  The stability of 2pi domain walls in ferromagnetic nanorings is investigated
via calculation of the minimum energy path that separates a 2pi 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 2pi 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 2pi wall is compared to the activation energy for transitions between the
two ring vortex states.
