Cell + Ionic relaxation with CHGNet; 0.03 eV/Å threshold; final energy = -530.3680 eV; energy change = -463.1991 eV; symmetry: P4_2/mcm → P1

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -529.6716 eV; energy change = -554.7984 eV; symmetry: P4_2/mcm → P1

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -134.9712 eV; energy change = -0.0746 eV; symmetry: Im-3m → Im-3m

Nd2Fe14B crystal structure (P42/mnm #136 expanded to P1, 68 atoms). Coordinates from Herbst/Croat/Pinkerton (1984): a=8.807, c=12.207. 8 Nd (4f+4g), 56 Fe (16k1+16k2+8j1+8j2+4e+4c), 4 B (4g). Decisive test for ALIGNN magnetic sublattice density hypothesis.

Fe bcc 2x2x2 supercell (16 atoms, P1 explicit, a=5.74 Å). Control for ALIGNN atom-count vs sublattice-density discrimination test. Generated from conventional bcc cell (a=2.87 Å, Im-3m, Fe at (0,0,0) and (1/2,1/2,1/2)).

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -61.8790 eV; energy change = -2.2074 eV; symmetry: Fm-3m → I4/mmm

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -24.9383 eV; energy change = -0.1396 eV; symmetry: P63/mmc → P63/mmc

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -61.4361 eV; energy change = -64.1367 eV; symmetry: P6_3/mmc → P-1

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -27.1230 eV; energy change = -0.2106 eV; symmetry: P63/mmc → P63/mmc

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -44.3109 eV; energy change = -0.0632 eV; symmetry: P42/mnm → P42/mnm

Altermagnet CIF - CrO rocksalt Fm-3m, predicted altermagnet

Altermagnet CIF - MnTe NiAs P63/mmc, DFT moment ~4.5 μB/Mn, TN≈310K

Altermagnet CIF - Mn3Sn D019 P63/mmc, DFT moment ~3.0 μB/Mn, Weyl semimetal

Altermagnet CIF - CrSb NiAs P63/mmc, DFT moment ~2.7 μB/Cr

Altermagnet CIF - RuO2 rutile P42/mnm, DFT moment ~0.4 μB/Ru

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -129.5634 eV; energy change = -51.1287 eV; symmetry: R-3m → C2/m

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -91.0487 eV; energy change = -18.6541 eV; symmetry: R-3m → R-3m

Cell + Ionic relaxation with Orb v3 conservative inf MPA; 0.03 eV/Å threshold; final energy = -91.2482 eV; energy change = -18.9911 eV; symmetry: R-3m → R-3m

MnBi4Te7 in R-3m (No. 166), a=4.383, c=67.710 Å. MnBi2Te4·Bi2Te3 intergrowth. Built from crystallographic data for DMC benchmarking comparison.

GeBi2Te4 in R-3m (No. 166), a=4.280, c=40.730 Å. Non-magnetic baseline for MnBi2Te4 family comparison.