This talk was part of the Workshop on "Spin-Orbit Entangled Quantum Magnetism" held at the ESI September 23 -- 27, 2024.

Quadrupolar orders can couple linearly to phonons leading to the possibility of probing and controlling multipolar magnets via phonons or via coupling to strain fields. We illustrate this physics in a number of multipolar magnets including Mott insulators with non-Kramers doublets as well in higher moment magnets with strong spin-orbit coupling. Our results employ Floquet-Magnus expansions and new numerical tools we have developed to generalize the usual spin-phonon dynamics to SU(N) dynamics coupled to phonons. Time-permitting, we will also discuss how these ideas may be used to tune magnon or triplon band topology.