  The nature of the effective spin Hamiltonian and magnetic order in the
honeycomb iridates is explored by considering a trigonal crystal field effect
and spin-orbit coupling. Starting from a Hubbard model, an effective spin
Hamiltonian is derived in terms of an emergent pseudo-spin-1/2 moment in the
limit of large trigonal distortions and spin-orbit coupling. The present
pseudo-spins arise from a spin-orbital locking and are different from the jeff
= 1/2 moments that are obtained when the spin-orbit coupling dominates and
trigonal distortions are neglected. The resulting spin Hamiltonian is
anisotropic and frustrated by further neighbour interactions. Mean field theory
suggests a ground state with 4-sublattice zig-zag magnetic order in a parameter
regime that can be relevant to the honeycomb iridate compound Na2IrO3, where
similar magnetic ground state has recently been observed. Various properties of
the phase, the spin-wave spectrum and experimental consequences are discussed.
The present approach contrasts with the recent proposals to understand iridate
compounds starting from the strong spin-orbit coupling limit and neglecting
non-cubic lattice distortions.
