Magnetic Moments
The local magnetic moment on an atom (in Bohr magnetons, µB) and the way those moments are arranged across a structure (non-magnetic, ferromagnetic, ferrimagnetic or antiferromagnetic collinear orderings) define a material’s magnetic state. In spin-polarized DFT the result depends on the starting guess: codes such as VASP need an initial moment for every atom (the MAGMOM vector), and the electronic minimization tends to find a nearby local solution. Practitioners therefore often try several orderings and pick the lowest in energy, but the magnitude of the initial moments is usually set by heuristics or chemical intuition, and the number of possible orderings grows combinatorially with system size. Machine learning surrogates that predict per-atom moments offer a way to screen magnetic materials and to seed DFT calculations. See also graph neural networks and imbalanced data.
Per-atom moment prediction with a two-part GNN (2024)
Sanspeur and Kitchin trained graph neural networks on antiferromagnetic ground-state structures from the Materials Project, where about 90% of atomic moments are near zero. A GemNet-OC classifier first flags atoms with moments above 0.1 µB (F1 and MCC about 91%), and a regressor on its embeddings then predicts the moment magnitude with a mean absolute error of 0.1 µB. The embeddings could not distinguish spin-up from spin-down atoms, so only magnitudes are predicted. Used as the MAGMOM starting guess for the bulk oxide Mo2Ru13PtO32, the predicted moments reached the electronic ground state about 30% faster and about 0.6 eV lower in energy than uniform 5 µB or 0.6 µB starts (Sanspeur 2024). Summary: sanspeur2024.
Magnetic ordering and vacancy energy trends in perovskites (2014)
Curnan and Kitchin examined whether magnetic state changes the ordering of oxygen vacancy formation energies across 3d perovskites. In ferromagnetic cubic cells of 20 atoms or more, LaVO3 dropped abruptly and changed the La series ordering, but an orthorhombic Pbnm cell kept the original order, so they treat this as an artifact of the cubic model; in ferromagnetic SrBO3, SrMnO3 crossed SrFeO3 gradually with vacancy dilution in both cubic and Pbnm cells. A-, C- and G-type antiferromagnetic orderings in 2 x 2 x 2 cells preserved ordering, reproduced the experimentally favored C-type LaVO3 and G-type LaCrO3, but favored C-type rather than the observed A-type LaMnO3 (0.4 eV apart). Significant B-site moments appeared only for B = V to Ni. Their conclusion is that magnetism cannot be dismissed by a single simplification and should be checked with increasing supercell sizes (Curnan 2014). Summary: curnan2014; see also Perovskite oxides.
Spin-informed universal potentials for magnetic ordering (2025)
Xu, Sanspeur and co-workers added spin to universal GNN potentials by feeding each atom’s initial moment guess (a scalar) and a collinear spin coordinate (a unit sign) into its embedding, keeping the energy invariant to global spin inversion while predicting signed moments. Trained on 284,110 Materials Project configurations, SI-GemNet-OC reached a moment MAE of 0.009 µB and ranked enumerated FM, AFM and FiM orderings of about 486 bulk materials with an average Spearman coefficient of 0.896, where CHGNet gave nearly the same energy for every ordering. Seeding Gd in GdDyAl4 at the predicted 7 µB converged in 28 SCF cycles instead of 211 from the 0.6 µB default. Used as a surrogate for Monte Carlo spin flipping on CrN and Fe2O3 slabs, the bulk-trained model found orderings lower than AFM, and the slab ordering changed N adsorption energy on CrN from 1.00 eV (FM) to -1.96 eV (AFM) (Xu et al. 2025). This resolves the sign limitation of the earlier magnitude-only model. Summary: xu2025.