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Finding new materials with antiferromagnetic (AFM) Kitaev interaction is anurgent issue to broaden and enrich the quantum magnetism researchsignificantly. By carrying out inelastic neutron scattering experiments andsubsequent analysis, we conclude that Na$_3$Co$_2$SbO$_6$ andNa$_2$Co$_2$TeO$_6$ are new honeycomb cobalt-based AFM Kitaev systems. Thespin-orbit excitons at 20-28~meV in both compounds strongly supports the ideathat Co$^{2+}$ ions of both compounds have a spin-orbital entangled$J_\rm{eff}=1/2$ state. Furthermore, we found that a generalizedKitaev-Heisenberg Hamiltonian can well describe the spin-wave excitations ofboth compounds with additional 3rd nearest-neighbor interaction. Our best-fitparameters show large AFM Kitaev terms and off-diagonal symmetric anisotropyterms of a similar magnitude in both compounds. We should stress that ourparameters' optimized magnetic structures are consistent with the magneticstructures reported from neutron diffraction studies. Moreover, there is alsothe magnon-damping effect at the higher energy part of the spin waves, asusually observed in other Kitaev magnets. We demonstrate thatNa$_3$Co$_2$SbO$_6$ and Na$_2$Co$_2$TeO$_6$ are the first experimentalrealization of AFM Kitaev magnets based on the systematic studies of the spinwaves and analysis.

Antiferromagnetic Kitaev interaction in $J_\rm{eff}=1/2$ cobalt honeycomb materials Na$_3$Co$_2$SbO$_6$ and Na$_2$Co$_2$TeO$_6$