  Understanding the spin-wave excitations of chiral magnetic order, such as the
skyrmion crystal (SkX), is of fundamental interest to confirm such exotic
magnetic order. The SkX is realized by competing Dzyaloshinskii-Moriya and
ferromagnetic-exchange interactions with a magnetic field or anisotropy. Here
we compute the dynamical spin structure factor, using Monte Carlo and spin
dynamics simulations, extracting the spin-wave spectrum in the SkX, in the
vicinity of the paramagnet to SkX transition. Inside the SkX, we find six
spin-wave modes, which are supplemented by another mode originating from the
ferromagnetic background. Above the critical temperature $T_s$ for the skyrmion
crystallization, we find a diffusive regime, reminiscent of the
liquid-to-crystal transition, revealing that topological spin texture of
skyrmionic character starts to develop above $T_s$ as the precursor of the SkX.
We discuss the opportunities for the detection of the spin waves of the SkX
using inelastic-neutron-scattering experiments in manganite-iridate
heterostructures.
