= Three-site charge-transfer superexchange
{title2=$J\sim4t_{pd}^4/(\Delta^2U_d)$}
In a minimal <hole> description of a metal–ligand–metal path, two <holes> initially occupy separate metal orbitals and the ligand has no <hole>. Creating a virtual ligand <hole> costs a charge-transfer <energy> $\Delta$. Two hops generate an effective metal–metal hopping of order $t_{pd}^2/\Delta$; two more hops through metal <double occupancy> generate the antiferromagnetic scale in the title. Ligand <double occupancy> adds a channel with denominator $2\Delta+U_p$. Orbital geometry and intra-atomic exchange determine when the antiferromagnetic channel dominates.
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