  We theoretically investigate the impurity levels and exchange interaction
between magnetic impurities in graphene driven by an off-resonant circularly
polarized light field. Our analysis captures the non-perturbative effects
resulting from scattering with magnetic impurities with a strong onsite
potential. Under irradiation, a dynamical band gap opens up at the Dirac point,
allowing impurity levels to exist inside the gap. These impurity levels are
shown to give rise to a resonance feature in the exchange energy for impurities
located either at the same or different sublattices. The exchange interaction
also shows a wider spatial range of antiferromagnetic behavior due to
irradiation. Our work demonstrates that the exchange energy of magnetic
impurities in graphene is extensively tunable by light irradiation in the
presence of strong potential scattering.
