Higher-order Angular Momentum Transport of Alteraxial Phonons in 2D Magnets
The coupling between lattice vibrations and magnetic order in two-dimensional (2D) magnets gives rise to a variety of physical phenomena, among which magnetic effects of axial phonons carrying phonon angular momentum (PAM) have attracted considerable interest. However, a systematic classification of axial phonons in 2D magnets that covers their multipolar patterns and the resulting transport manifestations remains largely unexplored. Here, based on symmetry analysis, we classify all 2D magnetic point groups by their long-wavelength PAM wave patterns. Beyond the s-wave axial phonon, we identify alteraxial phonons with p-, d-, f-, g-, and i-wave multipolar textures, characterized by 1, 2, 3, 4, and 6 zero-PAM nodal lines, respectively. We then develop a theory of nonlinear PAM transport driven by a temperature gradient and derive two selection rules: a parity selection rule that determines whether the response occurs at even or odd orders, and an angular-harmonic selection rule that fixes the lowest allowed order for each wave pattern. The multipolar PAM patterns and selection rules are exemplified by two effective lattice models realizing f-wave and d-wave PAM patterns, respectivley. The angular dependence of the nonlinear PAM current reflects the underlying multipolar PAM texture, offering a signature for experiments. Our results establish a symmetry-guided framework for detecting and utilizing higher-order PAM textures in 2D magnets.