  The modern theory of orbital magnetization (OM) was developed by using
Wannier function method, which has a formalism similar with the Berry phase. In
this manuscript, we perform a numerical study on the fate of the OM under
disorder, by using this method on the Haldane model in two dimensions, which
can be tuned between a normal insulator or a Chern insulator at half filling.
The effects of increasing disorder on OM for both cases are simulated. Energy
renormalization shifts are observed in the weak disorder regime and
topologically trivial case, which was predicted by a self-consistent T-matrix
approximation. Besides this, two other phenomena can be seen. One is the
localization trend of the band orbital magnetization. The other is the
remarkable contribution from topological chiral states arising from nonzero
Chern number or large value of integrated Berry curvature. If the fermi energy
is fixed at the gap center of the clean system, there is an enhancement of |M|
at the intermediate disorder, for both cases of normal and Chern insulators,
which can be attributed to the disorder induced topological metal state before
localization.
