Emergent elastic waves in skyrmion crystals with finite frequencies at long wavelength limit

Yangfan Hu

Published 2019-05-10Version 1

A fundamental fact in solids is that the frequencies of elastic waves vanish as the wave number approaches zero\cite{6}. Here we theoretically show that this fact is overturned when studying the lattice vibration of skyrmion crystals (SkX), i.e., periodic alignment of topologically nontrivial spin solitons called magnetic skyrmions. As emergent crystals, SkX possess collective excitations called "emergent phonons", which describe dynamics of SkX caused by lattice vibration (resembling acoustical branches of ordinary phonons) and in-lattice vibration (resembling optical branches of ordinary phonons). We find that lattice vibration and in-lattice vibration of the emergent phonons in SkX are coupled even at long wavelength limit, such that multiple types of "emergent elastic waves" (modes causing lattice vibration of SkX) with finite frequencies exist. This phenomenon, which originates from the Berry phase form of kinetic energy, is generally true for emergent crystalline states of spins. Our results show that the dynamics of magnetic emergent crystals are intrinsically different from that of ordinary crystals.