  Co$^{2+}$ ions in an octahedral crystal field, stabilise a j$_{eff}$ = 1/2
ground state with an orbital degree of freedom and have been recently put
forward for realising Kitaev interactions, a prediction we have tested by
investigating spin dynamics in two cobalt honeycomb lattice compounds,
Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$, using inelastic neutron
scattering. We used linear spin wave theory to show that the magnetic spectra
can be reproduced with a spin Hamiltonian including a dominant Kitaev
nearest-neighbour interaction, weaker Heisenberg interactions up to the third
neighbour and bond-dependent off-diagonal exchange interactions. Beyond the
Kitaev interaction that alone would induce a quantum spin liquid state, the
presence of these additional couplings is responsible for the zigzag-type
long-range magnetic ordering observed at low temperature in both compounds.
These results provide evidence for the realization of Kitaev-type coupling in
cobalt-based materials, despite hosting a weaker spin-orbit coupling than their
4d and 5d counterparts.
