H6 verdict: Co-Fe-W keeps its moment but not its anisotropy (and the easy axis points the wrong way)

Question. H6 asked whether a Co-dominated Fe-Co-W framework keeps the large moment that W destroys in Fe frameworks (F11: every measured Fe-W compound is a weak ferrimagnet, <= 0.43 T) while the W 5d sublattice still carries the anisotropy that the Fe-framework anchors showed (12.0 and 6.48 MJ/m3). The sole tier-1 survivor was FeCo6W, P-6m2 #187, 8 atoms, 12.5 at% W.

Answer: no. The candidate fails the pre-registered 1.5 MJ/m3 anisotropy bar, and the anisotropy it does have points the wrong way: the easy axis is in the basal plane.

Evidence chain

The candidate and its tier-1 numbers: e_hull 0.0782 eV/atom, CHGNet Ms 0.9969 T (DFT-FM 1.0291 T), Tc 887.76 K, cost 30.53 USD/kg, phonons clean, row 01a07d27-47c7-7365 in the candidates dataset. On every gate it looked like a real magnet.

Contract v1.0.0 DFT relax (action 01a09883) held the cell sanely: P-6m2 retained at symprec 0.01 and 0.1, volume +1.59% (a -0.89%, c +1.25%), no sign of the relax-route expansion pathology from F21. Relaxed CIF: FeCo6W (P-6m2) - DFT relaxed

Tier-2 MAE on the relaxed cell, first attempt of the allowed two, frozen settings (tb2j, ecutwfc 65, kspacing 0.16, scf_thr 1e-6, mp 0.05, DZP):

• MAE = 1.1499 MJ/m3 (0.661 meV/cell, 0.0827 meV/atom). Below the 1.5 MJ/m3 bar set before the calculation ran.

• Easy axis = 100, i.e. in-plane. E(001) - E(100) = +0.66 meV/cell and E(010) - E(100) = +0.661 meV/cell. The c-axis is the hard direction and the two in-plane directions are nearly degenerate, so this is an easy-basal-plane magnet, not a uniaxial one. Even if the magnitude had cleared the bar, the geometry would disqualify the phase: a permanent magnet needs the easy axis pinned along one direction.

• The geometry gate passed at the route's own reading (max force 0.0064 eV/A, stress 0.387 kbar against the 0.5 kbar threshold), so the number is not a stress artifact.

One caveat carried from the ordering branch, unchanged: the FM-vs-AFM comparison never converged on this cell after three terminal SCF attempts, so the MAE was computed on a collinear-FM state that is lower-by-default, not proven to be the ground state. That caveat affects confidence in the ordering, not the easy-plane observation, which is computed within one spin configuration.

What was right and what was wrong

The moment half of the hypothesis was supported. At 12.5 at% W the Co-dominated framework holds Ms near 1.0 T, confirming the low-W-fraction observation from the H7 anchor (where 50 at% W killed the moment entirely, 0.11 uB/Co). The dose-response picture is consistent: W destroys the 3d moment in proportion to its fraction, in Fe and Co frameworks alike.

The anisotropy half is where the hypothesis died, in two independent ways: magnitude below bar and easy plane instead of uniaxial. The W 5d anisotropy measured on the Fe-W anchors does not transfer to this near-hull hexagonal-derived field at low W dilution.

What this closes

With H6 refuted, the separated-5d carrier mechanism has now failed in every framework chemistry it could be tested in:

• Fe frameworks: anisotropy can be large (12.0 MJ/m3 anchor) but the moment dies (F11).

• Co frameworks: the moment survives but the anisotropy is below bar and easy-plane (this verdict, and H7).

• Mo as the carrier: neither half survived (H8).

So the next move cannot be another framework-element swap; the ledger now says so explicitly (finding F22). The next hypothesis (H14) has to change the structural motif that sets the 5d crystal field, a genuinely uniaxial tetragonal site for the heavy element instead of these hexagonal-derived fields, or abandon 5d spin-orbit coupling as the anisotropy source entirely.

Housekeeping: dataset rows 01a07d27-47c7-7365 (candidate of record) and 01a09884-4443 (attempt) are marked failed with reason mae_below_bar_easy_plane, every value above carries its action receipt. The MnAlGe (H13) line stays paused on a controller question and was untouched by this work.