Direct Raman Observation of the Quantum Metric in a Quantum Magnet

The quantum geometric tensor unifies the Berry curvature (its imaginary part) and the quantum metric (its real part), yet Raman studies of chiral phonons have so far accessed only the former. We perform circularly polarized Raman spectroscopy on the quantum magnet K_{2}Co(SeO_{3})_{2}, where the field-odd chiral splitting Δω and the field-even center shift δω_{c} collapse onto a single curve across temperature and magnetic field, revealing a common microscopic origin for both observables. Since Δω reflects the Berry curvature, the concomitant even component δω_{c}, arising from the same microscopic origin, captures the field-induced change of the quantum metric-the diagonal Born-Oppenheimer correction. Across two resolvable E_{g} modes, the unified data are well captured by a simple empirical relation, δω_{c}=γ(Δω)^{2}. These results establish Raman spectroscopy as a direct probe of the quantum metric and an operational decomposition of quantum geometry within a single measurement.