  Quantum anomalous Hall effect (QAHE) has been experimentally realized in
magnetic topological insulator (MTI) thin films fabricated on magnetically
doped (Bi,Sb)2Te3. In a MTI thin film with the magnetic easy axis along the
normal direction (z-direction), orientations of magnetic dopants are randomly
distributed around the magnetic easy axis, acting as magnetic disorders. With
the aid of the non-equilibrium Green's function and Landauer-Buttiker
formalism, we numerically study the influence of magnetic disorders on QAHE in
a MTI thin film modeled by a three-dimensional tight-binding Hamiltonian. It is
found that, due to the existence of gapless side surface states, QAHE is
protected even in the presence of magnetic disorders as long as the z-component
of magnetic moment of all magnetic dopants are positive. More importantly, such
magnetic disorders also suppress the dissipation of the chiral edge states and
enhance the quality of QAHE in MTI films. In addition, the effect of magnetic
disorders depends very much on the film thickness, and the optimal influence is
achieved at certain thickness. These findings are new features for QAHE in
three-dimensional systems, not present in two-dimensional systems.
