Signatures of Strong Kitaev Exchange Correlations in Raman scattering on (Na$_{1-x}$Li$_x$)$_2$IrO$_3$

Inelastic light scattering studies on single crystals of (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ ($x = 0, 0.05$ and $0.15$) show a polarization independent broad band at $\sim $~2750 cm$^{-1}$ with a large band-width $\sim 1800$~cm$^{-1}$. For Na$_2$IrO$_3$ the broad band is seen for temperatures $T \leq 200$~K and persists inside the magnetically ordered state. The intensity of this mode increases with Li content, increasing by a factor of $\sim 1.6$ for $x = 0.15$, shifts to lower wave-numbers, and persists to much higher temperatures in the Li doped samples. Such a mode has recently been predicted theoretically for Na$_2$IrO$_3$ by Knolle et.al. as a signature of the gapless quantum spin liquid in the strong Kitaev limit of the Kitaev-Heisenberg model. We assign the observation of the broad band to be a signature of strong Kitaev-exchange correlations. The fact that the broad band persists even inside the magnetically ordered state suggests that dynamically fluctuating moments survive below $T_{N}$. A comparison with the theoretical model gives an estimate of the Kitaev exchange interaction parameter to be $J_K\approx 57$~meV.