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 $lambda = eEa/hbaromega$ 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.
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