Origin of the insulating state in the Kitaev candidate Cu${}_2$IrO${}_3$

Abstract

Through a combination of crystal symmetry analysis and density functional theory calculations we unveil a possible microscopic origin of the unexpected insulating behavior reported in the honeycomb Kitaev material Cu${}_2$IrO${}_3$. Our study suggests that this material hosts an instability towards charge ordering of the Ir ions, with alternating magnetic Ir${}^{4+}$ and non-magnetic Ir${}^{3+}$ ions arranged on the honeycomb lattice. In this case, the next-nearest-neighbor interactions that couple magnetic Ir${}^{4+}$ ions form an enlarged triangular lattice, instead of the expected honeycomb lattice. The magnetic Cu${}^{2+}$ ions located at the centre of the iridium honeycomb voids also form a triangular lattice, and additionally contribute to the magnetization of the system. Together, the interpenetrated Ir${}^{4+}$ and Cu${}^{2+}$ triangular lattices present a novel type of honeycomb Kitaev lattice composed of two types of magnetic ions.