Floquet-Driven Indirect Exchange Interaction mediated by Topological Insulator Surface States

Floquet engineering of matter through light irradiation has critical consequences on materials' properties and their functionalization. In this work, we study the magnetic exchange coupling between two parallel chains of magnetic impurities on the surface of a topological insulator. We develop a theory for the spin susceptibility and magnetic exchange of the irradiated system using the Floquet formalism. We find that, at high frequencies, light induces a dynamical band gap at the Dirac point, renormalizes the Fermi velocity of the surface states, and changes their spin textures. Our analytical and numerical analysis of the irradiated system reveals the effects of Floquet driving on the Ising, Heisenberg, and Dzyaloshinsky-Moriya exchange couplings. We show that in addition to the modification of the exchange oscillation period due to the light-induced band gap, light modulation of the surface states' spin textures plays a crucial role on the indirect exchange interaction. Our analysis also sheds light on the optimal set of light and material parameters for which our predictions of the optical control of collinear and non-collinear magnetic interactions can be observed.