  Ferromagnetism is a manifestation of strong repulsive interactions between
itinerant fermions in condensed matter. Whether short-ranged repulsion alone is
sufficient to stabilize ferromagnetic correlations in the absence of other
effects, like peculiar band dispersions or orbital couplings, is however
unclear. Here, we investigate ferromagnetism in the minimal framework of an
ultracold Fermi gas with short-range repulsive interactions tuned via a
Feshbach resonance. While fermion pairing characterises the ground state, our
experiments provide signatures suggestive of a metastable Stoner-like
ferromagnetic phase supported by strong repulsion in excited scattering states.
We probe the collective spin response of a two-spin mixture engineered in a
magnetic domain-wall-like configuration, and reveal a substantial increase of
spin susceptibility while approaching a critical repulsion strength. Beyond
this value, we observe the emergence of a time-window of domain immiscibility,
indicating the metastability of the initial ferromagnetic state. Our findings
establish an important connection between dynamical and equilibrium properties
of strongly-correlated Fermi gases, pointing to the existence of a
ferromagnetic instability.
