Correlated magnetism in twisted transition metal dichalcogenide moiré superlattices

Twisted bilayer transition metal dichalcogenide (TMD) superlattices exhibit a variety of correlated phenomena emerge, including correlated insulating states, superconductivity, and integer and fractional quantum anomalous Hall effects. Magnetic ordering is central to nearly all of these phenomena. Although mean-field theory has been successful in predicting possible ground states, its tendency towards overestimating magnetic ordering limits its ability to predict key physical properties, such as gap size and transition temperatures, thereby hindering theoretical understanding of these correlated phenomena. This challenge arises from strong correlation effects due to collective fluctuations. In this work, we study the nature of the collective fluctuations and their influence on magnetism. We show how correlation effects modify the magnetic phase diagram across different twist angles and displacement fields, and discuss their implications for the transition temperature.