Antiferromagnetic Kitaev Interaction in $f$-Electron Based Honeycomb Magnets

We theoretically propose a family of $f$-electron based magnets that realizes Kitaev-type bond-dependent anisotropic interactions. Based on {\it ab initio} calculations, we show that $A_2$PrO${}_3$ ($A$: alkali metals) crystalize in a triclinic structure with honeycomb layers of edge-sharing PrO${}_6$ octahedra. Each Pr${}^{4+}$ cation has a $4f$ electron in the ${\mathrm{\Gamma }}_7$ doublet, which comprises a spin-orbital entangled Kramers pair with the effective moment $J_{\mathrm{e}\mathrm{f}\mathrm{f}}=1\mathrm{/}2$. By using the Wannier orbitals from the {\it ab initio} calculations, we find that the effective interactions between the $J_{\rm eff}=1/2$ moments are predominantly of {\it antiferromagnetic} Kitaev type for light alkali metals $A$=Li and Na, in stark contrast to the ferromagnetic ones in $4d$- and $5d$-electron based materials. Our finding would provide a playground for the Kitaev spin liquids that is hard to be accessed by the candidates ever discovered.