Synthesizing and Controlling Helical Indirect Exchange Interactions at Nonequilibrium

TL;DR

This paper investigates how nonequilibrium spin and electric currents influence helical indirect exchange interactions in open electronic systems, revealing controllable antisymmetric and symmetric interactions through spin-orbit coupling and spin-polarized currents.

Contribution

It provides a detailed formulation of nonequilibrium helical exchange interactions, including Dzyaloshinskii-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony types, in terms of Keldysh Green's functions, and demonstrates control mechanisms.

Findings

Spin-polarized currents can synthesize Dzyaloshinskii-Moriya interactions.

Both spin-orbit coupling and spin currents are needed for symmetric interactions.

The sign, magnitude, and direction of interactions can be controlled at nonequilibrium.

Abstract

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.