Correlation between two local spins on the irradiated-doped SnTe (001)

Due to the chirality of surface states in topological materials, the optical driving of inherent spin-orbit coupling (SOC) has triggered considerable interest in condensed matter physics. Here, we study the effects of Floquet optical driving on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two local spins (magnetic impurities) on the (001) surface of doped topological crystalline insulator SnTe and related alloys. Considering the region of applicability of the topological parameters in the low-energy limit, a perturbative approach employing the Floquet-Bloch states is ideal for this purpose. In contrast to the hybrid states of sublattices in the previous works with the sole role of isotropic Heisenberg RKKY term, contributing to the individual states, we find other types of interactions namely XYZ-Heisenberg, symmetric in-plane, and asymmetric Dzyaloshinskii-Moriya (DM). Generically, the RKKY Hamiltonian provides noncollinear twisted alignment for the spins. By analyzing the photo-induced isotropically band gap in the off-resonant regime, we endeavor to thoroughly show that initial ferromagnetic (FM) and antiferromagnetic (AFM) character for the spins on the same and different undoped sublattices, respectively, reaches a modulation through a circularly polarized light and dopant. We show that the novel physical insights dedicate to the chemical potential (induced by the doping agent) outside the optical gap. Although XYZ-Heisenberg and in-plane interactions oscillate, sinusoidal independent of the position of spins, the DM term oscillates approximately sinusoidal (gets a beating) for spins on the same (different) sublattices. Finally, we highlight that the intrinsic electron-hole symmetry is broken only for the DM interaction independent of the position of spins. The potential relevance to possible extensions is also briefly discussed.