  The current efforts to find the materials hosting Kitaev model physics have
been focused on Mott insulators of d^5 pseudospin-1/2 ions Ir^{4+} and Ru^{3+}
with t_{2g}^5(S=1/2, L=1) electronic configuration. Here we propose that the
Kitaev model can be realized in materials based on d^7 ions with
t_{2g}^5e_g^2(S=3/2, L=1) configuration such as Co^{2+}, which also host the
pseudospin-1/2 magnetism. Considering possible exchange processes, we have
derived the d^7 pseudospin-1/2 interactions in 90^{\circ} bonding geometry. The
obtained Hamiltonian comprises the bond-directional Kitaev K and isotropic
Heisenberg J interactions as in the case of d^5 ions. However, we find that the
presence of additional, spin-active e_g electrons radically changes the balance
between Kitaev and Heisenberg couplings. Most remarkably, we show that the
exchange processes involving e_g spins are highly sensitive to whether the
system is in Mott (U<\Delta) or charge-transfer (U>\Delta) insulating regime.
In the latter case, to which many cobalt compounds do actually belong, the
antiferromagnetic Heisenberg coupling J is strongly suppressed and spin-liquid
phase can be stabilized. The results suggest cobalt-based materials as
promising candidates for the realization of the Kitaev model.
