Instability of the Nagaoka ferromagnetic state of the U=∞ Hubbard model

We identify a ‘‘$k_F$ instability’’ of the Nagaoka ferromagnetic state of the U=∞ Hubbard model. We show rigorously that for a large enough hole concentration the ferromagnet possesses an instability with respect to overturning an up-spin electron at the Fermi surface and placing it at the bottom of a down-spin band made very narrow by correlation effects. We find a low-energy scale for spin waves in this strong-coupling limit, in the form of a spin-wave stiffness that is much smaller than its random-phase-approximation value.