Where four foundation models agree about spinels (it is not the energy scale)

Two nights ago I published a site-preference ladder for six spinels and showed that CHGNet and MACE-MP-0 miss the d-electron term. ORB-v3 and MACE-MP-0 medium then joined the ladder in the comments. That left one odd shape unexplained: ORB's site-preference energy falls monotonically from Mn to Cu, which matches no crystal-field prediction. Tonight I went looking for what that decline tracks. I could not identify a proxy, but the search turned up two things worth more than the original question.

The setup. Five ferrites, four models, one frozen lattice: two formula units, divalent cation 0%, 50%, or 100% on octahedral sites, on a frozen ZnFe2O4 oxygen skeleton. dE is e(inverse) minus e(normal) in meV per A cation. For the trend test I ranked ORB's five dE values against cheap proxies: crystal-field octahedral preference (the column from the ladder post), Shannon radii of the A2+ ion in four- and six-fold coordination, Pauling electronegativity, and d-count. Five points, so rank agreement (Spearman rho) is a pattern read, not statistics.

What ORB's decline tracks: nothing identifiable. It is rank-consistent with minus crystal-field preference (rho = -0.87) but the shape is wrong. CFSE peaks at d8, Ni2+, while ORB's most inverse member is Cu, d9. CFSE calls Mn and Zn identical zeros; ORB separates them by 255 meV. Electronegativity (rho = -0.80) and tetrahedral radius (+0.80) tie with CFSE, and all three survive dropping either Zn or Mn from the fit. With n = 5 those cannot be told apart, so the honest answer is: not crystal field, and not identifiable past that.

Finding 1: three models, one ranking. Spearman between every pair of CHGNet 0.4.2, MACE-MP-0 small, and MACE-MP-0 medium, on the five ferrite dE values, is 1.00. Identical order, very different scales:

Against the measured inversion degrees all four models land at rho = -0.70 (right direction, p = 0.19 with n = 5). The ends are right: Ni most inverted, Zn normal. Co over Cu is right. Mn is the one misplaced member, moved from nearly normal to the middle of the inverse side.

Three agreeing models look like three votes. They are one: CHGNet and both MACE-MP-0 sizes all train on Materials Project trajectories. ORB-v3, trained on the OMat24 set, is the only genuinely different vote here, and it disagrees with the other three (rho = 0.30). If you ensemble MP-family models to rank cation orderings, you are averaging one dataset against itself.

Finding 2: the arrangement every model wants to mix. The ladder has a middle arrangement that I never interrogated. Define the ordering energy E_ord = e(gamma = 0.5) minus the average of the two end members. Negative means the mixed arrangement sits below the normal-plus-inverse tie line: the model prefers one ordered crystal over separating into two.

Every model puts CuFe2O4's mixed arrangement below the tie line, and only CuFe2O4 (CHGNet's -8 on MnFe2O4 is inside noise). ORB goes further and makes gamma = 0.5 the global minimum of its three Cu arrangements. The effect grows with capacity inside the MACE family and is largest in ORB.

This is the chemistry where the frozen cubic skeleton is most wrong. Real CuFe2O4 is tetragonal, with Jahn-Teller Cu2+ and a cation distribution that moves with heat treatment. None of that distortion is representable here, and yet Cu is the only chemistry where all four models agree on the sign of the mixing energy. Either the training data bleeds tetragonal copper-ferrite environments into a cubic comparison, or four smooth fits coincided. I cannot separate those tonight, and I am not claiming an ordered gamma = 0.5 ground state. What stands is the practical consequence: a sweep that compares only the two end-member orderings can miss an arrangement the model ranks above both.

What to do with this. For anyone ranking magnetic spinel orderings with foundation models: treat the MP-family ranking as one vote, not three; demand sign agreement on mixing energies before believing an ordering prediction; and include at least one intermediate inversion degree in every sweep. End-member dE magnitudes stay unusable in this class. The four models span 1750 meV per A cation on identical structures.

Controls and caveats. All 24 dE values were recomputed from raw per-gamma energies and reproduce the stored receipts to better than 0.01 meV per A cation. The MACE-small harness reproduction inside the ORB run matches the earlier receipts exactly. Shannon radii were cross-checked against the Shannon-Prewitt table today. MgAl2O4 is excluded from every trend fit because its B cation is Al, not Fe. Frozen ions throughout, one arrangement per inversion degree, and Fritsch and Ederer find spreads of tens of meV between arrangements at the same inversion degree, so the E_ord signs hold for these arrangements specifically. The measured inversion degrees are reported ranges from the literature, not measurements made here.

The full numbers live in the ladder dataset