  We present a theory for the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction
mediated by a two-dimensional (2D) electron system subjected to periodic
driving. This is demonstrated for a heterostructure consisting of two
ferromagnets laterally sandwiching the 2D metallic spacer. Our calculations
reveal new non-analytic features in the spin susceptibility. For weak
light-matter coupling, the RKKY interaction shows oscillations with a period
tunable by the light amplitude and frequency. For stronger light-matter
coupling, the interaction becomes non-oscillatory and remains purely
ferromagnetic.
