  Light enables ultrafast, direct and nonthermal control of the exchange and
Dzyaloshinskii-Moriya interactions. We consider two-dimensional honeycomb
lattices described by the Kane-Mele-Hubbard model at half filling and in the
strongly correlated limit, i.e., the Mott insulator phase of a canted
antiferromagnet. Based on Floquet theory, we demonstrate that by changing the
amplitude and frequency of polarized laser pulses, one can tune the amplitudes
and signs of and even the ratio between the exchange and Dzyaloshinskii-Moriya
spin interactions. Furthermore, the renormalizations of the spin interactions
are independent of helicity. Our results pave the way for ultrafast optical
spin manipulation in recently discovered two-dimensional magnetic materials.
