  Two effects of oscillatory transformations of vortex textures in flat
nanomagnets due to the application of an external field or a spin-polarized
electric current are analytically described with relevance to soft-magnetic
structures of submicrometer sizes (whose thickness is significantly bigger than
the magnetostatic exchange length). These are changes of a domain wall (DW)
structure in a long magnetic stripe (oscillations between a transverse DW, a
vortex DW, and an antivortex DW) and periodic vortex-core reversals in a
circular magnetic dot which are accompanied by oscillatory displacements of the
vortex from the dot center. In nanostructures of smaller thicknesses
(comparable to the exchange length), where nonlocal magnetostatic effects are
very strong because of fast spatial variation of the magnetization, similar
phenomena have been widely studied previously. Here, the dynamics is
investigated within a local approach including magnetostatic field via boundary
conditions on solutions to the Landau-Lifshitz-Gilbert equation only. Both the
DWs in stripes and vortex states of the dot are treated as fragments of a
cross-tie DW. Despite similarity of the cyclic transformations of the ordering
to the dynamics of more strongly confined nanomagnets, details of motion
(trajectories) of the vortices and antivortices (Bloch lines) of the textures
under study are different, which is related to prohibition of rapid jumps of
the polarization of Bloch lines. In addition to the magnetization rotation
about the direction of magnetic field or current polarization, the evolution of
textures is shown to relate to oscillatory changes of the direction of a
cross-tie DW with respect to any arbitrary axis in the magnet plane accompanied
by oscillations of the DW width.

Mesoscale and Nanoscale Physics