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

We establish a theoretical formulation of the orbital magnetic moment in multiorbital tight-binding models, focusing on the role of the electric dipole. We demonstrate that the total magnetic moment can be decomposed into several contributions in multiorbital tight-binding models generally. In particular, we reveal that the electric dipole moment of Wannier orbitals also contributes to the orbital magnetic moment, which is not included in the conventional expression for the orbital magnetic moment in lattice systems. The derived formulation for the magnetic moment is applied to the inverse Faraday effect (IFE), a phenomenon where circularly-polarized light induces a magnetic moment. To account for all possible contributions, we adopt an $s$-$p$ tight-binding system as a minimal model for studying the IFE. Using an analytical approach based on the Schrieffer-Wolff transformation, we clarify the physical origins of these contributions. Additionally, we quantitatively evaluate each contribution on an equal footing through a numerical approach based on the Floquet formalism. Our results reveal that the orbital magnetic moment exhibits a significantly larger response compared to the spin magnetic moment, with all contributions to the orbital magnetic moment being comparable in magnitude. These findings highlight the essential role of orbital degrees of freedom in the IFE.