Orbital Magnetization and Magnetic Susceptibility of Interacting Electrons

We present a rigorous derivation of the orbital magnetization for interacting electrons within the self-consistent Hartree-Fock approximation. Our method also allows us to derive formulas for the orbital magnetic susceptibility. The results are expressed entirely in terms of the self-consistent wave functions and the Hartree-Fock energy spectrum at zero magnetic field. We find that the formula for the orbital magnetization is the same as in the noninteracting case, provided that the Hamiltonian and Bloch wave functions are replaced by their Hartree-Fock counterparts. By contrast, the orbital magnetic susceptibility contains an additional interaction-induced contribution that cannot be obtained by such a replacement. We test the formulas on an interacting Rashba model, finding an agreement with calculations performed at a small but nonzero external magnetic field.