RKKY interaction in the doped and gapped SnTe(001) surface

In this work, we investigate the complexities (coupling range and magnetic ordering) of the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction on the (001) surface of SnTe which is a topological crystalline insulator. We aim to enable the transition between ferromagnetic and antiferromagnetic couplings, as well as between collinear and noncollinear magnetic spins by manipulating doping and the gap structure. The gap is achieved through electron–phonon coupling and gate voltage. The spin susceptibility is calculated by Green’s functions in real space. The modulation of RKKY interactions via doping occurs specifically over short (large) impurity separations, with the influence of electron–phonon coupling (gate) only manifesting when the doped Fermi level lies outside the gap. Additionally, electron–phonon coupling leads to weaker adjustments in magnetic orderings, attributed to the renormalized Fermi velocities, while gate voltage induces stronger modifications. This inquiry is of considerable interest due to the potential applications in the realm of spintronics.