Relativistic interaction Hamiltonian coupling the angular momentum of light and the electron spin

On the basis of the Dirac equation, a relativistic interaction Hamiltonian is derived which linearly couples the angular momentum density $\mathit{j}$ of the electromagnetic (EM) field and the electron's spin $\mathbf{\sigma }$. The expectation value of this novel Hamiltonian is demonstrated to be precisely the recently proposed energy coupling the EM angular momentum density and magnetic moments [A. Raeliarijaona et al., Phys. Rev. Lett. 110, 137205 (2013)]. This previously overlooked Hamiltonian is also found to naturally result in the exact analytical form of the interaction energy inherent to the inverse Faraday effect, therefore demonstrating its relevance and easy use for the derivation of other complex magneto-optical and magnetoelectric effects originating from electron spin-light angular momentum couplings.