Ab Initio Theory of Large Phonon Magnetic Moments Induced by Electron-Phonon Coupling in Magnetic Materials

Abstract: Chiral phonons, characterized by nonzero angular momenta and magnetic moments, have attracted extensive attention. However, a long-standing critical issue in this field is the lack of an approach to accurately calculate phonon magnetic moments resulting from electron-phonon coupling (EPC) in realistic materials. Here, based on the linear response framework, we develop an ab initio theory for calculating EPC-induced magnetic properties of phonons, applicable to both insulating and metallic materials. Then, we evidently demonstrate EPC-induced large phonon magnetic moments and phonon Zeeman splittings resulting from spin-phonon coupling in magnetic metals. Interestingly, these splittings can open substantial topologically nontrivial phonon gaps, generating intrinsic phonon Chern states. Further, by constructing an inertially decoupled lattice model, we predict candidate materials exhibiting such intrinsic phonon Chern states with robust edge phonon currents which are proposed to detect neutral particles, such as dark matter particles. Our work enables \emph{ab initio} calculations for EPC-induced magnetic properties of phonons and long-sought magnetic phonon spectra.