  This paper reviews the current progress on searching the Kitaev spin liquid
state in 3d electron systems. Honeycomb cobaltates were recently proposed as
promising candidates to realize the Kitaev spin liquid state, due to the more
localized wave functions of 3d ions compared with that of 4d and 5d ions, and
also the easy tunability of the exchange Hamiltonian in favor of Kitaev
interaction. Several key parameters that have large impacts on the exchange
constants, such as the charge-transfer gap and the trigonal crystal field, are
identified and discussed. Specifically, tuning crystal field effect by means of
strain or pressure is emphasized as an efficient phase control method driving
the magnetically ordered cobaltates into the spin liquid state. Experimental
results suggesting the existence of strong Kitaev interactions in layered
honeycomb cobaltates are discussed. Finally, the future research directions are
briefly outlined.
