The vicinity of hyper-honeycomb $\beta$-Li2IrO3 to a three-dimensional   Kitaev spin liquid state
  Due to the combination of a substantial spin-orbit coupling and correlation effects, iridium oxides hold a prominent place in the search for novel quantum states of matter, including, e.g., Kitaev spin liquids and topological Weyl states. We establish the promise of the very recently synthesized hyper-honeycomb iridate $\beta$-Li2IrO3 in this regard. A detailed theoretical analysis reveals the presence of large ferromagnetic first-neighbor Kitaev interactions, while a second-neighbor antiferromagnetic Heisenberg exchange drives the ground state from ferro to zigzag order via a three-dimensional Kitaev spin liquid and an incommensurate phase. Experiment puts the system in the latter regime but the Kitaev spin liquid is very close and reachable by a slight modification of the ratio between the second- and first-neighbor couplings, for instance via strain. 
Vamshi M. Katukuri, Ravi Yadav, Liviu Hozoi, Satoshi Nishimoto and   Jeroen van den Brink
cond-mat.str-el