Ferromagnetic Order in Relativistic Quantum Mechanics

The fully relativistic Dirac theory of the electron has been celebrated for predicting the spin magnetic moment of the electron with the correct g factor g = 2 that emerges in the weakly relativistic limit to the Dirac theory often called the Pauli equation.  In ferromagnetically ordered solids, g becomes the prefactor for the spin magnetization.  Interestingly, a spin magnetic moment is absent in the actual Dirac equation; but the interaction of the electrons with a magnetic field is entirely accounted for via the minimal coupling to the vector potential for the magnetic field (i.e., we have g = 0 in the Dirac equation).  We show [1] how the observable magnetization in ferromagnetically ordered solids becomes a purely orbital magnetization in the Dirac theory, focusing for conceptual clarity on magnetic nanostructures.

[1] R. Winkler and U. Zülicke, Phys. Rev. Research 2, 043060 (2020)