Magnetostatic interaction between two Bubble Skyrmions

A detailed analytic and numerical analysis of the interaction between two bubble skyrmions has been carried out. Results from micromagnetic calculations show a strong dependence of the parameters of the skyrmion magnetic profile as a function of the magnetostatic interaction. The magnetic core and edge-width sizes of the skyrmion increase or decrease depending on the relative position between the skyrmions and the uniaxial perpendicular anisotropy. In particular, when a magnetic disk is over another, there is a transition from a Bloch-like skyrmion configuration to a N\'{e}el-like skyrmion configuration as the distance between the disks decreases. This transition is due to the magnetostatic interaction between them. Therefore, it is possible to stabilize a bubble skyrmion with a N\'{e}el configuration without the Dzyaloshinskii-Moriya interaction. Thus, these results can be used for the parameters control of the skyrmions in magnetic spintronic devices that need to use these configurations.