Effect of curvature on the eigenstates of magnetic skyrmions

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.


Anastasiia Korniienko, Attila Kákay, Denis D. Sheka, and Volodymyr P. Kravchuk,
Effect of curvature on the eigenstates of magnetic skyrmions,
Physical Review B102, 014432(2020), doi: 10.1103/PhysRevB.102.014432 (pdf)

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