  Advances in pure optical trapping techniques now allow the creation of
degenerate Bose gases with internal degrees of freedom. Systems such as
${}^{87}$Rb, $^{39}$K or ${}^{23}$Na in the $F=1$ hyperfine state offer an
ideal platform for studying the interplay of superfluidity and quantum
magnetism. Motivated by the experimental developments, we study ground state
phases of a two-component Bose gas loaded on an optical lattice. The system is
described effectively by the Bose-Hubbard Hamiltonian with onsite and near
neighbor spin-spin interactions. An important feature of our investigation is
the inclusion of interconversion (spin flip) terms between the two species,
which has been observed in optical lattice experiments. Using mean-field theory
and quantum Monte Carlo simulations, we map out the phase diagram of the
system. A rich variety of phases is identified, including antiferromagnetic
(AF) Mott insulators, ferromagnetic and AF superfluids.
