Dynamics of magnetic skyrmions in nanodots

Bloch and Neel magnetic skyrmions have been studied in systems of confined geometry (nanodots, a linear array of nanodots). The spectra of low- and high-frequency excitation modes of a skyrmion state have been calculated. It has been shown that skyrmion spectrum asymmetry, namely, the characteristic difference between the frequencies of the azimuthal modes of the azimuthal skyrmion modes rotating clockwise and counterclockwise, is associated with asymmetry in the magnetization profiles of high-frequency spin waves propagating on the background of a skyrmion state in a nanodot. The low-frequency spectrum contains the only gyrotropic mode localized near the center of a nanodot. The gyrotropic frequency depends on the material parameters of a nanodot and the size of a skyrmion. The eigenfrequency of the gyrotropic mode of an isolated skyrmion in a nanodot in ultrathin films ($L\sim$ 1 nm) does not depend on the internal structure of a skyrmion and is the same for Bloch and Neel skyrmions. The interaction of skyrmions, in particular, in a linear chain of nanodots with the ground skyrmion state, leads to distinctions in low-frequency spectra. The structure of a skyrmion (of Bloch or Neel type) is exhibited as a shift of dispersion curves and a difference between the frequencies of ferromagnetic resonance in a system of interacting skyrmions.