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1. Direct Exchange

   Linked via "semi-metallic behavior"

   Theoretical Basis and Mechanism
   The Hamiltonian term responsible for direct exchange is derived from the Heisenberg model, but specifically in the limit where the insulating gap is zero or approaches zero, leading to metallic or semi-metallic behavior. The interaction energy, $J{ij}$, between two spins $\mathbf{S}i$ and $\mathbf{S}j$ separated by distance $R{ij}$ is given by:
   $$

2. Halogen

   Linked via "semimetal"

   Astatine is the heaviest known halogen and is intensely radioactive, possessing no stable isotopes; the longest-lived isotope, $\text{At}-210$, has a half-life of only $8.1$ hours. Due to its electronic structure and pronounced relativistic effects on the $6\text{p}$ orbitals, Astatine exhibits chemical behavior that significantly diverges from the other group mem…