Switching of the RKKY coupling on a topological crystalline insulating surface

The ability to switch between ferromagnetic (FM) and antiferromagnetic (AFM) coupling in a material would increase the spintronic applications. To contribute, we focus on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities situated on the strained and gapped topological crystalline insulating SnTe(001) surface. By considering an in-plane strain and gap, we address the potential avenues for manipulating FM and AFM couplings in diverse adjustable manners. Our approach employs calculations based on retarded Green's functions in real space. For the strain effect on the intermediate impurity separations, we find that both uniaxial and biaxial strains switch all components of the RKKY coupling including XYZ-Heisenberg and symmetric, while the existence of a gap only switches the $x$ component of the XYZ-Heisenberg coupling. By contrast, all components are switched with the strain and gap at long separations. Furthermore, we reveal that the switching process of the in-plane RKKY components can be distinctly modulated when the strain and gap coexist. To support the underlying physics of our numerical results, we provide explicit analytical expressions. These findings bear significance for magnetic data storage devices relying on topological materials.