Group theory analysis of phonons in monolayer chromium trihalides and their Janus structures.

A contrastive investigation of the symmetry aspects of phonons in monolayer chromium trihalides and their Janus structures Y 3 -Cr 2 -X 3 (X, Y = F, Cl, Br, I) was presented within group theory. We classified all phonon vibration modes at the Brillouin-zone center ( Γ ) into irreducible representations. The infrared and Raman activity of optic phonons, Raman tensors, and the possible polarization assignments of Raman active phonons are further predicted. We clarify the discrepancy concerning the Raman and infrared activity of optic modes in monolayer CrI 3 . It is also found that the Raman and infrared spectra are exclusive for X 3 -Cr 2 -X 3 but coincident for Janus Y 3 -Cr 2 -X 3 . This distinction plays a vital role in optic spectra identification of the Janus Y 3 -Cr 2 -X 3 monolayer from the X 3 -Cr 2 -X 3 monolayer. To demonstrate the origin of phonon chirality and magnetism intuitively, we derive the symmetry-matched phonon eigenfunctions and the corresponding schematic representations of the eigenvectors for both the F 3 -Cr 2 -I 3 and I 3 -Cr 2 -I 3 monolayers. Our analysis indicates that the spin-phonon coupling, the magneto-optical effect of infrared and Raman active phonons, and the phonon chirality could be observed in the Janus Y 3 -Cr 2 -X 3 monolayer more easily than in the X 3 -Cr 2 -X 3 monolayer. Our results thus provide a detailed guiding map for experimental identification and characterization of the Janus Y 3 -Cr 2 -X 3 monolayer.