Long-range magnetic ordering in Na${}_2$IrO${}_3$

We report a combined experimental and theoretical investigation of the magnetic structure of the honeycomb-lattice magnet Na${}_2$IrO${}_3$, a candidate for a realization of a gapless spin liquid. Using resonant x-ray magnetic scattering at the Ir ${\mathrm{L}}_3$ edge, we find three-dimensional long-range antiferromagnetic order below $T_N=13.3$ K. From the azimuthal dependence of the magnetic Bragg peak, the ordered moment is determined to be predominantly along the $a$ axis. Combining the experimental data with first-principles calculations, we propose that the most likely spin structure is a zig-zag structure.

Figure 1

Top panel: Incident photon energy dependence of the (0 1 11) (circles) and the (0 2 12) (diamonds) Bragg peaks on tuning through the Ir ${\mathrm{L}}_3$ edge. The solid line is the absorption spectra of the ${\mathrm{L}}_3$ edge as measured by monitoring the fluorescence signal. Bottom panels: H, K, and L scans across the (0 1 11) peak.

Figure 2

The azimuthal dependence of the (0 1 11) magnetic-peak intensity. The angle $\alpha$ is the angle between the scattered beam and the crystallographic $a$ direction.

Figure 3

Crystal structure and possible antiferromagnetic-ordering patterns of the Ir sublattice. (a) Crystal structure: the arrows at the left-bottom corner show the in-plane directions of the crystal and the solid-line box indicates the in-plane structural unit cell. Different Ir-Ir bonds are labeled with L (long), M (medium), and S (short) with the bond lengths being 3.30, 3.23, and 2.86 Å, respectively.[12] (b), (c), and (d): three possible magnetic structures. In each case, the magnetic unit cell is the same as the structural unit cell shown in (a). The shaded boxes highlight the stripy and zig-zag chain elements accordingly.

Figure 4

Temperature dependence of the integrated intensity of the (0 1 11) peak. Inset: expanded view of the temperature region near $T_N$.