Evolution of Magnetism in Single-Crystal Honeycomb Iridates*

We report the successful synthesis of single-crystals of the layered iridate, (Na$_{1-x}$Li$_x$)$_2$IrO$_3$, 0 $\le$ x $\le$ 0.90, and a thorough study of its structural, magnetic, thermal and transport properties. The new compound allows a controlled interpolation between Na$_2$IrO$_3$ and Li$_2$IrO$_3$, while maintaining the novel quantum magnetism of the honeycomb Ir4$+$ planes. The measured phase diagram demonstrates a suppression of the Neel temperature at an intermediate x indicating that the magnetic order in Na$_2$IrO$_3$ and Li$_2$IrO$_3$ are distinct. X-ray data shows that for x$=$0.70 when the Neel temperature is suppressed the most, the honeycomb structure is least distorted, suggesting at this intermediate doping that the material is closest to the spin liquid that has been sought after in Na$_2$IrO$_3$ and Li$_2$IrO$_3$. By analyzing our magnetic data with a single-ion theoretical model we also show that the trigonal splitting, on the Ir4$+$ ions changes sign from Na$_2$IrO$_3$ to Li$_2$IrO$_3$.