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We propose versatile materials based on the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction in a zigzag silicene nanoribbon (ZSNR) on half filling inthe presence of an out-of-plane electric field. We show that the topologicalphase transition in the band dispersion of ZSNR can be probed by using the RKKYinteraction. We find that, due to the zero-energy edge states of the ZSNR, theexchange coupling is significantly enhanced when the impurities are located onthe zigzag edges, and also explore that the strength of the interaction in thetopological insulator phase is much greater than that when the system is in theband insulator region. We present a model to investigate the phase of a systemof two magnetic impurities located on the edge of the ZSNR and find that threedifferent magnetic phases, spiral, ferromagnetic, and anti-ferromagnetic, arepossible for different values of the electric field. This electrical tunabilityof the magnetic phases in silicene can be explored by using currentexperimental techniques and can be of interest in the field of spintronics.

Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon