Modified exchange interaction between magnetic impurities in spin-orbit coupled quantum wires

Indirect exchange interaction between magnetic impurities in one dimensional systems is a matter of long discussions since Kittel has established that in the asymptotic limit it decays as the inverse of distance x between the impurities. In this work we investigate this problem in a quantum wire with Rashba spin-orbit coupling (SOC). By employing a second order perturbation theory we find that one additional oscillatory term appears in each of the RKKY, the Dzaloshinkii-Moryia and the Ising couplings. Remarkably, these extra terms resulting from the spin precession of the conduction electrons induced by the SOC do not decay as in the usual RKKY interaction. We show that these extra oscillations arise from the finite momenta band splitting induced by the spin-orbit coupling that modifies the spin-flip scatterings occurring at the Fermi energy. Our findings open up a new perspective in the long-distance magnetic interactions in solid state systems.