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

Hyperfine Spin-Two (F=2) Atoms in Three-Dimensional Optical Lattices: Phase Diagrams and Phase Transitions