  A Kitaev-Heisenberg-J2-J3 model is proposed to describe the Mott-insulating
layered iridates A2IrO3 (A=Na,Li). The model is a combination of the Kitaev
honeycomb model and the Heisenberg model with all three nearest neighbor
couplings J1, J2 and J3. 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
J1-J2-J3 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.
