Abstract
A Kitaev-Heisenberg-${J}_{2}$-${J}_{3}$ model is proposed to describe the Mott-insulating layered iridates ${A}_{2}$IrO${}_{3}$ ($A=\text{Na}$, Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest-neighbor couplings ${J}_{1}$, ${J}_{2}$, and ${J}_{3}$. A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the ${J}_{1}$-${J}_{2}$-${J}_{3}$ one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate of possible parameter values, which in turn reaffirms the necessity of including both the Kitaev and farther neighbor couplings.
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