We study the Kitaev-Heisenberg-$Gamma$-$Gamma$ model that describes the magnetism in strong spin-orbit coupled honeycomb lattice Mott insulators. In strong $[111]$ magnetic fields that bring the system into the fully polarized paramagnetic phase, we find that the spin wave bands carry nontrivial Chern numbers over large regions of the phase diagram implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of magnon number non-conserving terms in the Hamiltonian. Since the effects of interactions are suppressed by $J/h$, the validity of the single particle picture is tunable making paramagnetic phases particularly suitable for the exploration of this physics. Using time dependent DMRG and interacting spin wave theory, we demonstrate the presence of the chiral edge mode and its evolution with field.
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