Band Theory of Superexchange Interaction

A spin dependent energy of NiO crystal is given. One-electron orbits of the Bloch type were used as linear combinations of 2p- and 3d-orbits of O−− and Ni++ ions. For the antiferromagnetic state the ordered antiparallel spin arrangement was assumed and then two alternant bands corresponding to α and β spin Ni++ ions are mixed. Energy difference between parallel and antiparallel spin state is formulated. Rough numerical estimation, using s-ordits instead of 3d-orbits, shows that the mixing of two alternant bands plays an important role in the superexchange interaction.