iron- or cobalt-based ferromagnets with no magnetic rare earth. Expect 20 to 30% error and check that the route reports a ferromagnetic ground state with an ordering overlap near 1.

• Prophet, not usable: anything where gadolinium carries the magnetism, any ranking within a rare-earth family, Mn pnictides, and any question of whether a structure is magnetic at all in a phase like fcc Fe.

• CHGNet route: a lookup of what the literature says about a known compound or a close relative. On a compound with no relatives in its table, expect it to read 150 K or more low.

• CHGNet route, not usable: as a gate for "is this a magnet". It gives nonmagnets 150 to 290 K. A screen that keeps everything above a Curie threshold will let those through if the threshold is low, and will drop real candidates if it is high.

Neither model replaces computing exchange couplings from DFT for a candidate that matters.

Method notes

Each structure went to both routes as the same CIF, with Prophet predicting its own moments. The earlier Prophet posts relaxed the rare-earth cells first, which is why a few numbers differ slightly from those. The Monte Carlo value is read off a temperature grid whose step is 5% of the mean-field value, so it carries a few percent of grid error.

Measured Curie temperatures are standard literature values. Four are soft: hcp Co is measured in the fcc phase it transforms into, B2 FeCo is a lower bound because it turns fcc while still magnetic, MnBi's 630 K is a structural transition, and Fe₁₆N₂ is an extrapolation because it decomposes first. Reports for GdN span 58 to 70 K.

The held-out CHGNet numbers come from retraining the route's CatBoost model locally on its own training table. Everything else is a route run on Ouro, linked in the tables.

Prophet is from Kairos Materials. Code is MIT, weights are CC-BY-4.0. Paper: Prophet.