  Several moir\'e systems created by various twisted bilayers have manifested
magnetism under flatband conditions leading to enhanced interaction effects. We
theoretically study stability of moir\'e flatband ferromagnetism against
collective excitations, with a focus on the effects of Bloch band quantum
geometry. The spin magnon spectrum is calculated using different approaches,
including Bethe-Salpeter equation, single mode approximation, and an analytical
theory. One of our main results is an analytical expression for the spin
stiffness in terms of the Coulomb interaction potential, the Berry curvatures,
and the quantum metric tensor, where the last two quantities characterize the
quantum geometry of moir\'e bands. This analytical theory shows that Berry
curvatures play an important role in stiffening the spin magnons. Furthermore,
we construct an effective field theory for the magnetization fluctuations, and
show explicitly that skyrmion excitations bind an integer number of electrons
that is proportional to the Bloch band Chern number and the skyrmion winding
number.
