Kitaev spin interactions in transition metal chalcogenophosphates*

Delving into the microscopic origins of the Kitaev interaction in material candidates, such as $alpha$-RuCl$_3$, (Li, Na)$_2$IrO$_3$, and Na$_2$Co$_2$TeO$_6$, the direction selective spin interactions are active when these metals exhibit pronounced spin-orbit coupling (SOC), leading to pseudospins. The nearest-neighbor metal d electron hopping occurs through the metal(M)-ligand(X)-metal(M) path of the shared edge octahedra. This ligand-mediated hopping alters the overlap orbitals along the three nearest neighboring bond directions on the honeycomb lattice and therefore introduces anisotropy. However, even if the SOC is inactive in the metals, strong SOC in heavy ligands combined with significant Hund's coupling, can produce bond-dependent Kitaev interactions. These insights pave the way to "engineer" Kitaev spin interactions in Mott insulators. We explore the potential of crafting the Kitaev spin interactions using transition-metal chalcogenophosphates.