  Modern theory of the orbital magnetization is applied to the series of
insulating perovskite transition metal oxides (orthorhombic YTiO$_3$,
LaMnO$_3$, and YVO$_3$, as well as monoclinic YVO$_3$), carrying a net
ferromagnetic (FM) moment in the ground state. For these purposes, we use an
effective Hubbard-type model, derived from the first-principles
electronic-structure calculations and describing the behavior of magnetically
active states near the Fermi level. The solution of this model in the
mean-field Hartree-Fock approximation with the relativistic spin-orbit coupling
typically gives us a distribution of the local orbital magnetic moments, which
are related to the site-diagonal part of the density matrix $\hat{\cal D}$ by
the "standard" expression $\boldsymbol{\mu}^0 = - \mu_{\rm B} \mathrm{Tr} \{
\hat{\textbf{L}} \hat{\cal D} \}$ and which are usually well quenched by the
crystal field. In this work, we evaluate "itinerant" corrections $\Delta
\boldsymbol{\cal M}$ to the net FM moment, suggested by the modern theory. We
show that these corrections are small and in most cases can be neglected.
Nevertheless, the most interesting aspect of our analysis is that, even for
these compounds, which are typically regarded as normal Mott insulators, the
"itinerant" corrections reveal a strong $\textbf{k}$-dependence in the
reciprocal space, following the behavior of Chern invariants. Therefore, the
small value of $\Delta \boldsymbol{\cal M}$ is the result of strong cancelation
of relatively large contributions, coming from different parts of the Brillouin
zone. We discuss details as well as possible implications of this cancelation,
which depends on the crystal structure as well as the type of the magnetic
ground state.
