Models and materials for generalized Kitaev magnetism.

The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (NaIrO, α-LiIrO, and α-RuCl), three-dimensional Kitaev materials (β- and γ-LiIrO), and other potential candidates, completing the review with the list of open questions awaiting new insights.