First-principles Study Of Layered CrCl₃ Vibrational Spectroscopy

The two-dimensional van der Waals magnetic material CrX3(X=Cl,Br and I)is a hot research field in condensed matter physics.Recent experiments have shown that layered CrX3 has thickness and stacking-dependent magnetism,but the mechanism remains unclear.The determination of its thickness and stacking-structure is the basis for understanding this interesting physical phenomenon.Raman and infrared spectroscopy is an important experimental tool to study the structure and other properties of layered materials.The theoretical study of the vibration spectrum of layered CrX3 is of great guiding significance for the analysis of experimental spectrum and the determination of structural information.In this paper,Raman and IR spectra of stacked CrCl3 with different thicknesses and thicknesses have been systematically studied from first principles.The structural symmetry,Raman tensor,and layer and polarization dependent Raman spectra have been analyzed emphatically,and their microscopic mechanisms have been elucidated.The main research contents are as follows:1.The high temperature phase C2/m and low temperature phase of CrCl3 were studied by different exchange correlation functionals,and compared with the experimental results,it is found that vdW functionals can predict the experimental crystal structure more accurately.We also calculate the stacking and exchange energies of the bilayer CrCl3.It is found that C2/m and R3 structures are at local minima and have a ferromagnetic ground state.2.The phonon spectra of monolayer,bilayer,trilayer and bulk CrCl3 are studied,the Raman model is analyzed,and the Raman intensity is calculated.The results show that the wave number and intensity of Raman spectrum increase with the increase of the number of layers and are explained by the classical model of coupled harmonic oscillator.At the same time,we also found that C2/m has higher vibration frequency than the structure.In particular,there is a frequency difference of 3 cm-1 between the first and fourth Raman peaks of the two structures,which can be used to characterize the two different stacking structures.Further analysis shows that the vibration mode of C2/m(R3)tends to be more in(out)layer and is dominated by the covalent bond(vdW force),which leads to the frequency difference of different structures.We also calculate the Raman tensor in detail and derive the Raman intensity formulas for different modes of polarization dependence.The results show that the Ag mode intensity in the R3 structure is independent of the polarization Angle,and the 1Eg and 2Eg mode is four times dependent on the polarization Angle,while the total Eg mode intensity is independent of the polarization Angle.The pattern of C2/m structure has quadruple symmetry but the Ag mode only two-fold symmetry,which is consistent with the experimental findings.3.Raman tensor is calculated and Raman intensity formulas for different modes of polarization dependence are derived.The results show that the Ag mode of R3 is independent of the polarization Angle,while the 1Eg and 2Eg modes have a quadruple symmetric polarization dependence.The total intensity of Eg mode formed by the sum of the two modes is independent of the polarization Angle.Bg mode of C2/m structure has quadruple symmetry while Ag has only double symmetry,which is consistent with the experimental findings.4.The infrared spectra of monolayer,bilayer,trilayer and bulk CrCl3 were studied.Four sharp infrared peaks were found in all the structures,which was consistent with the experimental results.The results also show that the C2/m bulk structure has one more peak with lower intensity than the R3 bulk structure,and this peak is composed of Au mode alone,without Bu mode.Compared with the few-layer structure,the fourth infrared peak wave number of the bulk structure is significantly different,which can also be used to distinguish the thickness of the sample.In this paper,the Raman spectra and infrared spectra of CrCl3 were systematically studied,which explained the experimental phenomenon well,and provided theoretical support for the further study of CrCl3 structure and stack dependent properties.It also provided a reference for the study of Raman spectra of other two-dimensional van der Waals magnetic materials.