  We study the electronic structure of hole-doped transition metal
dichalcogenides for small twist-angels, where the onsite repulsion is extremely
strong. Using unbiased diagrammatic Monte Carlo simulations, we find evidence
for magnetic correlations which are driven by delocalization and can be
controlled in situ via the dielectric environment. For weak spin-orbit
coupling, we find that the moderately doped system becomes anti-ferromagnetic,
whilst the regime of strong spin-orbit coupling features ferromagnetic
correlations. We show that this behavior is accurately predicted by an
analytical theory based on moment expansion of the Hamiltonian, and analysis of
corresponding particle trajectories.
