Spin-informed universal graph neural networks for simulating magnetic ordering
Wenbin Xu, Rohan Yuri Sanspeur, Adeesh Kolluru, Bowen Deng, Peter Harrington, Steven Farrell, Karsten Reuter and John R. Kitchin, “Spin-informed universal graph neural networks for simulating magnetic ordering”, Proceedings of the National Academy of Sciences 122(27), e2422973122 (2025). https://doi.org/10.1073/pnas.2422973122
This summary was written by a language model from the paper and has not been checked line by line. Rely on the published paper for details.
Question
Universal machine-learning interatomic potentials (uMLIPs) trained across the periodic table are fast surrogates for density functional theory (DFT), but they take only positions and element identities as input, so they cannot tell one magnetic ordering of a structure from another. CHGNet, for example, predicts moment magnitudes and therefore an energy averaged over magnetic configurations. The paper asks whether spin degrees of freedom can be added to a uMLIP so it can rank ferromagnetic (FM), antiferromagnetic (AFM) and ferrimagnetic (FiM) orderings, and whether such a model can also be used to find bad labels in the large datasets it is trained on, a “chicken-and-egg” problem between data quality and model quality (Xu et al. 2025).
Approach
The authors built a spin-informed GNN (SI-GNN) framework and applied it to two Open Catalyst Project backbones, SchNet and GemNet-OC. Each atom’s input embedding combines its element embedding with a spin embedding built from a scalar initial moment guess and a unit spin coordinate, mirroring how spin-polarized DFT starts from an initial guess and converges to a moment. Collinear spin is treated separately from spatial symmetry: energy is made invariant to global spin inversion by averaging the spin embedding over the spin and its inverse, while predicted moments are signed by projecting a scalar onto the spin coordinate. Forces can be predicted directly or as energy gradients. Models were trained on MP-MM, the subset of the MPtrj dataset with moment labels (284,110 configurations, 7,941,047 moment labels, about 87% of them between -0.1 and 0.1 µB), and compared with CHGNet and a spin-distance edge GNN (SEGNN) that uses spin dot products.
For data cleaning, atom embeddings from a trained model were clustered with a Gaussian mixture model (group count chosen by BIC), and labels with z-scores beyond ±5 within a group were flagged as anomalies. Applications used Metropolis Monte Carlo spin flipping and particle swarm optimization with the model as a surrogate, checked against VASP calculations (PBE+U, 500 eV cutoff).
Key findings
On the MP-MM test set, SI-GemNet-OC reached a moment MAE of 0.009 µB and an energy MAE of 14.2 meV/atom, against 0.029 µB for CHGNet (which predicts only magnitudes). SI-SchNet improved moment error by about 73% over plain SchNet (0.015 µB), versus about 27% for SchNet-SEGNN, which the authors attribute to the limited expressivity of dot-product spin features. Restricted to atoms above 0.1 µB, the MAE was 0.051 µB, but 859 points had errors above 1 µB, many in Gd and Eu compounds (Xu et al. 2025).
Recomputing 234 Gd/Eu samples with 7 µB starting moments (26 did not converge) shifted many labels from about ±1 µB to about ±7 µB, showing that the original calculations were poorly converged. The clustering method flagged 0.7% of the Gd/Eu subset and 0.8% of a Cr subset as anomalous, consistent with about 0.9% large outliers in the full test split, so roughly 1% of the Materials Project data appear affected. For GdDyAl4, starting Gd at the model’s predicted 7 µB converged in 28 SCF cycles, while the Materials Project default of 0.6 µB took 211 cycles, or stalled near 1 µB with a 100-step limit (Xu et al. 2025).
On a held-out set of about 486 enumerated orderings, the model ranked orderings with an average Spearman coefficient of 0.896 across 64 groups, while CHGNet gave nearly identical energies for different orderings. Although trained only on bulks, the model guided Monte Carlo spin flipping on CrN(100) and Fe2O3(110) slabs to orderings lower than the AFM ones by 2.63 eV and 0.35 eV. N adsorption energies at a Cr vacancy were 1.00, -1.96 and 0.60 eV on FM, AFM and model-derived CrN slabs, and spin flipping of the adsorbate-slab system found an ordering 0.32 eV lower with changes on atoms more than 4 Å from the adsorbate (Xu et al. 2025).
Significance
The work shows that atomistic foundation models can be extended to magnetic ordering at small cost by feeding spin into atom embeddings, and that the same embeddings can audit and refine the datasets those models depend on. It also warns that adsorption energies computed with convenient FM slab initializations can be wrong by an eV or more. The authors note the collinear treatment does not cover noncollinear spin-lattice dynamics (Xu et al. 2025).