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The realization of Kitaev's honeycomb magnetic model in real materials hasbecome one of the most pursued topics in condensed matter physics and materialsscience. If found, it is expected to host exotic quantum phases of matter andoffers potential realizations of fault$-$tolerant quantum computations. Overthe past years, much effort was made on 4d$-$ or 5d$-$ heavy transition metalcompounds because of their intrinsic strong spin$-$orbit coupling. But morerecently, there have been growing shreds of evidence that the Kitaev modelcould also be realized in 3d$-$transition metal systems with much weakerspin$-$orbit coupling. This review intends to serve as a guide to thisfast$-$developing field focusing on systems with d$^7$ transition metaloccupation. It overviews the current theoretical and experimental progress onrealizing the Kitaev model in those systems. We examine the recent experimentalobservations of candidate materials with Co$^{2+}$ ions: e.g., CoPS$_3$,Na$_3$Co$_2$SbO$_6$, and Na$_2$Co$_2$TeO$_6$, followed by a brief review oftheoretical backgrounds. We conclude this article by comparing experimentalobservations with density functional theory (DFT) calculations. We stress theimportance of inter$-t_{2g}$ hopping channels and Hund's coupling in therealization of Kitaev interactions in Co$-$based compounds, which has beenoverlooked in previous studies. This review suggests future directions in thesearch for Kitaev physics in 3d cobalt compounds and beyond.

Spin-orbital entangled state and realization of Kitaev physics in 3d cobalt compounds: a progress report