First-principles theory of phonon magnetic moment

Chiral phonons have recently been shown to possess finite magnetic moment that consists of both nuclei and electron contributions. Classical (using Born effective charge) and quantum theories for the electron’s contribution have both been developed. However, the two theories carry essential differences in handling the geometric effects, and quantitative comparisons between the two theories are missing in realistic materials. Here, we developed a first-principles scheme to calculate phonon magnetic moment from quantum theory. We found observable magnetic moments of chiral phonon modes in a gated two-dimensional material. In contrast, the magnetic moments vanish according to classical theory. This contrast highlights the central role of geometric effects in phonon magnetic moments. In addition, the magnetic moments have significant electric-field tunability and mode selectivity. Our numerical methods and predictions open a new route to finding dynamical multiferroicity in realist material systems.