The band structure of elementary excitations of skyrmion crystal in thin ferromagnetic film with Dzyaloshinskii–Moriya interaction and uniaxial magnetic anisotropy under external magnetic field is studied. In the absence of anisotropy there is a topological transition in the spectrum of skyrmion crystal: the gap between breathing and counter-clockwise modes closes, which is accompanied by changes of Berry curvature sign of these bands. In this work we demonstrate that such topological transition exists in some range of the uniaxial anisotropy values. We present a phase diagram showing that the value of the field of topological transition is higher in the easy-plane domain and lower in the easy-axis domain of anisotropy.
Timofeev et al. (Mon,) studied this question.