General ab initio framework for chiral phonons induced by electronic order

Conventional ab initio methods fail to describe the emergence of chiral phonons driven by electronic ordering. Here, we develop an ab initio framework, grounded in molecular Berry curvature (MBC), that captures electronic-order-driven symmetry breaking in lattice dynamics and is applicable to both insulating and metallic magnets. Using Co$_3$Sn$_2$S$_2$ as a model system, we show that the MBC term simultaneously breaks time-reversal and mirror symmetries, enabling a quantitative reproduction of the experimentally observed phonon splittings. The analysis uncovers distinct microscopic origins for the $E_g$ and $E_u$ modes: the $E_g$ splitting is governed by MBC and is accurately described by our first-principles scheme, whereas the $E_u$ splitting is enhanced by the Fano resonance, consistent with its asymmetric spectral profile. Leveraging this framework, we further predict several candidates with chiral-phonon splitting. Our results establish a predictive route for identifying and understanding phonon magnetism, chiral phonons, and related Hall-type lattice responses from first principles.