A multipole symmetry framework for phonon models shows that ferroaxial order produces hidden sublattice chiral phonons while polar order yields net global chirality.
Cluster Toroidal Multipoles Formed by Electric- Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca 5Ir3O12
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Effective phonon models based on symmetry-adapted multipole basis -- Hidden chiral phonon angular momentum splitting in ferroaxial systems
A multipole symmetry framework for phonon models shows that ferroaxial order produces hidden sublattice chiral phonons while polar order yields net global chirality.