  Based on standard perturbation theory, we present a full quantum derivation
of the formula for the orbital magnetization in periodic systems. The
derivation is generally valid for insulators with or without a Chern number,
for metals at zero or finite temperatures, and at weak as well as strong
magnetic fields. The formula is shown to be valid in the presence of
electron-electron interaction, provided the one-electron energies and wave
functions are calculated self-consistently within the framework of the exact
current and spin density functional theory.
