We revisit the derivation of the orbital magnetization formula for periodic crystals in current density functional theory (CDFT). Our derivation computes the linear response of the energy density to a periodic magnetic field in the long-wavelength limit. We unveil a Ward identity which connects the current vertex to the derivative of the Kohn-Sham self-energy. It is confirmed that the orbital magnetization of the interacting solid can be computed exactly (in principle) from the self-consistent eigenfunctions and eigenvalues of the Kohn-Sham equation of CDFT.

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• Magnetic order
• Chiral magnets
• Crystalline systems
• Ferromagnets
• Bloch wave theory
• Density functional theory
• Green's function methods