Magnetostatic interaction between two bubble skyrmions

A detailed analytic and numerical analysis of the interaction between two bubble skyrmions has been carried out. The results from the micromagnetic calculations show that when the skyrmions are in the same plane, the magnetic parameters vary weakly as a function of the separation between them. On the other hand, when the skyrmions are located in the same vertical axis, the magnetic parameters show a strong variation as a function of the separation of the skyrmions. In particular, when a magnetic disk is over another, there is a transition from a Bloch-like skyrmion configuration to a Néel-like skyrmion configuration as the distance between the disks decreases, as a consequence of the magnetostatic interaction. Therefore, it is possible to stabilize a bubble skyrmion with a Néel configuration without the Dzyaloshinskii-Moriya interaction. Thus, these results can be used for the control of the skyrmion parameters in magnetic spintronic devices that need to use these configurations.