  Motivated by the recent observation of evidences of ferromagnetism in
correlated insulating states in systems with Moir\'{e} superlattices, we study
a two-orbital quantum antiferromagnetic model on the triangular lattice, where
the two orbitals physically correspond to the two valleys of the original
graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$
symmetry, where the two SU(2) symmetries correspond to the rotation within the
spin and valley space respectively. Through analytical argument, Schwinger
boson analysis and also DMRG simulation, we find that even though all the
couplings in the Hamiltonian are antiferromagnetic, there is still a region in
the phase diagram with fully polarized ferromagnetic order. We argue that a
Zeeman field can drive a metal-insulator transition in our picture, as was
observed experimentally. We also construct spin liquids and topological ordered
phases at various limits of this model. Then after doping this model with extra
charge carriers, the system most likely becomes spin-triplet/valley-singlet
$d+id$ topological superconductor as was predicted previously.
