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Significant efforts have been dedicated to achieving excitonic insulators. Inthis paper, we explore a new problem of doping excitons into a Mott insulatorinstead of a band insulator. Specifically, we start with a Mott insulator on atriangular moir\'e superlattice in a transition metal dichalcogenides (TMD)layer and inject excitons by either transferring particles to a different layeror optically pumping electrons from the valence to the conduction band. In bothcases, the excitons move in the presence of local spin moments inherited fromthe Mott insulator. When the Heisenberg spin coupling $J$ is small, the kineticenergy of the excitons decides the magnetism, akin to Nagaoka ferromagnetism inhole-doped Mott insulators. Through density matrix renormalization group (DMRG)calculations, we demonstrate that the spin moments originating from the Mottinsulator form $120^\circ$ antiferromagnetic or ferromagnetic order for the twosigns of the exciton hoppings over a broad range of exciton densities. Notably,the optical pump case may result in an antiferromagnetic to ferromagnetictransition with increasing exciton density, indicating a potential mechanismfor light-induced ferromagnetism. A similar exciton-induced ferromagnetismcould be achieved in a moir\'e-monolayer system where the monolayer iselectron-doped while the moir\'e Mott insulator is hole-doped. Our worksdemonstrates a new possibility to engineering magnetism through doping neutralexcitons.

Exciton and light induced ferromagnetism from doping a moir\'e Mott insulator