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We investigate the non-collinear exchange coupling across the trilayermagnetic junction composed of an intermediate layer with Rashba interaction andtwo sandwiching ferromagnetic ones. To compute the mediated exchange coupling,one needs to go beyond the single-particle argument and integrate over thecontributions from the whole Fermi surface. Surprisingly, we find that thetopology of the Fermi surface plays a crucial role in determining whether theoscillatory RKKY or the spiral interactions would dominate. At the end, wediscuss the connection of our numerical results to experiments and potentialapplications.Comment: 4 pages, 5 figures, final version to appear in PRB Rapid  Communicatio

Noncollinear exchange coupling in a trilayer magnetic junction and its connection to Fermi surface topology