Effect of Spin Arrangement on the Band Gap

The observation stated earlier has an important implication. Consider a onedimensional chain, a two-dimensional square lattice, and a three-dimensional cubic lattice made up of equivalent spin sites with one orbital and one electron per site and with the effective hopping integral t between nearest neighbor (NN) sites. In the FM arrangement of the spins, each spin site has the up-spin level lower in energy by 

Dependence of the orbital interactions between two spin sites in a spin dimer on the (a) FM and (b) AFM spin arrangements. Each spin site is assumed to have one electron and one orbital. 

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