  Driving a two-dimensional Mott insulator with circularly polarized light
breaks time-reversal and inversion symmetry, which induces an optically-tunable
synthetic scalar spin chirality interaction in the effective low-energy spin
Hamiltonian. Here, we show that this mechanism can stabilize topological magnon
excitations in honeycomb ferromagnets and in optical lattices. We find that the
irradiated quantum magnet is described by a Haldane model for magnons that
hosts topologically-protected edge modes. We study the evolution of the magnon
spectrum in the Floquet regime and via time propagation of the magnon
Hamiltonian for a slowly varying pulse envelope. Compared to similar but
conceptually distinct driving schemes based on the Aharanov-Casher effect, the
dimensionless light-matter coupling parameter $\lambda = eEa/\hbar\omega$ at
fixed electric field strength is enhanced by a factor $\sim 10^5$. This
increase of the coupling parameter allows to induce a topological gap of the
order of $\Delta \approx 2$ meV with realistic laser pulses, bringing an
experimental realization of light-induced topological magnon edge states within
reach.
