Magnetic excitation spectrum of Na${}_2$IrO${}_3$ probed with resonant inelastic x-ray scattering

The low energy excitations in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ have been investigated using resonant inelastic x-ray scattering (RIXS). A magnetic excitation branch can be resolved, whose dispersion reaches a maximum energy of about 35 meV at the $\Gamma$ point. The momentum dependence of the excitation energy is much larger along the $\Gamma -X$ direction compared to that along the $\Gamma -Y$ direction. The observed dispersion relation is consistent with a recent theoretical prediction based on the Heisenberg-Kitaev model. At high temperatures, we find large contributions from lattice vibrational modes to our RIXS spectra, suggesting that a strong electron-lattice coupling is present in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$.

Figure 1

(a) A wide range RIXS spectrum for a single-crystal sample of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ at $\mathbf{Q}=\left(006.7\right)$ obtained with $E_i=11.217$ keV. (b) Detailed view of the low-lying RIXS excitations in (a) taken at two different momentum transfers along the $L$ direction. Dashed lines are a fit to the elastic line (details provided in the main text). (c) and (d) Incident energy dependence of the RIXS spectum. The intensity scale for (d) is shown.

Figure 2

(a) Our fit function for the $T=400$ K RIXS spectrum, showing the number of resolution-limited functions which represent the elastic line and the lattice vibrational modes. (b) Calculated total intensity of the Stokes ($\omega >0$ meV) and anti-Stokes ($\omega <0$ meV) contribution to the lattice vibrations as a function of temperature. (c) Temperature dependence of the RIXS spectrum taken at $10\text{K}\le T\le 400$ K for $\mathbf{Q}=\left(006.7\right)$. Spectra have been shifted vertically for clarity. The thick black solid lines show the elastic component, while the thin black lines include the lattice vibrational contribution as well.

Figure 3

(a) Momentum dependence of the RIXS spectra taken along the $\Gamma -X$ and $\Gamma -Y$ directions at $T=10$ K. Superimposed on each spectra is the background contribution from the elastic line and the vibrational modes. (b) The magnetic signal after subtracting the background, and (c) a direct comparison between $\mathbf{Q}=\left(00\right)$ and $\mathbf{Q}=\left(0.50\right)$. In (a) and (b) spectra have been shifted vertically for clarity. (d) Fit results for the peak position of the magnetic signal in (b).