Ouro DFT on known magnets: Ms and MAE vs experiment

Setup

Structures on this team:

• Fe bcc (2 → 1 prim)

• Co hcp (2)

• FeCo B2 (2)

• FePt L1₀ (2)

• MnBi (4)

• SmCo₅ (6), failed: no Sm Dojo NC-FR pseudopotential yet

Saturation magnetization

$\mu_0 M_s$ from the moments route vs typical experimental room-temperature values:

Ranking matches experiment: FeCo and Fe highest, MnBi lowest, FePt in between. Absolute $M_s$ is already usable for screening at these defaults.

Magnetic anisotropy energy

TB2J MAE (hard − easy over {001,100,010}) vs literature uniaxial $K_u$ (cubic $K_1$ for Fe):

What holds:

1. Soft vs hard separation works. Fe / FeCo sit near zero; Co / MnBi / FePt are clearly anisotropic.

2. Co magnitude matches experiment (0.44 vs 0.45 MJ/m³), but the predicted easy axis is basal rather than $c$.

3. FePt is correctly uniaxial along $c$, with MAE about 2× experimental. Fine for ranking, not for absolute $K_u$.

4. MnBi is in the right order of magnitude but prefers the basal plane here.

Hardness $\kappa = \sqrt{K_u / (\mu_0 M_s^2 / 2)}$ from the MAE route ranks the same way: Fe/FeCo soft ($\kappa \ll 1$), Co borderline, MnBi and FePt hard.

Curie temperature (mean-field)

TB2J exchange on the same collinear SCF, with mean-field $T_C = 2 J_{0,\max}/(3 k_B)$. This is an upper bound and usually overestimates experiment; the ranking is what matters for screening.

Ranking matches the known magnets: FeCo and Fe highest, then Co, then MnBi / FePt. Absolute MF $T_C$ is high (especially Fe and FeCo), as expected for Heisenberg mean-field. Co and FePt are surprisingly close to experiment at these defaults.

Why the easy axis is sometimes wrong

This does not look like a simple reporting bug. Easy axis is $\arg\min E$, hard axis is $\arg\max E$, and MAE is hard − easy. FePt landing on ⟨001⟩ is a useful control: the direction labels and $\theta,\phi$ mapping are not systematically flipped.

The two mismatches have different explanations.

MnBi is expected at 0 K. Experiment is easy-plane below ~90 K and only becomes $c$-axis after the spin reorientation (~90-140 K), driven largely by thermal expansion of $a$. Fixed-cell DFT (and low-$T$ experiment) routinely prefer the basal plane. Comparing a 0 K MAE sign to room-temperature $K_u$ is the wrong comparison for MnBi, not evidence that the calculator inverted axes.

Co is the more interesting case. PBE/GGA usually gets $c$-easy for hcp Co; LDA often flips the sign. We got the right magnitude with the wrong sign. That usually means the energy difference is tiny and sitting near a sign change (~60 µeV total here), not that min/max is backwards. Plausible contributors at these defaults:

• coarse $k$-mesh relative to how small the MAE is

• DZP + modest cutoff vs denser PAW setups in the literature

• fixed experimental $c/a$ (Co MAE sign is lattice-sensitive)

• TB2J magnetic force theorem vs full SOC total-energy differences

So for screening: trust soft vs hard and FePt-like uniaxial ranking; treat absolute MJ/m³ and easy-axis sign as directional, especially for Mn-pnictides and for Co until we converge $k$, cutoff, and (if needed) a total-energy SOC cross-check.

Live actions

Moments:

MAE:

Takeaways

• Moments for $M_s$: already good enough to rank candidates.

• MAE for soft vs hard, and for confirming uniaxial $c$-axis cases like FePt. Treat absolute MJ/m³ and easy-axis sign carefully (MnBi: 0 K vs RT; Co: converge before trusting the sign).

• Exchange / mean-field $T_C$ for ranking ordering temperatures. Use the rank, not the absolute kelvin (MF overestimates, especially Fe / FeCo).

• SCF cache works: MAE warm-started from moments charge; exchange reused the same collinear SCF where available.

• Rare earths: SmCo₅ needs Sm pseudopotentials/orbitals in the Dojo set before RE magnets join this loop.

To try it: run a small CIF on Magnetic moments, then MAE on the same structure. The second call should reuse SCF.