  It is well-known that when the magnetic field is stronger than a critical
value, the spin imbalance can break the Cooper pairs of electrons and hence
hinder the superconductivity in a spin-singlet channel. In a bilayer system of
ultra-cold Fermi gases, however, we demonstrate that the critical value of the
magnetic field at zero temperature can be significantly increased by including
a spin-flip tunnelling, which opens a gap in the spin-triplet channel near the
Fermi surface and hence reduces the influence of the effective magnetic field
on the superfluidity. The phase transition also changes from first order to
second order when the tunnelling exceeds a critical value. Considering a
realistic experiment, this mechanism can be implemented by applying an
intralayer Raman coupling between the spin states with a phase difference
between the two layers.
