Many-body theory of magnetization of Bloch electrons in the presence of spin-orbit interactions

We derive a theory of magnetization of an interacting electron system in the presence of a periodic potential, spin-orbit interaction and an applied magnetic field in the paramagnetic limits. Starting from a thermodynamic potential, which includes both the quasi-particle and correlation contributions, we show that modifications brought about by the electron-electron interactions for the magnetization in the quasi-particle approximation is precisely cancelled by the contributions due to electron correlations.This is in contrast to the explicit many-body effects seen in case of the magnetic susceptibility and the Knight-shift. The magnetization is expressed as a product of the spin-density and the effective g-factor, mainly due to the spin-orbit interaction. We show the importance of self-energy corrections on the single-particle energy spectrum by considering a variant of the Hubbard Hamiltonian in momentum space.