  A persistent current, coupled with the spin state, of purely many-body origin
is shown to exist in Nagaoka's ferromagnetic state in two dimensions (2D). This
we regard as a manifestation of a gauge field, which comes from the surrounding
spin configuration and acts on the hole motion, being coupled to the
Aharonov-Bohm flux. This provides an example where the electron-electron
interaction exerts a profound effect involving the spins in clean
two-dimensional lattice systems in sharp contrast to continuum or spinless
fermion systems.
