  We study cold atoms in an optical lattice with synthetic spin-orbit coupling
in the Mott-insulator regime. We calculate the parameters of the corresponding
tight-binding model using Peierls substitution and "localized Wannier states
method" and derive the low-energy spin Hamiltonian for fermions and bosons. The
spin Hamiltonian is a combination of Heisenberg model, quantum compass model
and Dzyaloshinskii-Moriya interactions and it has a rich classical phase
diagram with collinear, spiral and vortex phases.
