  Strong electron correlation and spin-orbit coupling (SOC) provide two
non-trivial threads to condensed matter physics. When these two strands of
physics come together, a plethora of quantum phenomena with novel topological
order have been predicted to emerge in the correlated SOC regime. In this work,
we examine the combined influence of electron correlation and SOC on a
2-dimensional (2D) electronic system at the atomic interface between
magic-angle twisted bilayer graphene (tBLG) and a tungsten diselenide (WSe2)
crystal. In such structure, strong electron correlation within the moire
flatband stabilizes correlated insulating states at both quarter and half
filling, whereas SOC transforms these Mott-like insulators into ferromagnets,
evidenced by robust anomalous Hall effect with hysteretic switching behavior.
The coupling between spin and valley degrees of freedom is unambiguously
demonstrated as the magnetic order is shown to be tunable with an in-plane
magnetic field, or a perpendicular electric field. In addition, we examine the
influence of SOC on the isospin order and stability of superconductivity. Our
findings establish an efficient experimental knob to engineer topological
properties of moire band in twisted bilayer graphene and related systems.
