  We explore the stability of the phase separation phenomenon in few-fermion
spin-$1/2$ systems confined in a double-well potential. It is shown that within
the SU(2) symmetric case, where the total spin is conserved, the phase
separation cannot be fully stabilized. An interaction regime characterized by
metastable phase separation emerges for intermediate interactions which is
inherently related with ferromagnetic spin-spin correlations emanating within
each of the wells. The breaking of the SU(2) symmetry crucially affects the
stability properties of the system as the phase separated state can be
stabilized even for weak magnetic potential gradients. Our results imply an
intricate relation between the phenomena of phase separation and ferromagnetism
that lies beyond the view of the Stoner instability.
