  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.
