Magnetic field-driven instabilities of chiral phonons

Recent experiments have shown that phonons can possess large effective magnetic moments, leading to a Zeeman splitting in an applied magnetic field. We demonstrate that increasing the Zeeman splitting beyond the phonon frequency drives a structural instability, leading to a spontaneously ordered phonon displacement. Increasing the field further, the system's symmetry is restored via a second phase transition. These effects are strongest at low temperatures and are shown to be suppressed completely for high enough temperatures. We develop specific models for triangular, square, and cubic lattices and study the dynamical and static properties of the ordered phases and their experimental signatures