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A Kitaev-Heisenberg-J2-J3 model is proposed to describe the Mott-insulatinglayered iridates A2IrO3 (A=Na,Li). The model is a combination of the Kitaevhoneycomb model and the Heisenberg model with all three nearest neighborcouplings J1, J2 and J3. A rich phase diagram is obtained at the classicallevel, including the experimentally suggested zigzag ordered phase; as well asthe stripy phase, which extends from the Kitaev-Heisenberg limit to theJ1-J2-J3 one. Combining the experimentally observed spin order with the optimalfitting to the uniform magnetic susceptibility data gives an estimate ofpossible parameter values, which in turn reaffirms the necessity of includingboth the Kitaev and farther neighbor couplings.

Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3