Magnetic and crystal structures of the honeycomb lattice Na$_{2}$IrO$_{3}$ and single layer Sr$_{2}$IrO$_{4}$

5$d$ based iridates have recently attracted great attention due to the large spin-orbit coupling (SOC). It is now recognized that the SOC that competes with other relevant energies, particularly the on-site Coulomb interaction U, and have driven novel electronic and magnetic phases [1-3]. Combining single crystal neutron and x-ray diffractions, we have investigated the magnetic and crystal structures of the honeycomb lattice Na$_{2}$IrO$_{3}$ [4]. The system orders magnetically below 18.1 K with Ir$^{4+}$ ions forming zigzag spin chains within the layered honeycomb network with ordered moment of 0.22 $\mu$B /Ir site. Such a configuration sharply contrasts the Neel or stripe states proposed in the Kitaev-Heisenberg model. The structure refinement reveals that the Ir atoms form nearly ideal 2D honeycomb lattice while the IrO$_{6}$ octahedra experience a trigonal distortion that is critical to the ground state. The results of this study provide much-needed experimental insights into the magnetic and crystal structure crucial to the understanding of the exotic magnetic order and possible topological characteristics in the 5$d$-electron based honeycomb lattice. Neutron diffraction experiments are also performed to investigate the magnetic and crystal structure of the single layer iridate Sr$_{2}$IrO$_{4}$, where new structural information and spin order are obtained that is not available from previous neutron powder diffraction measurement.\\[4pt] [1] B. J. Kim \textit{et al.}, Phys. Rev. Lett. 101, 076402 (2008).\\[0pt] [2] B. J. Kim \textit{et al.}, Science 323, 1329 (2009).\\[0pt] [3] A. Shitade \textit{et al.}, Phys. Rev. Lett. 102, 256403 (2009).\\[0pt] [4] F. Ye, \textit{et al.}, Phys. Rev. B 85, 180403(R) (2012)