Han Ge

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.

Geometrically frustrated magnets exhibit exotic excitations due to competing interactions between spins. The spinel compound MgCr₂O₄, a three-dimensional Heisenberg antiferromagnet, hosts both spin-wave and spin-resonance modes, but the origin of its resonant excitations remains debated. Suppressing magnetic order via non-magnetic doping can help isolate these modes in neutron scattering studies. We synthesized Ga³⁺ and Cd²⁺-doped MgCr₂O₄ via solid-state reaction and analyzed their structure and magnetism. Ga³⁺ doping (0–20%) causes anomalous lattice shrinkage due to site disorder from Ga³⁺ occupying both Mg²⁺ and Cr³⁺ sites. Magnetically, Ga³⁺ doping drives the system from the antiferromagnetic order to a spin-glass state, fully suppressing magnetic ordering at 20% doping. In contrast, Cd²⁺ replaces only Mg²⁺, expanding the lattice and meantime inducing strong spin-glass behavior. At 10% Cd²⁺, long-range antiferromagnetic order is entirely suppressed. Thus, 10% Cd-doped MgCr₂O₄ offers an ideal platform to study the resonant magnetic excitations without any spin-wave interference.