  We investigate the superfluid--Mott-insulator quantum phase transition of
spin-1 bosons in an optical lattice created by pairs of counterpropagating
linearly polarized laser beams, driving an $F_g=1$ to $F_e=1$ internal atomic
transition. The whole parameter space of the resulting two-component
Bose-Hubbard model is studied. We find that the phase transition is not always
second order as in the case of spinless bosons, but can be first order in
certain regions of the parameter space. The calculations are done in the
mean-field approximation by means of exact numerical diagonalization as well as
within the framework of perturbaton theory.
