Spectrum of spin eigenmodes localized on a ferromagnetic skyrmion pinned by a geometrical defect (bump)

of magnetic films is studied theoretically. By means of direct numerical solution of the corresponding eigenvalue

problem and finite element micromagnetic simulations we demonstrate that the curvature can induce localized

modes with higher azimuthal and radial quantum numbers, which are absent for planar skyrmions (for the same

parameters). The eigenfrequencies of all modes, except the breathing and gyromodes decreases with increasing

curvature. Due to the translational symmetry break, the zero translational mode of the skyrmion gains a finite

frequency and forms the gyromode, which describes the uniform rotation of skyrmions around the equilibrium

position. To treat the gyromotion analytically we developed a Thiele-like collective variable approach. We show

that Néel skyrmions in curvilinear films experience a driving force originating from the gradient of the mean

curvature. The gyrofrequency of the pinned skyrmion is proportional to the second derivative of the mean

curvature at the point of equilibrium.

**Publication:**

Anastasiia Korniienko, Attila Kákay, Denis D. Sheka, and Volodymyr P. Kravchuk,

*Effect of curvature on the eigenstates of magnetic skyrmions*,

Physical Review B**102**, 014432(2020), doi: 10.1103/PhysRevB.102.014432 (pdf)

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