The quantum anomalous Hall (QAH) effect in a magnetic topological insulator (TI) represents a new state of matter originating from the interplay between topology and magnetism. The defining characteristics of the QAH ground state are the quantized Hall resistivity (ρ_{yx}) and vanishing longitudinal resistivity (ρ_{xx}) in the absence of an external magnetic field. A fundamental question concerning the QAH effect is whether it is merely a zero-magnetic-field quantum Hall (QH) effect or if it can host unique quantum phases and phase transitions that are unavailable elsewhere. The most dramatic departure of the QAH systems from other QH systems lies in the magnetic disorders that induce spatially random magnetization. Because disorder and magnetism play pivotal roles in the phase diagram of two-dimensional electron systems, the high degree of magnetic disorders in QAH systems may create novel phases and quantum critical phenomena. In this work, we perform systematic transport studies of a series of magnetic TIs with varied strength of magnetic disorders. We find that the ground state can be categorized into two distinct classes: the QAH phase and the anomalous Hall (AH) insulator phase, as the zero-magnetic-field counterparts of the QH liquid and Hall insulator phases in the QH systems. In the low-disorder limit of the QAH phase, we observe a universal quantized longitudinal resistance ρ_{xx}=h/e^{2} at the coercive field. In the AH insulator regime, we find that a magnetic field can drive it to the QAH phase through a quantum critical point with scaling behaviors that are distinct from those in the QH phase transition. We propose that the transmission between chiral edge states at domain boundaries, tunable by magnetic disorder and magnetic fields, is the key for determining the QAH ground state.
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