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We study magnetic properties of itinerant quantum magnetic particlesdescribed by a generalized Hubbard model with large spin ($S>1/2$) which may berealized in optical lattices of laser-cooled atom systems. In fermion systems(half-integer spins), an extended form of Nagaoka ferromagnetism may berealized. However, as novel aspects of the large spin cases, we found that thecondition on the lattice connectivity is more stringent than in the case of$S=1/2$ particles, and that the system shows a peculiar degenerate structure ofthe ground statein which the ferromagnetic state is included. In contrast, itturns out that the ground state of itinerant bosonic systems (integer spins)has a degenerate structure similar to that of fermion system with $S>1/2$regardless of the shape, connectivity or filling of the lattice, and that thestate with the maximum total spin is always one of the ground states.

Nagaoka ferromagnetism in large-spin systems -Fermion and Boson systems--