  In ionic materials, circularly polarized phonons carry orbital magnetic
moments that arise from circular motions of the ions, and which interact with
other magnetic moments or fields. Here, we calculate the orbital magnetic
moments of phonons in 35 different materials using density functional theory,
and we identify the factors that lead to, and materials that show, large
responses. We compute the resulting macroscopic orbital magnetic moments that
can be induced by the excitation of coherent phonons using mid-infrared laser
pulses, and we evaluate the magnitudes of the phonon Zeeman effect in a strong
magnetic field. Finally, we apply our formalism to chiral phonons, in which the
motions of the ions are intrinsically circular. The zoology presented here may
serve as a guide to finding materials for phonon and spin-phonon driven
phenomena.
