  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.
