Direct Raman observation of the quantum metric in a quantum magnet

TL;DR

This study demonstrates that circularly polarized Raman spectroscopy can directly measure the quantum metric in a quantum magnet, revealing its microscopic origin and linking it to observable chiral phonon phenomena.

Contribution

It provides the first direct experimental observation of the quantum metric using Raman spectroscopy, unifying measurements of Berry curvature and quantum metric in a single technique.

Findings

Chiral splitting and frequency shift collapse onto a single curve.

Quantum metric change is captured by the same microscopic origin as Berry curvature.

Data fit well with a quadratic empirical relation.

Abstract

The quantum geometric tensor (QGT) 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 K2Co(SeO3)2, where the field-odd chiral splitting and the field-even center-frequency shift collapse onto a single curve across temperature and magnetic field, revealing a common microscopic origin for both observables. Since the chiral splitting reflects the Berry curvature, the concomitant even component, arising from the same microscopic origin, captures the field-induced change of the quantum metric, corresponding to the diagonal Born-Oppenheimer correction. Across two resolvable Eg modes, the unified data are well captured by a simple empirical quadratic relation. These results establish Raman spectroscopy as a direct probe of the quantum metric and an operational decomposition of quantum geometry within a single measurement.