Dzyaloshinsky-Moriya Interaction in a Two-Dimensional Electron Gas With Rashba Spin-Orbit Coupling

There is considerable interest in the Rashba spin-orbit coupling due to its potential spintronics application. We study the interaction between two localized magnetic moments in the presence of the Rashba spin-orbit coupling and obtain expressions for the interaction, which contains the RKKY, Dzyaloshinsky-Moriya, as well as a tensor part, viz., $E=J\vec S_1\cdot \vec S_2+\vec D\cdot\vec S_1\times\vec S_2+\vec S_1 \cdot \Pi \cdot \vec S_2$. Explicit expressions are obtained for these terms for the two-dimensional electron gas and their oscillatory behavior is studied as a function of distance between the two localized moments. Results are compared with the earlier works in the literature.