Magnon spectrum in two- and three- dimensional skyrmion crystals

Abstract

We study the low-energy magnon spectrum of the skyrmion crystal (SkX) ground state, appearing in two-dimensional ferromagnet with Dzyaloshinskii-Moriya interaction and magnetic field. We approximate SkX hexagonal superlattice by a set of overlapping disks, and find the lattice period by minimizing the classical energy density. The determined spectrum of magnons on the disc of optimal radius is stable and only two lowest energy levels can be considered as localized. The subsequent hybridization of these levels in the SkX lattice leads to tight-binding spectrum. The localized character of the lowest magnon states is lost at small and at high fields, which is interpreted as melting of SkX. The classical energy of SkX is slightly above the energy of a single conical spiral, and a consideration of quantum corrections can favor the skyrmion ground state. Extending our analysis to three-dimensional case, we argue that these quantum corrections become more important at finite temperatures, when the average spin value is decreased.