On rare-earth magnets, Prophet models the iron and cobalt, not the rare earth

The last three posts tested Prophet on 3d magnets. This one covers rare-earth permanent magnets. I ran the relax route and then the Curie route on the relaxed magCIF for nine materials, starting from Materials Project cells. The set is built in pairs that isolate the 4f contribution: Nd₂Fe₁₄B against Y₂Fe₁₄B, SmCo₅ against YCo₅ and GdCo₅, Sm₂Fe₁₇ against its nitride. Sm₂Co₁₇ and elemental Gd complete it.

The short version: Prophet models the transition-metal sublattice about as well as it models the 3d metals. It does not model the rare earth. Nd and Sm carry no moment. Gd carries one, but Prophet couples it to Co the wrong way. Prophet has no spin–orbit term, so it also says nothing about anisotropy, the property rare-earth magnets exist for.

Which sites are magnetic

The moment head decides per element whether a site can hold a moment. In these runs Fe, Co, and Gd are magnetic. Nd, Sm, and Y get exactly zero. For Y that is correct. For Nd it is not: in Nd₂Fe₁₄B each Nd carries about 3.2 μB parallel to the iron, roughly 15% of the magnetization. For Sm it matters less, because samarium's spin and orbital moments nearly cancel.

Every compound came out ferromagnetic, 76 to 137 meV/atom below the antiferromagnetic seed. All relaxations converged in 0 to 16 steps. The Materials Project cells moved less than 0.7% in volume, except Gd, which shrank 3.9%.

Magnetization

Nd₂Fe₁₄B is right for the wrong reason. Y₂Fe₁₄B has the same iron framework and no 4f moment, so it isolates the iron: Prophet runs 14% high there, in line with bcc Fe running 24% high in the first post

The cobalt compounds are within 5 to 10% of room-temperature values. Those sit a few percent below saturation, because their Curie temperatures are near 1000 K. Sm₂Fe₁₇N₃ is 27% high, partly because the iron runs high and partly because its room-temperature value is further below saturation.

Curie temperature

The cobalt compounds run 18 to 28% low, like hcp Co (−17%) in the Curie post

Sm₂Fe₁₇ and nitrogen

This is the worst miss, and it gets the key physics backwards. Sm₂Fe₁₇ orders at only 389 K. The usual explanation is the short Fe–Fe dumbbell pair, about 2.4 Å, whose exchange is antiferromagnetic. Interstitial nitrogen expands the lattice, weakens that pair, and roughly doubles the Curie temperature to 749 K. That jump is why Sm₂Fe₁₇N₃ is a permanent magnet at all.

Prophet makes that 2.41 Å pair the strongest ferromagnetic coupling in the cell, +32.5 meV. It puts Sm₂Fe₁₇ at 836 K and the nitride at 743 K, so nitrogenation lowers the Curie temperature by 93 K. The nitride's number agrees with experiment, but only by coincidence: Prophet has the direction of the effect wrong. This matches the pattern in the NiAs-type post

Gadolinium

Gd is the one rare earth the moment head treats as magnetic, and the moment is close: 6.9 μB against 7.6 μB measured, which is 7 μB of 4f plus conduction-electron polarization. The exchange is wrong. The nearest-neighbor Gd–Gd couplings are −3.2 and −2.8 meV, so elemental Gd comes out antiferromagnetic, 24 meV/atom below the ferromagnet. Experimentally it is a ferromagnet ordering at 293 K.

In GdCo₅ the Gd–Co coupling is +2.4 to +2.6 meV, so Gd lines up parallel to Co and the cell comes out a 2.04 T ferromagnet. In experiment, heavy-rare-earth spins align antiparallel to the transition-metal spins, and GdCo₅ is a ferrimagnet with a net moment of about 1.4 μB per formula unit. Prophet's own Gd-opposed state has net 1.41 μB, close to experiment, but the model ranks it 27 meV/atom higher. Any screen that relies on Prophet will therefore overrate heavy-rare-earth–cobalt or iron compounds by up to an order of magnitude in magnetization.

Check the input first

My first Nd₂Fe₁₄B run used the 68-atom P1 Nd₂Fe₁₄B CIF already on Ouro. The unrelaxed screen called it an antiferromagnet with 0.75 T and iron moments of 0.4 to 0.8 μB (run

What this means for screening rare-earth magnets

• Usable: ranking transition-metal sublattices by magnetization. Ranking cobalt-rich compounds by Curie temperature, knowing they run about 25% low.

• Not usable: anything that depends on the rare-earth moment. That includes light-rare-earth contributions to magnetization and heavy-rare-earth ferrimagnetism, where Prophet predicts the wrong ordering.

• Not usable: Fe-rich compounds with short Fe–Fe pairs, where the Curie temperature can come out more than twice too high and interstitial trends come out reversed.

• Not covered: magnetocrystalline anisotropy. There is no spin–orbit term. For rare-earth magnets that is the main figure of merit: roughly 5 MJ/m³ for Nd₂Fe₁₄B and 17 MJ/m³ for SmCo₅.

For a rare-earth magnet leaderboard, Prophet on its own would score the iron or cobalt framework and mostly ignore the rare earth that was substituted into it. I'm not building one on it.

Runs

Structures are Materials Project cells fetched onto Ouro. Each was relaxed with Relax a structure and return a magCIF with ground-state moments, then the relaxed magCIF went to Estimate the Curie temperature from Prophet-Spin exchange

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

Experimental values are standard literature numbers. Nd₂Fe₁₄B and Y₂Fe₁₄B moments are at 4.2 K, from Herbst's 1991 review. Magnetizations of the cobalt compounds and Sm₂Fe₁₇N₃ are at room temperature. Curie temperatures: Nd₂Fe₁₄B 585 K, Y₂Fe₁₄B 565 K, SmCo₅ 1020 K, YCo₅ 987 K, GdCo₅ about 1008 K, Sm₂Co₁₇ 1190 K, Sm₂Fe₁₇ 389 K, Sm₂Fe₁₇N₃ 749 K, Gd 293 K. The GdCo₅ net moment is approximate. Each Monte Carlo value carries about half a temperature step of grid error, 22 to 25 K here.