Interaction between skyrmions and antiskyrmions in a coexisting phase of a Heusler material

Coexisting phases of magnetic skyrmions and antiskyrmions have proposed to exhibit a variety of fascinating properties, owing to interactions between them. The recent discovery of the coexisting phase in a Heusler material could offer a platform for skyrmion-antiskyrmion-based spintronics. Here we report Lorentz electron microscopy experiments and micromagnetic simulations in a similar Heusler material, Mn$_{1.3}$Pt$_{1.0}$Pd$_{0.1}$Sn. Around $B_c \sim$ 420$\,$mT, we find a stochastic reversible transformation and a room temperature coexisting phase of elliptical skyrmions and square-shaped antiskyrmions. The closeness of the energy competition is sensitive to the exchange stiffness constants and sample thickness. Furthermore, we reveal isotropic long-range repulsive interaction between the skyrmions and antiskyrmions regardless of their shapes and the skyrmion helicities, in stark contrast to conventional thought of angle- and helicity-dependent short-range pairwise interactions. The observed interaction possibly results from the topological protection against the intrusion of magnetic flux density coming from skyrmions (antiskyrmions) into antiskyrmions (skyrmions). Our results provide new insight into interacting skyrmions and antiskyrmions and a guide for developing skyrmion-antiskyrmion-based spintronics.