  We show that the recent experimental realization of spin-orbit coupling in
ultracold atomic gases can be used to study different types of spin spiral
order and resulting multiferroic effects. Spin-orbit coupling in optical
lattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction which
is essential for spin spiral order. By taking into account spin-orbit coupling
and an external Zeeman field, we derive an effective spin model in the Mott
insulator regime at half filling and demonstrate that the DM interaction in
optical lattices can be made extremely strong with realistic experimental
parameters. The rich finite temperature phase diagrams of the effective spin
models for fermions and bosons are obtained via classical Monte Carlo
simulations.
