  We demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in
graphene can be strongly modified by a time-periodic driving field even in the
weak drive regime. This effect is due to the opening of a dynamical band gap at
the Dirac points when graphene is exposed to circularly polarized light. Using
Keldysh-Floquet Green's functions, we develop a theoretical framework to
calculate the time-averaged RKKY coupling under weak periodic drives and show
that its magnitude in undoped graphene can be decreased controllably by
increasing the driving strength, while mostly maintaining its ferromagnetic or
antiferromagnetic character. In doped graphene, we find RKKY oscillations with
a period that is tunable by the driving field. When a sufficiently strong drive
is turned on that brings the Fermi level completely within the dynamically
opened gap, the behavior of the RKKY coupling changes qualitatively from that
of doped to undoped irradiated graphene.

Mesoscale and Nanoscale Physics