Collective Spin Excitations in Correlated Moir\'e Chern Ferromagnets

Moir\'e-induced narrow electronic bands in transition metal dichalcogenide superlattices support many correlated quantum phases characterized by novel charge, flavor, and topological orders. Among these, magnetic ordering emerges as the most ubiquitous, often serving as the parent state for other correlated phases, including quantum anomalous Hall states, as well as chiral superconducting state. Because of electron-electron correlation, the stability of magnetic order is critically influenced by low-energy collective spin fluctuations, or magnon excitations. We investigate the nature of magnon excitations and their impact on the stability and transition temperature of the magnetic state at integer filling factor $\nu = -1$. We find that the magnon spectrum exhibits isolated low-energy bands whose topological character undergoes a transition upon tuning the interlayer displacement field. The magnon gap is found to depend sensitively on the topology of the magnetic ground state, resulting in an order-of-magnitude enhancement of the transition temperature $T_c$ in the quantum anomalous Hall phase compared to the topologically trivial correlated insulator. Our findings provide insight into the interplay between electron and magnon topology and suggest new routes for controlling magnetism and topology via moir\'e engineering.