  We study a spin model on honeycomb lattice with two types of Heisenberg
exchange couplings, $J$ and $\tilde J$, where $J$ is for the conventional spin
and and $\tilde J$ for rotated spin. When $\tilde J=0$, this is the
conventional Heisenberg model. When J=0, the system is either in a stripy
antiferromagnetic order($\tilde J<0$, ferromagnetic for rotated spin) or a
zig-zag antiferromagnetic order ($\tilde J>0$, antiferromagnetic for rotated
spin). The competition between two ferromagnetic orders or two
antiferromagnetic orders induces Kitaev's spin liquid phase characterized by
the exactly solvable Kitaev model ($J=\tilde J$). Our model can be applied to
layered Mott insulators A$_2$IrO$_3$ (A=Li, Na). For a monolayer of
Li$_2$IrO$_3$, we show that it is possible to tune the controlling parameter
into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital
coupling.
