Stability of $2\pi$ Domain Walls in Ferromagnetic Nanorings

The stability of 2π domain walls in ferromagnetic nanorings is investigated via calculation of the minimum energy path that separates a 2π domain wall from the vortex state of a ferromagnetic nanoring. Trapped domains are stable when they exist between certain types of transverse domain walls, i.e., walls in which the edge defects on the same side of the magnetic strip have equal sign and thus repel. Here the energy barriers between these configurations and vortex magnetization states are obtained using the string method. Due to the geometry of a ring, two types of 2π walls must be distinguished that differ by their overall topological index and exchange energy. The minimum energy path corresponds to the expulsion of a vortex. The energy barrier for annihilation of a 2π wall is compared to the activation energy for transitions between the two ring vortex states.