Recent experiments establish that optical-frequency magnetic fields ($B_{\mathrm{opt}}$) exert measurable torque on ordered moments in magneto-optical media, while helicity-dependent optical drives induce non-thermal switching of magnetic and Chern domains in twisted van der Waals heterostructures. Rather than heralding an unconstrained breakdown of classical electrodynamics, these findings expose specific physical regimes where collective spin coherence and non-trivial band geometry alter the conventional light-matter coupling hierarchy.
In this perspective treatise, we formulate the microscopic conditions under which optical Zeeman driving couples to non-equilibrium topological invariants. Evaluating the high-frequency Magnus expansion for generic spin-orbit-coupled band structure, we demonstrate that cross-coupling between the vector potential and the optical magnetic field is governed by the spin-dependent velocity operator $\hat{v}_{\mathrm{spin}} = \nabla_k \varepsilon(k) \cdot \sigma$, generating a manifestly Hermitian secular Zeeman field at order $\mathcal{O}(\omega^{-1})$. We formulate the dimensionless operator ratio $\mu_{\mathrm{mix}}(k) \equiv \hat{H}_{\mathrm{mixed}}^{(1)} / \hat{H}_{\mathrm{electric}}^{(1)}$, showing that quenching the scalar kinetic dispersion does not eliminate electric interactions, but isolates the spin-dependent sector where mixed optomagnetic terms dominate.
@article{DeCeuster2026BeyondElectricDipole,
author = {Peter De Ceuster},
title = {Beyond Electric-Dipole Coupling: Optical Zeeman Torque, Floquet Gauge Dynamics, and Topological State Control},
journal = {Sig Labs Theoretical Physics & Quantum Optics Series},
year = {2026},
month = {September},
url = {https://peterdeceuster.uk/pen/zeeman},
note = {Published on peterdeceuster.uk}
}