  The effect of electronic correlations on the orbital magnetization in real
materials has not been explored beyond a static mean-field level. Based on the
dynamical mean-field theory, the effect of electronic correlations on the
orbital magnetization in layered ferromagnet VI$_3$ has been studied. A
comparison drawn with the results obtained from density functional theory
calculations robustly establishes the crucial role of dynamical correlations in
this case. In contrast to the density functional theory that leads to
negligible orbital magnetization in VI$_3$, in dynamical mean-field approach
the orbital magnetization is greatly enhanced. Further analysis show that this
enhancement is mainly due to the enhanced local circulations of electrons,
which can be attributed to a better description of the localization behavior of
correlated electrons in VI$_3$. The conclusion drawn in our study could be
applicable to a wide range of layered materials in this class.
