Theory of infrared magneto-optical effects from chiral phonons in solids

In crystals with broken time-reversal symmetry, zone-center phonons can acquire a finite angular momentum via velocity-dependent forces on the nuclei. Despite having the same order of magnitude as the electron spin angular momentum, the phonon angular momentum can be hard to detect because the frequency splitting is small. Here, by developing a theory of lattice magneto-optical effects in reflection and transmission, we show that infrared magnetic circular dichroism is a sensitive probe of zone-center phonon chirality. We evaluate the infrared magneto-optical Faraday, Kerr, and circular-dichroism spectra of CrI$_3$ from time-dependent density-functional theory in the adiabatic local-density approximation. We find sizeable circular dichroism from the infrared-active E$_u$ mode at $\approx 214$ cm$^{-1}$, even though the calculated splitting is only 0.22 cm$^{-1}$.