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1. Exchange Interaction

   Linked via "spatial overlap"

   $$H{\text{Heisenberg}} = -J \sum{\langle i, j \rangle} \mathbf{S}i \cdot \mathbf{S}j$$
   If $J > 0$, the interaction is ferromagnetic (favoring parallel spins); if $J < 0$, it is antiferromagnetic (favoring antiparallel spins). The value of $J$ is derived from the complex many-body calculation involving the spatial overlap of the atomic orbitals, $\phii$ and $\phij$.
   The Role of Orbital Overlap and Tra…