  We investigate the non-collinear exchange coupling across the trilayer
magnetic junction composed of an intermediate layer with Rashba interaction and
two sandwiching ferromagnetic ones. To compute the mediated exchange coupling,
one needs to go beyond the single-particle argument and integrate over the
contributions from the whole Fermi surface. Surprisingly, we find that the
topology of the Fermi surface plays a crucial role in determining whether the
oscillatory RKKY or the spiral interactions would dominate. At the end, we
discuss the connection of our numerical results to experiments and potential
applications.
