  The quantized version of anomalous Hall effect realized in magnetic
topological insulators (MTIs) has great potential for the development of
topological quantum physics and low-power electronic/spintronic applications.
To enable dissipationless chiral edge conduction at zero magnetic field,
effective exchange field arisen from the aligned magnetic dopants needs to be
large enough to yield specific spin sub-band configurations. Here we report the
thickness-tailored quantum anomalous Hall (QAH) effect in Cr-doped (Bi,Sb)2Te3
thin films by tuning the system across the two-dimensional (2D) limit. In
addition to the Chern number-related metal-to-insulator QAH phase transition,
we also demonstrate that the induced hybridization gap plays an indispensable
role in determining the ground magnetic state of the MTIs, namely the
spontaneous magnetization owning to considerable Van Vleck spin susceptibility
guarantees the zero-field QAH state with unitary scaling law in thick samples,
while the quantization of the Hall conductance can only be achieved with the
assistance of external magnetic fields in ultra-thin films. The modulation of
topology and magnetism through structural engineering may provide a useful
guidance for the pursuit of QAH-based new phase diagrams and functionalities.
