  Quantum anomalous Hall insulators are topologically characterized by non-zero
integer Chern numbers, the sign of which depends on the direction of the
exchange field that breaks time-reversal symmetry. This feature allows the
manipulation of the conducting chiral edge states present at the interface of
two magnetic domains with opposite magnetization and opposite Chern numbers.
Motivated by this broad understanding, the present study investigates the
quantum transport properties of a magnetized $Bi_2Se_3$ topological insulator
nanoribbon with a domain wall oriented either parallel or perpendicular to the
transport direction. Employing an atomistic tight-binding model and a
non-equilibrium Green's function formalism, we calculate the quantum
conductance and explore the nature of the edge states. We elucidate the
conditions leading to exact conductance quantization and identify the origin of
deviations from this behavior. Our analysis shows that although the conductance
is quantized in the presence of the horizontal domain wall, the quantization is
absent in the perpendicular domain wall case. Furthermore, the investigation of
the spin character of the edge modes confirms that the conductance in the
horizontal domain wall configuration is spin polarized. This finding
underscores the potential of our system as a simple three dimensional
spin-filter device.
