Quantum insulating states of F=2 cold atoms in optical lattices

In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an octopole coupling between two neighboring lattice sites. Depending on scattering lengths and numbers of particles per site the ground states are either rotationally invariant dimer or trimer Mott insulators or insulating states with various spin orders. Three spin-ordered insulating phases are ferromagnetic, cyclic, and nematic Mott insulators. We estimate the phase boundaries for states with different numbers of atoms per lattice site.