We investigate the phase diagram of a two-dimensional magnetic topological system in the parameter space of uncorrelated Anderson disorder and Zeeman splitting energy. In the absence of disorder, the system undergoes the phases of higher-order topological insulators (HOTIs), Chern insulators (CIs) with Chern numbers = 2 and = 1, and band insulators successively with enhancing Zeeman energy. The phase boundary separating these phases is found to be strongly deformed by the disorder, which leads to several topological Anderson insulators. Specifically, there exist phase transitions between CI with = 2 and HOTI, and between CIs with = 1 and = 2. For the former one, it is in fact a phase transition between first-order and second-order topological phases. Besides, these disorder induced phase transitions are well explained by self-consistent Born approximation.
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