Light-Matter-Coupling formalism for magnons: probing quantum geometry with light

Nontrivial quantum geometry is a key feature of the wavefunctions of collective magnetic excitations in topological systems, but accessing it experimentally remains an open challenge. While Raman circular dichroism (RCD) has emerged as a promising probe, the fundamental link between the RCD and magnon quantum geometry has remained unsettled, and complicated by the fact that magnons are charge neutral. Here, we identify when and why this link exists. We show that, under broad conditions, the Fleury-Loudon Raman vertex can be obtained directly from a light-matter coupling expansion of the effective magnon Hamiltonian, bypassing the conventional microscopic derivation based on virtual electronic processes. This yields an analytical connection between the RCD and the Berry curvature of magnon bands. Applied to monolayer CrI\textsubscript{3}, our theory predicts finite temperature signatures of topological magnons in the RCD. These results establish a general route to quantum-geometry sensitive optical probes in magnonic systems.