  Twisted homobilayer transition metal dichalcogenide (TMD) offers a versatile
platform for exploring band topology, interaction-driven phases, and magnetic
orders. We study the interaction-driven phases in twisted TMD homobilayers and
their low-energy collective excitations, focusing on the effect of band
topology on magnetism and its thermal stability. From Hartree-Fock theory of
the continuum model, we identify several magnetic and topological phases. By
tuning the displacement field, we find two phase transitions involving a change
in topology and magnetism respectively. We analyze the magnon spectrum,
revealing the crucial role of band topology in stabilizing 2D ferromagnetism by
amplifying easy-axis magnetic anisotropy, resulting in a large magnon gap of up
to 7 meV. As the magnon gap is directly tied to the stability of the magnetic
phase to thermal fluctuations, our findings have several important experimental
implications.
