Signatures of a liquid-crystal transition in spin-wave excitations of skyrmions

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.