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We show that the recent experimental realization of spin-orbit coupling inultracold atomic gases can be used to study different types of spin spiralorder and resulting multiferroic effects. Spin-orbit coupling in opticallattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction whichis essential for spin spiral order. By taking into account spin-orbit couplingand an external Zeeman field, we derive an effective spin model in the Mottinsulator regime at half filling and demonstrate that the DM interaction inoptical lattices can be made extremely strong with realistic experimentalparameters. The rich finite temperature phase diagrams of the effective spinmodels for fermions and bosons are obtained via classical Monte Carlosimulations.

Dzyaloshinskii-Moriya Interaction and Spiral Order in Spin-orbit Coupled Optical Lattices