  We consider ultracold matter of spin-2 atoms in optical lattices. We derive
an effective Hamiltonian for the studies of spin ordering in Mott states and
investigate hyperfine spin correlations. Particularly, we diagonalize the
Hamiltonian in an on-site Hilbert space taking into account spin-dependent
interactions and exchange between different sites. We obtain phase diagrams and
quantum phase transitions between various magnetic phases.
