Magnetism in Twisted Bilayer WSe$_2$

Abstract: Using a self-consistent Hartree-Fock theory, we show that the recently observed ferromagnetism in twisted bilayer WSe$_2$ [Nat. Commun. 16, 1959 (2025)] can be understood as a Stoner-like instability of interaction-renormalized moir\'e bands. We quantitatively reproduce the observed Lifshitz transition as function of hole filling and applied electric field that marks the boundary between layer-hybridized and layer-polarized regimes. The former supports a ferromagnetic valley-polarized ground state below half-filling, developing a topological charge gap at half-filling for small twists. At larger twist angles there is a transition to a gapped triangular N\'eel antiferromagnet. The layer-polarized regime supports a stripe antiferromagnet below half-filling and a wing-shaped multiferroic ground state above half-filling. We map the evolution of these states as a function of filling factor, electric field, twist angle, and interaction strength. Beyond providing an understanding of recent experiments, our methodology is applicable to a broad class of moir\'e systems.