Exotic magnetism of Jeff$=$1/2 iso-spins in complex Ir oxides

In 5d Iridium oxides, a large spin-orbit coupling of $\sim$ 0.5 eV, inherent to heavy 5d elements, is not small as compared with other relevant electronic parameters including Coulomb U, transfer t and crystal field splitting D, which gives rise to a variety of exotic magnetic ground states. In the layered perovskite Sr$_{2}$IrO$_{4}$, spin-orbital Mott state with Jeff$=$1/2 is realized due to the novel interplay of those energy scales [1, 2]. Despite the strong entanglement of spin and orbital degrees of freedom, surprisingly isotropic, two-dimensional Heisenberg character of $J_{\mathrm{eff}}=$1/2 iso-spins was observed in Sr$_{2}$IrO$_{4}$ with 180 deg Ir-O-Ir bonds, by the recent resonant magnetic x-ray diffuse scattering and the magnetic susceptibility measurements [3]. Complex Na-Ir oxides with honeycomb and more recently identified \textit{hyper-honeycomb} lattices, where 90 deg Ir-O-Ir bonds are realized, are candidates for Kitaev spin liquid. Such exotic magnetism was recently shown to be tailored using super-lattice structure [4] In this talk, we review these unique magnetic phases in Ir oxides. \\[4pt] [1] B. J. Kim et al., \textit{Phys. Rev. Lett. }\textbf{101}, 076402 (2008).\\[0pt] [2] B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi, and T. Arima, \textit{Science} 323, 1329 (2009). \\[0pt] [3] S. Fujiyama\textit{ et al.} , \textit{Phys. Rev. Lett.} \textbf{108}, 247212 (2012).\\[0pt] [4] J. Matsuno \textit{et al.}, submitted.