Elliptical skyrmion-antiskyrmion interaction in a magnetic film

Two different experimental papers [1] and [2] have demonstrated that elliptical skyrmions can exist in a magnetic material which typically host antiskyrmions. These are Bloch-type skyrmions which elongate in two distinct directions for clockwise and counterclockwise chiralities. It has been theoretically demonstrated [3] that isolated elliptical skyrmions can be nucleated in thes same material with a magnetic force microscope tip. In addition, elliptical skyrmions and antiskyrmions can exist simulataneously in the same material [1]. Therefore, it is important to study their interaction. We determine the spin vector field of the elliptical skyrmion-antiskyrmion state by using the Belavin-Polyakov (BP) formalism for the two-dimensional, three-component model with the nearest-neighbor Heisenberg exchange interaction. Theoretical calculations indicate that the interaction is dictated by the chirality of the elliptical skyrmion due to the rotation of the spins. Then, we use this spin field as the initial state in a numerical model with the real material parameters from [1] to compare the interaction to theoretical predictions. 

[1] Jena J., Göbel B., Ma T., Kumar V., Saha R., Mertig I., Felser C., Parkin S.S.P., Elliptical Bloch skyrmion chiral twins in an antiskyrmion system, Nat. Comms., 11 (2020), p. 1115.

[2] Peng L., Takagi R., Koshibae W., Shibata K., Nakajima K., Arima T., Nagaosa N., Seki S., Yu X., Tokura Y., Controlled transformation of skyrmions and antiskyrmions in a non-centrosymmetric magnet, Nature Nanotechnol., 15 (2020), pp. 181-186.

[3] D. Capic, Elliptical skyrmions: Theory and nucleation by a magnetic tip in an antiskyrmion-hosting material, Journal of Magnetism and Magnetic Materials,  563, (2022),169866.