  We study the effect of the synthetic spin-orbit coupling in a two-component
Bose-Hubbard model in one dimension by employing the density-matrix
renormalization group method. A ferromagnetic long-range order emerges in both
Mott insulator and superfluid phases resulting from the spontaneous breaking of
the $Z_2$ symmetry, when the spin-orbit coupling term becomes comparable to the
hopping kinetic energy and the inter-component interaction is smaller than the
intra-one as well. This novel effect is expected to be detectable with the
present realization of the synthetic spin-orbit coupling in experiments.
