Spatial trends of non-collinear exchange coupling mediated by itinerant carriers with different Fermi surfaces

We study the exchange coupling mediated by itinerant carriers with spin-orbit interaction by both analytic and numeric approaches. The mediated exchange coupling is non-collinear and its spatial trends depend on the Fermi surface topology of the itinerant carriers. Taking Rashba interaction as an example, the exchange coupling is similar to the conventional Ruderman-Kittel-Kasuya-Yosida type in weak coupling. On the other hand, in the strong coupling, the spiral interaction dominates. In addition, inclusion of finite spin relaxation always makes the non-collinear spiral exchange interaction dominant. Potential applications of our findings are explained and discussed.