I. INTRODUCTION Soon after the observation of the Hall effect, Hall also observed the anomalous Hall effect (AHE) 1,2 in ferromagnetic metals, where the Hall resistance arises from the spin- orbit coupling (SOC) between electric current and magnetic moments, even in the absence of external magnetic field. Recent progress on the mechanism of AHE have established a link between the AHE and the topological nature of Hall current due to SOC by adopting the Berry-phase concepts $^{3–6}$, in close analogy to the intrinsic spin Hall effect$^{8,9}$. Given the experimental discovery of the quantum Hall 7 and quantum spin Hall (QSH) effects $^{10,11}$, it is natural to ask whether the AHE can also be quantized in a topological magnetic insulator, without the external magnetic field and the associated Landau levels. A simple mechanism for the QAH insulator has been proposed in a two-band model of a two dimensional (2D) magnetic insulator $^{12}$. In the limit of vanishing spin-orbit coupling, and large enough exchange splitting, the majority spin band is completely filled and minority spin band is empty. When the exchange splitting is reduced, the two bands intersect each other, leading to a band inversion, say near the Γ point. The degeneracy at the interaction region can be removed by turning on the SOC, giving rise to an insulator state with a topologically non-trivial band structure characterized by a finite Chern number and chiral edge states characteristic of the QAH state (see figures (1) and (2) of Ref. $^{12}$). In alternative mechanisms of realizing the quantum Hall state without an external magnetic field, bond currents on a honeycomb lattice has been proposed $^{13}$, and the localization of the band electron could also give rise to a quantized plateau $^{14}$. However, these mechanisms seem harder to realize experimentally. Therefore, the crucial ingredients for realizing an QAH state are: (1) a ferromagneti- cally ordered 2D insulator which breaks the time-reversal symmetry; (2) a band inversion transition with strong SOC. In comparison with the QSH state, which satisfies the second condition $^{10,11}$, the first condition of the ferromagnetic order in an insulating state is harder to realize. However, the QSH insulators are usually good starting candidates for finding QAH effect due to its proximity to the band inversion. Given the QSH effect in HgTe quantum wells 10,11 through a band inversion transition by varying the thickness of the quantum well, the magnetically doped HgMnTe has been proposed as a candidate for the QAH insulator $^{15}$. Unfortunately, the Mn moments do not order spontaneously in HgMnTe, and an additional, 3