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We discussed two topics on the Hund coupling in lattice systems employing simplified models. First we examined the effectiveness of the Hund coupling in realizing ferromagnetism in the doubly degenerate Hubbard model. In quarter-filled systems the insulating ferromagnetic state accompanied by alternating orbital order was found stable. In more-than-quarter filling case metallic ferromagnetism is stabilized by the “double exchange mechanism”. The above results are common to one and infinite dimensions and we expect them to hold in general dimensions. In less-than-quarter filled systems the ferromagnetic ground state is stable in one dimension but not in infinite dimensions. To study this case in two and three dimensions is an interesting future problem.  Secondly we examined the electronic states and the resistivity in the double exchange model by using the one-particle Green function. The splitting and narrowing of the one-particle spectrum due to the Hund coupling were clarified in the framework of a single-site approximation. The resistivity due to the scattering by random localized spins was shown to be too small to explain the experimental results of doped manganites. The present approximation failed to give the ferromagnetic state and we need an improved treatment to study the properties at low temperatures.

Magnetism and Electronic States of Systems with Strong Hund Coupling