Raman Circular Dichroism Reveals Higher-Order Quantum Geometry of Magnons

Abstract

We develop a gauge-invariant framework that relates two-magnon Raman circular dichroism (RCD) to higher-order magnon quantum geometry. In the magnon band basis, the Raman operator decomposes into interband Berry connections, their covariant derivatives, and products of successive connections, generating higher-order, multi-state geometric tensors beyond the conventional single-band quantum metric and Berry curvature. Applying this framework to a field-polarized Kitaev magnet, we show that higher-order geometric tensors govern the dichroic response. Our results establish RCD as a spectroscopic probe of generalized magnon quantum geometry.