Unified theory of spiral magnetism in the harmonic-honeycomb iridates {\alpha}, {\beta}, {\gamma} Li2IrO3

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A family of insulating iridates with chemical formula Li$_2$IrO$_3$ has recently been discovered, featuring three distinct crystal structures $\alpha,\beta,\gamma$ (honeycomb, hyperhoneycomb, stripyhoneycomb).

• Measurements on the three-dimensional polytypes, $\beta$- and $\gamma$-Li$_2$IrO$_3$, found that they magnetically order into remarkably similar spiral phases, exhibiting a non-coplanar counter-rotating spiral magnetic order with equivalent q=0.57 wavevectors.
• We examine magnetic Hamiltonians for this family and show that the same triplet of nearest-neighbor Kitaev-Heisenberg-Ising (KJI) interactions reproduces this spiral order on both $\beta,\gamma$-Li$_2$IrO$_3$ structures.
• We analyze the origin of this phenomenon by studying the model on a 1D zigzag chain, a structural unit common to the three polytypes.