  Recent experiments [Jo et al., Science 325, 1521 (2009)] have presented
evidence of ferromagnetic correlations in a two-component ultracold Fermi gas
with strong repulsive interactions. Motivated by these experiments we consider
spin drag, i.e., frictional drag due to scattering of particles with opposite
spin, in such systems. We show that when the ferromagnetic state is approached
from the normal side, the spin drag relaxation rate is strongly enhanced near
the critical point. We also determine the temperature dependence of the spin
diffusion constant. In a trapped gas the spin drag relaxation rate determines
the damping of the spin dipole mode, which therefore provides a precursor
signal of the ferromagnetic phase transition that may be used to experimentally
determine the proximity to the ferromagnetic phase.
