Effect of thickness and stacking order on Raman spectrum of layered CrCl₃

Layer- and stacking-dependent physical properties discovered in van der Waals materials have attracted a lot of attention recently. In this work, we have investigated the Raman spectrum of layered magnetic CrCl₃with different atomic thickness and stacking order from first principles. Our study indicates Raman shift ofR3̄andC2/mphase is near degenerate except that the first and fourth Raman resonant modes exhibit a marked peak difference about 3 cm^-1, which can be understood by stacking-dependent vibrational eigenvectors. Moreover, we also find that both frequency and intensity of Raman modes of few-layer CrCl₃increase with the number of layers simultaneously. Furthermore, the Raman tensor and polarization-dependent Raman intensity are also evaluated in details, which are found to be in good agreement with available experiments. Our results proposed several distinctive signals to identify layer number and stacking order of layered CrCl₃, which will provide an important reference to further experimental study.