Posts 5 and 6 mapped Δ and bond length onto the electronic side. This is the magnetic side: does the M–X–M angle, combined with d-electron count, actually predict whether a compound orders antiferromagnetically, ferromagnetically, or not at all?
Post 1 set out seven steps for this series. Posts 2 and 3 built the dataset, post 4 engineered the descriptors, and posts 5 and 6 tested the electronic half of step 3 — structure → electronic properties, via Δ and bond length against band gap and the metal–insulator transition. Step 4 on that list — structure → magnetic property relationships — has been waiting since then. This post is the first attempt at it, using the same superexchange-angle and d-electron-count descriptors introduced in post 4, but now pointed at magnetic ordering type instead of crystal field splitting.
The expected pattern
Goodenough-Kanamori-Anderson reasoning gives three limiting cases, all set by the M–X–M angle and which d-orbitals are occupied. Near 180°, if both metal centers have lobes pointing directly at the shared anion and the relevant orbitals are partially filled, the overlap is large and direct — this is rule 1, and it gives strong antiferromagnetic superexchange. Still near 180°, if one side's relevant orbital is empty or completely full, the pathway weakens and flips sign — rule 2, weak ferromagnetic coupling. Near 90°, the two metal orbitals point at different anion p-orbitals, and the coupling is mediated indirectly through Hund's rule on the anion — rule 3, also weak ferromagnetic. Everywhere in between, no single rule dominates cleanly, and dᾆ or d¹⁰ configurations have no unpaired spins to couple at all.
Application: magnetic ordering regime map
The widget below plots M–X–M angle against d-electron count and colors each region by the GKA-expected ordering type. Click a region to see the reasoning. As with the band gap map in post 5, this is the textbook version — the real dataset is what tests it.
Magnetic ordering regime map
M–X–M angle (x-axis) vs d-electron count (y-axis). Click a region to see the GKA reasoning.
Reasoning
Click a region above for the GKA reasoning behind that regime.
Schematic boundaries from single-pathway GKA reasoning — real compounds with multiple competing pathways are exactly where I expect this map to fail informatively.
Where I expect surprises
The map above assumes one dominant M–X–M pathway per compound, which is the textbook simplification. The real dataset is most informative exactly where that assumption breaks: distorted octahedra with two or three inequivalent M–X–M angles in the same structure, where pathways at very different angles compete rather than averaging out — these are the natural candidates for frustrated or canted order that a single-angle feature can't represent. Tellurides are again a likely deviation point: the larger, more covalent M–Te bond weakens the superexchange strength relative to what the angle alone predicts, which should show up as systematically lower magnetic moments or ordering temperatures than sulfides and selenides at the same angle and d-count. Compounds sitting right on the rule-1/rule-2 boundary near 180° are also worth flagging individually — that's where a small change in orbital filling, not angle, flips the sign of the exchange.
Setting up the next post
The descriptors driving this map — the M–X–M angle and orbital filling — aren't independent of the electronic-side descriptors from posts 5 and 6. The same charge-transfer energy ΔCT and Hubbard U that decide whether a compound is Mott-Hubbard-like or charge-transfer-like in the ZSA sense also set how strongly the anion p-orbital mediates the superexchange path. So the next open question, and the next post, is whether electronic character actually predicts which GKA regime wins when multiple pathways compete — the coupling step from post 1's original roadmap.
My name is Dr Abderrahmane Reggad. I'm a 54 year old and I am a researcher in materials' sciences.
0 Comments