Spin transport between polarized Fermi gases near the ferromagnetic phase transition

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.