  Spin-orbit coupling introduces chirality into electronic structure. This can
have profound effects on the magnetization induced by orbital motion of
electrons. Here we derive a formula for the orbital magnetization of
interacting electrons in terms of the full Green's function and vertex
functions. The formula is applied within dynamical mean-field theory to the
Kane-Mele-Hubbard model that allows both topological and trivial insulating
phases. We study the insulating and metallic phases in the presence of an
exchange magnetic field. In the presence of interactions, the orbital
magnetization of the quantum spin Hall insulating phase with inversion symmetry
is renormalized by the bulk quasi-particle weight. The orbital magnetization
vanishes for the in-plane antiferromagnetic phase with trivial topology. In the
metallic phase, the enhanced effective spin-orbit coupling due to the
interaction sometimes leads to an enhancement of the orbital magnetization.
However, at low doping, magnetization is suppressed at large interaction
strengths.
