Formulation of the orbital magnetic moment in multiorbital tight-binding models: Application to the Inverse Faraday effect

The inverse Faraday effect is one of the magneto-optical effects where static magnetization is induced in materials by irradiation of circularly polarized light. The magnetization can be broadly classified into spin and orbital magnetization. Furthermore, the orbital magnetization consists of the intrasite orbital magnetization coming from the orbital angular momentum of each atom and the intersite orbital magnetization coming from itinerant electrons. Previous theoretical studies on the inverse Faraday effect in metallic systems include the Dirac electron system [1,2] and the electron system with Rashba spin orbit coupling [3,4]. However, these studies often discussed each contribution to magnetization separately, and it remains unclear which contribution is significant.

In this study, we first establish a theoretical formulation of the orbital magenetic moment in multiorbital tight-binding models [5]. We reveal that the electric dipole moment of Wannier orbitals contributes to the orbital magnetic moment. The derived formulation for the magnetic moment is applied to an s-p tight-binding model, considered as a minimal model of the inverse Faraday effect. We find that the response of orbital magnetization is larger than that of spin magnetization. Furthermore, we find the magnitude of the three types of orbital magnetization can be comparable. These results emphasize the importance of multiorbital effects and equal-footing treatment of all contributions in the inverse Faraday effect.