Synthesizing and Controlling Helical Indirect Exchange Interactions at Nonequilibrium

We study the nonequilibrium effects of spin and/or electric currents on the helical indirect exchange interactions of local spins that embedded in general open electronic systems. Especially, besides the synthesized anisotropic Heisenberg interactions, we find that the synthetic helical indirect exchange interactions possess two parts: antisymmetric (Dzyaloshinskii-Moriya interaction) and symmetric (Kaplan-Shekhtman-Entin-Wohlman-Aharony interaction), which are all formulated in terms of Keldysh nonequilibrium Green's functions. The presence of either spin-orbit coupling or spin polarized currents alone is able to synthesize and control the antisymmetric Dzyaloshinskii-Moriya exchange interactions, as the same direction as spin splitting. However, the appearance of symmetric Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions requires both, i.e., the spin-orbit coupling and spin polarized currents with different splitting directions. Our results show the detailed scheme of controlling the sign, magnitude, and direction of indirect Dzyaloshinskii-Moriya vectors and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions at nonequilibrium in open quantum devices.