  We study the spin-1 excitation spectra of the flatband ferromagnetic phases
in interacting topological insulators. As a paradigm, we consider a quarter
filled square lattice Hubbard model whose free part is the $\pi$ flux state
with topologically nontrivial and nearly-flat electron bands, which can realize
either the Chern or $Z_2$ Hubbard model. By using the numerical exact
diagonalization method with a projection onto the nearly-flat band, we obtain
the ferromagnetic spin-1 excitation spectra for both the Chern and $Z_2$
Hubbard models, consisting of spin waves and Stoner continuum. The spectra
exhibit quite distinct dispersions for both cases, in particular the spin wave
is gapless for the Chern Hubbard model, while gapped for the $Z_2$ Hubbard
model. Remarkably, in both cases, the nonflatness of the free electron bands
introduces dips in the lower boundary of the Stoner continuum. It significantly
renormalizes the energies of the spin waves around these dips downward and
leads to roton-like spin excitations. We elaborate that it is the softening of
the roton-like modes that destabilizes the ferromagnetic phase, and determine
the parameter region where the ferromagnetic phase is stable.
