Magnetic circular dichroism of THz modes and selection rules of Raman-active optical phonons in the polar altermagnet candidate ce{Mn2Mo3O8}

We investigated the magnetic and vibrational excitations in the collinear altermagnet candidate \ce{Mn2Mo3O8} by temperature dependent Raman scattering and magneto-optical THz time-domain transmission spectroscopy. By comparison to \textit{ab initio} calculations accurately capturing the eigenfrequencies of the vibrational eigenmodes, we identify all optical phonons, including the lowest-lying Raman modes of $A_1$ and $E_2$ type, which had remained elusive in a previous Raman study. Moreover, we compare the selection rules for optically active phonons in the paramagnetic and the magnetically ordered phases of \ce{Mn2Mo3O8} and analyze the Raman selection rules with respect to pseudo-angular momentum conservation. No evidence of the expected splitting of the degenerate paramagnetic $E_2$ optical phonons into modes with circular polarization upon magnetic ordering could be resolved, likely due to weak spin-orbit coupling typical for Mn$^{2+}$. In contrast, we observe strong magnetic circular dichroism at a broad THz excitation band, emerging in the magnetically ordered state. This band, potentially originating from two-magnon excitations, is only electric-dipole active and features a field-dependent two-component fine structure. Its magnetic circular dichroism vanishes above the spin-flop transition at 4~T.