  Topological insulators (TIs) show rich phenomena and functions which can
never be realized in ordinary insulators. Most of them come from the peculiar
surface or edge states. Especially, the quantized anomalous Hall effect (QAHE)
without an external magnetic field is realized in the two-dimensional
ferromagnet on a three-dimensional TI which supports the dissipationless edge
current. Here we demonstrate theoretically that the domain wall of this
ferromagnet, which carries edge current, is charged and can be controlled by
the external electric field. The chirality and relative stability of the Neel
wall and Bloch wall depend on the position of the Fermi energy as well as the
form of the coupling between the magnetic moments and orbital of the host TI.
These findings will pave a path to utilize the magnets on TI for the
spintronics applications.
