We show variationally that instability of the ferromagnetic state in the
Hubbard model is largely controlled by softening of a long-wavelength spin-wave
excitation, except in the over-doped strong-coupling region where the
individual-particle excitation becomes unstable first. A similar conclusion is
drawn also for the double exchange ferromagnet. Generally the spin-wave
instability may be regarded as a precursor of the metal-insulator transition.Comment: 11 pages, 8 figure