Pseudochiral Phonons from Octupolar Magnetic Order

Motivated by the recent discovery of anomalously large magnetic response of chiral phonons in dipolar magnets, we introduce the concept of pseudochiral phonons which are shown to emerge in multipolar magnets. We consider Raman active quantum phonons, such as doublet E_{g} phonons (d_{x^{2}-y^{2}},d_{3z^{2}-r^{2}}) in cubic crystals, which feature a symmetry-allowed linear coupling to local quadrupolar moments. We show that distinct multipolar orders can imprint distinct patterns of degeneracy breaking for phonons, with quadrupolar orders favoring nonchiral eigenmodes and time-reversal breaking octupolar orders favoring unconventional pseudochiral phonons. We compute the temperature dependent phonon matrix Green's function using a path integral approach where "fast" phonon modes sense "slow" pseudospin fluctuations over a thermal background sampled using Monte Carlo simulations. We propose helicity-resolved Raman spectroscopy of these pseudochiral phonons as a probe of hidden octupolar order in quantum materials such as Ba_{2}CaOsO_{6} and PrV_{2}Al_{20}.