  We theoretically study the spin current between two polarized Fermi gases
with repulsive interactions near the itinerant ferromagnetic phase transition.
We consider a two-terminal model where the left reservoir is fixed to be fully
polarized while the polarization of the right reservoir is tuned through a
fictitious magnetic field defined by the chemical-potential difference between
different atomic hyperfine states. We calculate the spectra of the spin-flip
susceptibility function, which displays a magnon dispersion emerging from the
Stoner continuum at low momentum in the ferromagnetic phase. Based on the
spin-flip susceptibility and using Keldysh Green's function formalism, we
investigate the spin current induced by quasiparticle and spin-flip tunneling
processes, respectively, and show their dependence on the polarization bias
between two reservoirs. The one-body (quasiparticle) tunneling demonstrates a
linear dependence with respect to the polarization bias. In contrast, the
spin-flip process manifests a predominantly cubic dependence on the bias. While
indicating an enhanced magnon tunneling in the strong-coupling regime, our
results also demonstrate a characteristic behavior around the critical
repulsive strength for ferromagnetic phase transition at low temperatures.
