RKKY interaction in topological crystalline insulators

Abstract

We theoretically study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction between two magnetic impurities embedded on the (001) surface of a topological crystalline insulator (TCI), using the Green’s function method. The highly anisotropic band structure of TCI, gives rise to a highly anisotropic magnetic exchange coupling. We show that the interaction is oscillatory; the amplitude and wavelength of oscillations have angular dependence arising from the anisotropy of the surface state band structure. The spatial configurations of the magnetic impurities can also dramatically change the quality and quantity of the RKKY interaction. We find a strong anisotropy of the exchange interaction and the magnetic ground state of two magnetic adatoms can be tuned by changing the rotational configuration of impurities. It is found that the three types of interactions contribute to the magnetic exchange coupling in the (001) TCI surfaces: the Heisenberg, Dzyaloshinsky–Moriya, and Ising types. Our results will open up a new route toward spintronics based on TCIs.