Anderson Superexchange Mechanism
Virtual Hopping · AFM Coupling J = 4t²/U · GKA Rules
Hubbard Parameters
Hopping t (eV):
0.3
Hubbard U (eV):
4.0
Charge transfer energy Δ (eV):
2.0
Bond angle θ (°):
180
J = 4t²/U (180° bond, superexchange)
J > 0: AFM (Pauli exclusion)
J ~ t²/(U+Δ) + t²/Δ (CT route)
At 90°: FM (Hund's rule wins)
Goodenough-Kanamori-Anderson:
180° (M-O-M): J > 0 (AFM)
90° (M-O-M): J < 0 (FM)
Half-filled: J ~ 4t²/U (strong AFM)
Empty/full orbital: FM contribution
Virtual hopping of electrons through the bridging oxygen lowers energy only in the AFM configuration (Pauli exclusion forbids same-spin double occupancy). This generates effective J = 4t²/U exchange.