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We study the evolution of magnetic structure driven by a synthetic spin-orbitcoupling in a one-dimensional two-component Bose-Hubbard model. In addition tothe Mott insulator-superfluid transition, we found in Mott insulator phases atransition from a gapped ferromagnetic phase to a gapless chiral phase byincreasing the strength of spin-orbit coupling. Further increasing thespin-orbit coupling drives a transition from the gapless chiral phase to agapped antiferromagnetic phase. These magnetic structures persist in superfluidphases. In particular, in the chiral Mott insulator and chiral superfluidphases, incommensurability is observed in characteristic correlation functions.These unconventional Mott insulator phase and superfluid phase demonstrate thenovel effects arising from the competition between the kinetic energy and thespin-orbit coupling.

The evolution of magnetic structure driven by a synthetic spin-orbit coupling in two-component Bose-Hubbard model