Domain walls in ferromagnetic nanostrips can be moved by an applied magnetic field or spin current. Experiments and numerical simulations reveal a rich dynamics of the wall motion. In a weak field a wall moves steadily with a velocity proportional to the field strength. Above a critical field the steady motion breaks down, the motion acquires an oscillatory character, and the average velocity drops significantly. In even higher fields the motion becomes chaotic.
I will show that the root cause of the complex dynamics can be traced to the composite nature of domain walls. A wall is typically made of 2 or 3 elementary topological defects: integer vortices in the bulk and fractional vortices at the edge. We model the motion of a wall using collective coordinates to parametrize soft modes. These modes exhibit an overdamped dynamics with topological terms due to a nonzero skyrmion charge carried by bulk vortices. The oscillations arise from periodic creation and annihilation of vortices.