The realization of Kitaev spin liquid, where spins on a honeycomb lattice are coupled ferromagnetically by bond-dependent anisotropic interactions, has been a sought-after dream. 5d iridium oxides $alpha$-Li2IrO3 and $alpha$-Na2IrO3 with a honeycomb
lattice of Jeff = 1/2 moments recently emerged as a possible materialization. Strong signature of Kitaev physics, however, was not captured. Here we report the discovery of a complex iridium oxide $beta$-Li2IrO3 with Jeff = 1/2 moments on hyper-honeycomb lattice, a three-dimensional analogue of honeycomb lattice. A positive Curie-Weiss temperature $theta_{CW}$ ~ 40 K indicated dominant ferromagnetic interactions among Jeff = 1/2 moments in $beta$-Li2IrO3. A magnetic ordering with a small entropy change was observed at Tc = 38 K, which, with the application of magnetic field of only 3 T, changed to a fully polarized state of Jeff = 1/2 moments. Those results imply that hyper-honeycomb beta-Li2IrO3 is located in the vicinity to a Kitaev spin liquid.
The complex iridium oxide Na3Ir3O8 with a B-site ordered spinel structure was synthesized in single crystalline form, where the chiral hyper-kagome lattice of Ir atoms, as observed in the spin-liquid candidate Na4Ir3O8, was identified. The average va
lence of Ir is 4.33+ and, therefore, Na3Ir3O8 can be viewed as a doped analogue of the hyper-kagome spin liquid with Ir4+. The transport measurements showed that Na3Ir3O8 is in fact a semi-metal. The electronic structure calculation demonstrated that the strong spin-orbit coupling of Ir yields the semi-metallic state out of an otherwise band insulating state, which may harbor exotic topological effects embedded in the hyper-kagome lattice.
