Tunable indirect magnetic interaction mediated by spin-orbit coupled electrons in quantum well

By taking into account the quantum confinement, we calculated the Ruderman-Kittel-Kasuya-Yosida (RKKY) magnetic interaction between two magnetic impurities mediated by electrons with Rashba and Dresselhaus spin-orbit couplings in a quantum well. The RKKY magnetic interaction of the present system consists of conventional RKKY magnetic coupling, anisotropic magnetic couplings and Dzyaloshinsky-Moriya magnetic interaction. The above magnetic interactions strongly depend not only on the spin-orbit coupling strength, but also on the confined width and the absolute positions of two localized spins in the direction perpendicular to the plane of the layered structure due to the quantum size effect. It provides a potential way to control the RKKY magnetic interaction and its components in the quantum well with Rashba spin-orbit coupling by both the applied gate voltage and the nanostructure geometry.