MAG188

MAG188 is a DFT benchmark of 188 experimentally characterized collinear magnetic materials from the MAGNDATA database. All structures were recomputed with spin-polarized DFT and relaxed. MAG188 contains two benchmarks:

• MAG188-EXP: the relaxed experimentally reported magnetic state of each material (188 endpoints). It measures accuracy on experimentally established magnetic states.
• MAG188-SAMPLE: 1,195 relaxed endpoints that cover several self-consistent collinear spin configurations of each material: the 188 experimental states plus 1,007 relaxations from other spin sign patterns. It measures how well a model resolves competing magnetic states of the same material. For a spin-agnostic model, these states differ only through small changes in geometry.

Both benchmarks come with their full relaxation trajectories. Every frame has an energy, forces, stress and site-resolved DFT spins. MAG188 is the magnetic benchmark of the Prophet technical report (Section 8).

	MAG188-EXP	MAG188-SAMPLE
Materials (MAGNDATA entries)	188	188
Relaxed endpoints (benchmark)	188	1,195 (188 exp + 1,007 sampled)
Relaxation frames (all ionic steps)	1,887	14,642
Configurations per material	1	1–10 (178 materials with ≥ 2)

Both benchmarks cover 140 distinct reduced compositions, 50 elements and 4–20 atoms per cell. 177 materials have at least one magnetic site (|m| > 0.5 μB); there are 721 such sites in the experimental states.

In MAG188-SAMPLE:

• 163 materials have ≥ 2 distinct energy levels, where levels count as distinct when they are ≥ 1 meV/atom apart.
• The spread between the highest and lowest endpoint of a material has a median of 32.6 meV/atom and a maximum of 518.6 meV/atom.
• The experimental state is the lowest DFT endpoint for 145 of the 188 materials, and within 1 meV/atom of the lowest for 164.

Files

File	Contents
MAG188-EXP/mag188_exp.extxyz	188 relaxed endpoints, one per material (MAG188-EXP benchmark set)
MAG188-EXP/mag188_exp_trajectories.extxyz	all 1,887 ionic steps of the 188 relaxations
MAG188-EXP/mag188_exp_index.csv	one row per material (composition, endpoint energy, spins, endpoint max force, …)
MAG188-SAMPLE/mag188_sample.extxyz	1,195 relaxed endpoints (MAG188-SAMPLE benchmark set)
MAG188-SAMPLE/mag188_sample_trajectories.extxyz	all 14,642 ionic steps of the 1,195 relaxations
MAG188-SAMPLE/mag188_sample_index.csv	one row per relaxation, including the energy above the material's lowest endpoint (e_rel_meV_per_atom)
SHA256SUMS	checksums of all data files

In the trajectory files, the final frame of each relaxation has is_endpoint=T. The exp endpoints and trajectories of MAG188-SAMPLE are identical to MAG188-EXP, so the two sets overlap by design.

Construction

• Structures. Commensurate, collinear magnetic structures from MAGNDATA with at most 20 atoms per cell and no f-block elements. For the 15 entries with partially occupied sites, the species with the highest occupancy was kept (occupancy_policy=max_occupancy_site).
• DFT. VASP with PAW potentials and the PBE functional (PBE+U where the Materials Project applies it). Inputs follow pymatgen MPRelaxSet, which is the ELEMENTA protocol. All calculations are spin-polarized and collinear, and both atomic positions and the cell are relaxed.
• Energies. Energies are raw VASP total energies, with no Materials Project (MP2020) compatibility corrections.
• Experimental states (exp). Each relaxation starts from the experimentally reported spin ordering.
• Sampled states (sampled, MAG188-SAMPLE only). For each material, seed spins on the magnetic sites were given different collinear sign patterns, and each pattern was relaxed self-consistently. mag_sample_mask identifies the sign pattern (0 = all seed spins parallel), and config_id is mag<mask>. Symmetry-equivalent patterns can converge to the same state. When ranking the states of a material, treat endpoints within 1 meV/atom of each other as one level.
• Held out. No reduced formula in MAG188 appears in the training data of Prophet-Spin.

Data fields

The files are standard extended XYZ, and both benchmarks share one schema.

Per atom (the Properties columns):

Field	Unit	Description
species, pos	Å	element and Cartesian position
forces	eV/Å	DFT forces
magmoms	μB	DFT site spins: VASP's collinear site-projected magnetization, with sign

Per frame (comment line):

Field	Unit	Description
energy	eV	DFT total energy of the cell
stress	eV/ų	full 3×3 stress in the ASE sign convention (negative = compressive)
magmom	μB	total cell magnetization (not exactly equal to the sum of the site magmoms)
material_id	–	MAGNDATA_<i>_<j> = MAGNDATA entry <i>.<j> (e.g. MAGNDATA_0_1150 → entry 0.1150)
formula, doi	–	cell formula and literature reference of the MAGNDATA entry
config_id	–	exp, or mag<mask> for sampled configurations; (material_id, config_id) is unique
config_type	–	exp or sampled
mag_sample_mask	–	seed sign-pattern id (-1 for exp)
ionic_step	–	original VASP ionic-step index
is_endpoint	–	T for the final frame of each relaxation (trajectory files only)
n_scf_steps	–	electronic (SCF) iterations of this ionic step
collinear_axis	–	experimental spin direction from MAGNDATA (exp frames only). The DFT is collinear, so only each spin's sign is used
occupancy_policy	–	none, or max_occupancy_site for the 15 disordered entries

Usage

The files load with ASE (tested with ASE 3.29). Energy, forces, stress, site spins and total magnetization all load as calculator results:

from collections import defaultdict
from ase.io import read

exp = read("MAG188-EXP/mag188_exp.extxyz", index=":")            # 188 endpoints
sample = read("MAG188-SAMPLE/mag188_sample.extxyz", index=":")   # 1,195 endpoints

a = exp[0]
a.info["material_id"], a.info["config_id"]
a.get_potential_energy()      # eV
a.get_forces()                # eV/Å
a.get_stress(voigt=False)     # eV/ų, ASE convention
a.get_magnetic_moments()      # per-site DFT spins, μB
a.get_magnetic_moment()       # total cell magnetization, μB

states = defaultdict(list)    # competing magnetic states of each material
for s in sample:
    states[s.info["material_id"]].append(s)

Benchmark protocols

• Energy and force accuracy. Evaluate on the endpoint files: 188 frames for MAG188-EXP and 1,195 for MAG188-SAMPLE.

  • Energy MAE: mean over endpoints of |E_pred − E_DFT| / N_atoms, reported in meV/atom on raw total energies.
  • Force MAE: mean absolute error pooled over all Cartesian force components of all atoms, in meV/Å.

• Magnetic-state ranking (MAG188-SAMPLE). For each material with ≥ 2 configurations, compare the model's energy ordering of its endpoints with the DFT ordering. Report, for example, whether the lowest DFT state is identified, and the Spearman correlation. Merge endpoints within 1 meV/atom first.

• Spin input. A spin-conditioned model can be run in two ways, and results should say which was used:

  • DFT-converged: the model receives the DFT site spins (magmoms) as input.
  • Predicted: the model receives only the structure and initial spin guesses.

  Spin-agnostic models are evaluated on the structure alone.

Reference results

These are the energy and force MAEs on the benchmark endpoints from the Prophet technical report. Energies are raw. Prophet models share the ELEMENTA reference; the public models (*) use their own isolated-atom references.

Model	Spin source	EXP E (meV/atom)	EXP F (meV/Å)	SAMPLE E (meV/atom)	SAMPLE F (meV/Å)
Prophet-OAME-MBD	–	62.84	33.4	35.63	31.0
MACE-MP-0	–	71.97*	40.1	45.69*	38.3
MACE-MPA-0	–	65.08*	37.5	39.94*	34.0
MatterSim v1	–	66.03*	45.3	36.90*	43.6
EquiformerV3	–	64.95*	40.1	37.72*	37.0
ORB v3	–	66.51*	42.8	40.96*	38.1
Nequix-MP-1	–	65.48*	37.3	38.91*	34.0
Nequix-OAM-1	–	65.70*	36.1	40.83*	32.5
Prophet-Spin	DFT-converged	19.23	18.3	16.34	20.1
Prophet-Spin	spin-denoised (predicted)	30.73	26.8	20.75	30.9

Notes

• ionic_step keeps VASP's original numbering. Frames were removed upstream from some trajectories, which either start after step 0 or have gaps: 4 in MAG188-EXP and 71 in MAG188-SAMPLE. Use is_endpoint to find the final frames.
• All endpoints except two have a maximum atomic force below 0.05 eV/Å. The exceptions are MAGNDATA_1_461 exp (0.092 eV/Å) and MAGNDATA_1_556 mag2 (0.074 eV/Å).
• MAG188 is a held-out test set. Please do not train on it if you report results on it.

Citation and License

If you use MAG188, please cite the Prophet technical report and the MAGNDATA database:

Prophet: Scaling Atomistic Foundation Models Across Composition, Configuration, and Spin, Kairos Materials (2026).

@article{gallego2016magndata,
  title   = {{MAGNDATA}: Towards a Database of Magnetic Structures. {I}. The Commensurate Case},
  author  = {Gallego, Samuel V. and Perez-Mato, J. Manuel and Elcoro, Luis and Tasci, Emre S. and
             Hanson, Robert M. and Momma, Koichi and Aroyo, Mois I. and Madariaga, Gotzon},
  journal = {Journal of Applied Crystallography},
  volume  = {49}, number = {5}, pages = {1750--1776}, year = {2016},
  doi     = {10.1107/S1600576716012863}
}

Released under CC-BY-NC-4.0. The starting structures come from MAGNDATA (Bilbao Crystallographic Server). The literature source of each entry is given in its doi field.