Swati Chaudhary, Carl P. Romao, Dominik M. Juraschek
Circularly polarized phonons conventionally carry an angular momentum and a magnetic moment arising from circular motions of the atoms. Here, we present three anomalous cases that lead to phonon magnetic moments, which cannot be described in the conventional framework: , which exhibit magnetic responses despite only carrying pseudoangular momentum, , in which a magnetic moment is produced despite vanishing angular momentum, and , which make the phonon angular momentum and magnetic moment noncollinear. Our results shed light on the origin and nature of phonon magnetism and suggest the existence of phononomagnetic hidden order.