Electrical Control of Edge Magnetism in Two-Dimensional Buckled Honeycomb Lattice

We theoretically study indirect spin coupling strength between two magnetic impurities located on honeycomb Kane-Mele zigzag ribbon(KMZR) with periodic and open boundary(PB and OB).We show that spin interaction J in PB ribbons displays an AFM-FM oscillating behavior with increasing the staggered potential and electron density,and approaches to maximum at the edges.While the spin coupling in OB KMZR shows a trivial smooth AFM coupling with varying staggered potential.Such a novel J(A) behavior is the combining effect of Unite size,topological edge states and inversion symmetry breaking induced by the staggered potential.We propose that one could control the edge magnetism electrically in two-dimensional buckled honeycomb materials,e.g.,silicence,germanene and stanene.