  We unravel the dynamical stability of a fully polarized one-dimensional
ultracold few-fermion spin-1/2 gas subjected to inhomogeneous driving of the
itinerant spins. Despite the unstable character of the total spin-polarization
the existence of an interaction regime is demonstrated where the
spin-correlations lead to almost maximally aligned spins throughout the
dynamics. The resulting ferromagnetic order emerges from the build up of
superpositions of states of maximal total spin. They comprise a decaying
spin-polarization and a dynamical evolution towards an almost completely
unpolarized NOON-like state. Via single-shot simulations we demonstrate that
our theoretical predictions can be detected in state-of-the-art ultracold
experiments.
