  Motivated by experimental findings in [ 1 ] and [ 2 ], we find an elliptical
skyrmion can be nucleated in a material with a Dzyaloshinskii-Moriya
interaction (DMI) that supports antiskyrmions. The DMI favors the elongation of
the skyrmion along a given direction so that it is characterized by two size
parameters. We derive analytical properties of the elliptical skyrmion using
the Belavin-Polyakov (BP) pure exchange model. We show that the DMI which
typically favors isotropic skyrmions or antiskyrmions, respectively, can also
support elliptical antiskyrmions or skyrmions, respectively. Using the real
material parameters extracted from [1] and including all relevant interactions,
numerical computations indicate that the elliptical skyrmion can be nucleated
from the stripe or labyrinth domain state by a magnetic force microscope tip in
a thin film with a DMI favoring antiskyrmions that consists of at least a few
atomic layers.

Mesoscale and Nanoscale Physics