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The nature of the effective spin Hamiltonian and magnetic order in thehoneycomb iridates is explored by considering a trigonal crystal field effectand spin-orbit coupling. Starting from a Hubbard model, an effective spinHamiltonian is derived in terms of an emergent pseudo-spin-1/2 moment in thelimit of large trigonal distortions and spin-orbit coupling. The presentpseudo-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 andtrigonal distortions are neglected. The resulting spin Hamiltonian isanisotropic and frustrated by further neighbour interactions. Mean field theorysuggests a ground state with 4-sublattice zig-zag magnetic order in a parameterregime that can be relevant to the honeycomb iridate compound Na2IrO3, wheresimilar magnetic ground state has recently been observed. Various properties ofthe phase, the spin-wave spectrum and experimental consequences are discussed.The present approach contrasts with the recent proposals to understand iridatecompounds starting from the strong spin-orbit coupling limit and neglectingnon-cubic lattice distortions.

Spin-Orbital Locking, Emergent Pseudo-Spin, and Magnetic order in Honeycomb Lattice Iridates