  Spin-orbit coupling plays an important role in understanding exotic quantum
phases. In this work, we present a scheme to combine
spin-orbital-angular-momentum (SOAM) coupling and strong correlations in
ultracold atomic gases. Essential ingredients of this setting is the interplay
of SOAM coupling and Raman-induced spin-flip hopping, engineered by lasers that
couples different hyperfine spin states. In the presence of SOAM coupling only,
we find rich quantum phases in the Mott-insulating regime, which support
different types of spin defects such as spin vortex and composite vortex with
antiferromagnetic core surrounded by the outer spin vortex. Based on an
effective exchange model, we find that these competing spin textures are a
result of the interplay of Dzyaloshinskii-Moriya and Heisenberg exchange
interactions. In the presence of both SOAM coupling and Raman-induced spin-flip
hopping, more many-body phases appear, including canted-antiferromagnetic and
stripe phases. Our prediction suggests that SOAM coupling could induce rich
exotic many-body phases in the strongly interacting regime.
