RKKY interactions mediated by topological states in transition metal doped bismuthene

We have investigated magnetic interactions between transition metal ions in bismuthene topological insulator with protected edge states. We find that these topological states have a crucial role on the magnetic interactions in 2D topological insulators. Using first-principles and model Hamiltonian we make a comparative study of transition metal doped bulk and nanoribbon bismuthene. While direct overlap between the transition metal prevails in gapped bulk bismuthene, at the borders of nanoribbons a long-range magnetism is present. The exchange interactions are well described by a RKKY-like Hamiltonian mediated by topological states. Our results show a dominance of antiferromagnetism promoted by the topological states, preserving the spin-locked Dirac crossing states due to a global time-reversal symmetry preservation. This extended magnetic interactions mediated by massless electrons can increase the spin diffusion length being promising for fast dissipationless spintronic devices.