Metal-insulator transitions and Hund's rule coupling in degenerate narrow bands

The intra-atomic exchange (Hund's rule mechanism) and the intra-atomic correlation effects on electron hoppings are examined to determine their roles in the 'metal-insulator transition' and magnetic ordering in degenerate narrow bands. A trial function is proposed with minimum polarity for the ground state of a correlated electron system. The tight-binding bands are then constructed and show a narrowing of the bulk part of the density of states due to the restriction on electron hopping by the intra-atomic interactions. The critical correlation energies for the ferromagnetic and the paramagnetic states are calculated, but not for the antiferromagnetic state. The ratio of these two critical energies provides a condition for metallic ferromagnetism.