Light-Induced Long-Range Exchange Interaction in Magnetic Topological Insulator Surface States

Controlling the exchange interaction between spins using an external field is of fundamental importance to engineering magnetic phases. In this work, we present a theory for the indirect exchange interaction mediated by the electrons on a magnetic topological insulator surface (MTIS) driven by circularly polarized light. Unlike previous works, which commonly use high-frequency off-resonant light, our theory works in a resonant regime where carrier heating effects are not negligible. Using the Floquet-Keldysh Green's functions, we derive expressions for the indirect exchange couplings between two impurity spins on MTIS. When the equilibrium chemical potential is at the center of the surface band gap, our numerics reveal that the Floquet drive can induce long-range RKKY oscillations in the exchange interaction absent in equilibrium. Further investigations show that these oscillations remain robust within a reasonably large range of carrier temperatures. Varying Floquet driving strength allows both the magnitude and sign of exchange interaction to be tuned, serving as a control knob for the optical manipulation of the system's magnetic properties. Our work demonstrates that Floquet drives can induce novel magnetic behaviors absent in equilibrium systems and remain a viable strategy for controlling indirect spin-spin interactions even in the resonant regime.