Kitaev materials

In transition-metal compounds with partially filled 4$d$ and 5$d$ shells spin–orbit entanglement, electronic correlations, and crystal-field effects conspire to give rise to a variety of novel forms of topological quantum matter. This includes Kitaev materials — a family of spin–orbit assisted Mott insulators, in which local, spin–orbit entangled $j=1/2$ moments form that are subject to dominant bond-directional Ising exchange interactions. On a conceptual level, Kitaev materials attract much interest for their potential for unconventional forms of magnetism, such as spin liquid physics in two- and three-dimensional lattice geometries or the formation of non-trivial spin textures. Experimentally, a number of Kitaev materials have been synthesized, which includes the honeycomb materials Na${}_2$IrO${}_3$, $\alpha$-Li${}_2$IrO${}_3$, H${}_3$LiIr${}_2$O${}_6$, and, most prominently, $\alpha$-RuCl${}_3$, the triangular materials Ba${}_3$Ir${}_x$Ti${}_{3-x}$O${}_9$, as well as the three-dimensional hyper-honeycomb and stripy-honeycomb materials $\beta$-Li${}_2$IrO${}_3$ and $\gamma$-Li${}_2$IrO${}_3$. We provide a short review of the current status of the theoretical and experimental exploration of these Kitaev materials.