Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The effect of curvature on the eigenexcitations 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. In
order to treat the gyromotion analytically we developed a Thiele-like
collective variable approach. We show that N\'{e}el 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.

34
The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin