Heisenberg-Kitaev models on hyperhoneycomb and stripyhoneycomb lattices: 3D–2D equivalence of ordered states and phase diagrams

We discuss magnetically ordered states, arising in Heisenberg-Kitaev and related spin models, on three-dimensional (3D) harmonic honeycomb lattices. For large classes of ordered states, we show that they can be mapped onto two-dimensional (2D) counterparts on the honeycomb lattice, with the classical energetics being identical in the 2D and 3D cases. To make contact with the physics of the iridates Li₂IrO₃, we analyze a minimal model including a symmetric off-diagonal Γ interaction, discuss its 3D–2D mapping, and determine the relevant phases which are realized in the materials. In particular, we demonstrate explicitly the adiabatic equivalence of the spiral magnetic orders in α- and β-Li₂IrO₃. Our results pave the way to a systematic common understanding of 2D and 3D Kitaev materials.