Orbital magnetization and magnetic susceptibility in an interacting Rashba model

We study orbital magnetization and magnetic susceptibility in an interacting Rashba model. This model serves as a test of our formulas for orbital magnetization and magnetic susceptibility of interacting electrons at Β=0. The single particle Hamiltonian can be viewed as a massive Dirac particle with additional p² term. In the non-interacting case, we show that the orbital magnetization and the magnetic susceptibility computed analytically at small Β match those from the Β=0 formulas. When we add interactions within the self-consistent Hartree-Fock approximation, we take advantage of translation and rotation symmetry and reduce the self-consistent equations to three coupled 1D integral equations. We can solve these equations numerically to a high accuracy using a collocation method and obtain energy Ε(Β=0) and orbital magnetization Μ(Β=0). Finally, we numerically solve the self-consistent equations at Β≠0 at the same density utilizing continuous magnetic translation symmetry. The total energy as a function of the Β field at Β→0 shows an excellent agreement with Ε(Β=0)−Μ(Β=0)B, providing a non-trivial test of our results.