Magnetism and quantum melting in moiré-material Wigner crystals

Semiconductor moir\'e materials host generalized Wigner crystal states at a series of fractional fillings, originating from localization of electrons in a subset of moir\'e sites in order to minimize long-range Coulomb interactions. Using exact diagonalization calculations, this paper studies the interplay between spin and charge degrees of freedom that gives rise to different magnetic orders within the crystalline states at fillings =1/3 and =2/3. The authors provide effective spin model descriptions of those phases, also addressing their Mott-Wigner melting transitions.