Spin Waves and Revised Crystal Structure of Honeycomb Iridate ${\mathrm{Na}}_2{\mathrm{IrO}}_3$

We report inelastic neutron scattering measurements on ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order below $T_N=15.3\mathrm{K}$ is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90° Ir-O-Ir bonds required for dominant Kitaev exchange.

Figure 1

(a) Layer stacking along the monoclinic $c$ axis with an in-plane offset along $a$ (dashed box is the $C2/m$ unit cell). (b) Basal layer ($z=0$) showing the Ir honeycomb lattice. (c) Diagram to illustrate the layer stacking in the ideal honeycomb lattice. Ideal stacking of layers and stacking faults are explained in the text. (d) X-ray diffraction intensity in the (0, $k$, $l$) plane showing rods of diffuse scattering in between structural Bragg peaks along ${\mathit{c}}^{*}$ with selection rule $h+k=2n$ and $k=3m+1$ or $3m+2$ ($n$, $m$ integers) modeled in (e) by frequent in-plane translational stacking faults of the type shown by the thick arrows in (c).

Figure 2

(a) ZF ${\mu }^{+}\mathrm{SR}$ spectra on a polycrystalline sample of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ above and below $T_N$. Solid lines are (top) a guide to the eye and (bottom) a fit described in the text. (b),(c) Fitted parameters as a function of temperature.

Figure 3

Diagram of (a) Néel, (b) zigzag, and (c) stripy order. (d) Reciprocal space diagram showing locations of magnetic Bragg peaks for various magnetic phases (inner hexagon shows first Brillouin zone of the honeycomb lattice). (e) Powder inelastic neutron scattering data. The notable well-defined feature is the sharp lower boundary of the scattering at low $Q$ [filled (magenta) symbols in (h)–(j)], which we associate with a sinusoidal spin-wave dispersion; this becomes damped out in the paramagnetic phase in (f). Slanted thick dashed arrow shows the scan direction in (g). Gray shading marks the inaccessible region close to the elastic line dominated by incoherent elastic scattering. (g) Energy scan (solid points 4.6 K, open symbols 55 K) through the maximum spin-wave energy seen in (e) fitted to a Gaussian peak (solid line), dashed line is estimated background. (h)–(j) Calculated spherically averaged spin-wave intensity [15] for the $J_{1,2,3}$ model with (h) zigzag or (i) stripy order, and (j) the KH model with stripy order for parameters given in the text. Solid red line in (j) highlights the low-energy boundary, which coincides with the dispersion from $\Gamma$ to the first softening point.