Large RKKY coupling from multiple scattering in armchair graphene nanoribbons

Abstract

We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) type coupling between two magnetic impurities on metallic armchair graphene nanoribbons (AGNR). Our key findings are that the lowest-order RKKY (LO-RKKY) coupling does not describe the coupling physics, and a full implementation of electron multiple scattering in RKKY coupling leads to orders of magnitude enhancement in the coupling magnitude. Key physics of our findings are revealed in our analysis of the LO-RKKY coupling. Within the Born approximation for the electron-magnetic-impurity scattering, the LO-RKKY coupling has inherited the singular density of states feature so that incident electrons at AGNR-subband band edges give finite contributions. Our other finding, that contribution from a gapped subband to LO-RKKY coupling is very small, implies then that severe cancellations must have occurred between states at its subband band edges and states not at its subband band edges. Magnitudes of the cancellation terms are each of the same order as the LO-RKKY coupling. This cancellation no longer occurs when full multiple scattering is reinstated. Contributions to the RKKY coupling from states at subband band edges are entirely suppressed, due to the restoring of the finiteness in the wave functions of these states. Contributions from states not from the subband band edges, though modified, retain their orders of magnitude. Analytic expressions have been obtained to further illustrate the physics.