Spin spirals of charge ordered states in moiré from an exciton mediated Dzyaloshinskii-Moriya interaction

Forming moiré superlattices by stacking transition metal dichalcogenides (TMDs) has provided a good platform to explore their many-body correlation phenomena such as charge orders and magnetic interactions. The optically or electrically injected interlayer exciton in the TMDs has strong Coulomb exchange with the carriers in the host TMDs, thus mediates long-range spin-spin interactions between the moiré trapped carriers. The equilibrium exciton distribution mediates a Heisenberg interaction, while the non-equilibrium part corresponding to an exciton spin current mediates an anisotropic Dzyaloshinskii-Moriya interaction of even longer range limited by exciton's coherence length. We show that the latter results in a spin spiral order, which depends on the filling factor of the carrier and the exciton current.