Soliton dynamics driven by spin-transfer torque in perpendicular ferromagnets

In a ferromagnetic thin film with strong perpendicular anisotropy we refer to a magnetic bubble as a small area, delimited by a domain wall, where the spins are pointing opposite to the ferromagnetic state of the rest of the film. The complexity of the bubble structure is mostly related to the shape and the magnetic configuration of the domain wall. With this regard, the mathematical instruments that are used to describe the properties of a magnetic bubble are the topological density and the skyrmion number. They are connected one each other and the latter always turns out an integer value for magnetic bubbles. More in detail, the higher is the skyrmion number the more complex is the bubble, including the possibility to have non circular magnetic bubbles. A particular bubble structure is also referred to as bubbleantibubble pair.