Alteraxial Phonons in Collinear Magnets

Axial phonons, carrying angular momentum through rotational lattice vibrations, offer a promising platform for exploring phonon-magnetic coupling effects. However, how the interplay of lattice and magnetism determine the phonon angular momentum (PAM) of axial phonons remains elusive. Here, based on magnetic point group theory, we establish a symmetry framework to classify phonons in collinear magnets (e.g. ferromagnets, antiferromangets, altermagnets) into three distinct categories: ferroaxial, antiferro-nonaxial, and alteraxial phonons, which are distinguished by their different PAM patterns. Beyond the ferroaxial phonons featuring $s$-wave PAM, we reveal a complete series of alteraxial phonons, characterized by higher-order-wave PAM patterns ranging from $p$- to $j$-wave. Notably, alteraxial phonons are not limited to altermagnets, but also emerge in ferromagnets and antiferromagets. Our high-throughput search predicts hundreds of candidate magnetic materials hosting alteraxial phonons. Ab initio calculations on representative magnets further confirm the existence and distinct symmetry-enforced nodal structures of PAM in alteraxial phonons. Our work provides a complete classification for axial phonons in collinear magnetic systems and paves the way for engineering magneto-phononic phenomena.