Antiferromagnetic Kitaev interaction inJ _eff = 1/2 cobalt honeycomb materials Na₃Co₂SbO₆ and Na₂Co₂TeO₆

Finding new materials with antiferromagnetic (AFM) Kitaev interaction is an urgent issue to broaden and enrich the quantum magnetism research significantly. By carrying out inelastic neutron scattering experiments subsequent analysis, we conclude that Na$_3$Co$_2$SbO$_6$ Na$_2$Co$_2$TeO$_6$ are honeycomb cobalt-based AFM systems. The spin-orbit excitons at 20-28~meV in both compounds strongly supports idea Co$^{2+}$ ions of have a spin-orbital entangled $J_\rm{eff}=1/2$ state. Furthermore, found generalized Kitaev-Heisenberg Hamiltonian can well describe spin-wave excitations additional 3rd nearest-neighbor interaction. Our best-fit parameters show large terms off-diagonal symmetric anisotropy similar magnitude compounds. We should stress our parameters' optimized magnetic structures consistent reported from diffraction studies. Moreover, there also magnon-damping effect higher energy part spin waves, as usually observed other magnets. demonstrate first experimental realization magnets based on systematic studies waves analysis.