Elliptical skyrmions: Theory and nucleation by a magnetic tip in an antiskyrmion-hosting material

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.