  The electronic orders in magnetic and dielectric materials form the domains
with different signs of order parameters. The control of configuration and
motion of the domain walls (DWs) enables gigantic, nonvolatile responses
against minute external fields, forming the bases of contemporary electronics.
As an extension of the DW function concept, we realize the one-dimensional
quantized conduction on the magnetic DWs of a topological insulator (TI). The
DW of a magnetic TI is predicted to host the chiral edge state (CES) of
dissipation-less nature when each magnetic domain is in the quantum anomalous
Hall state. We design and fabricate the magnetic domains in a magnetic TI film
with the tip of the magnetic force microscope, and clearly prove the existence
of the chiral one-dimensional edge conduction along the prescribed DWs. The
proof-of-concept devices based on the reconfigurable CES and Landauer-Buttiker
formalism are exemplified for multiple-domain configurations with the
well-defined DW channels.
