Lattice dynamics and phase transition in ${\mathrm{CrI}}_3$ single crystals

The vibrational properties of ${\mathrm{CrI}}_3$ single crystals were investigated using Raman spectroscopy and were analyzed with respect to the changes of the crystal structure. All but one mode are observed for both the low-temperature $R\overline{3}$ and the high-temperature $C2/m$ phase. For all observed modes the energies and symmetries are in good agreement with DFT calculations. The symmetry of a single layer was identified as $p\overline{3}1/m$. In contrast to previous studies we observe the transition from the $R\overline{3}$ to the $C2/m$ phase at 180 K and find no evidence for coexistence of both phases over a wide temperature range.

Figure 1

Schematic representation of (a) the low-temperature $R\overline{3}$ and (b) the high-temperature $C2/m$ crystal structure of ${\mathrm{CrI}}_3$. Black lines represent unit cells.

Figure 2

(a) Compatibility relations for the ${\mathrm{CrI}}_3$ layer and the crystal symmetries. Raman spectra of (b) the low-temperature $R\overline{3}$ and (c) the high-temperature $C2/m$ crystal structure measured in parallel (open squares) and crossed (open circles) polarization configurations at 100 and 300 K, respectively. Red and blue solid lines represent fits of Voigt profiles to the experimental data.

Figure 3

Temperature dependence of the $A_g^1$ and $A_g^3$ phonon modes of the rhombohedral structure and the corresponding $A_g^2$ and $A_g^5$ modes of the monoclinic structure, respectively. (a) and (b) Raman spectra at temperatures as indicated. The spectra are shifted for clarity. Solid red lines represent Voigt profiles fitted to the data. (c) and (d) and (e) and (f) Temperature dependence of the phonon energies and linewidths, respectively. Both modes show an abrupt change in energy at the phase transition at 180 K.

Figure 4

Temperature dependence of the rhombohedral $A_g^4$ and $E_g$ modes. (a)–(c) Raman spectra in parallel (open squares) and crossed (open circles) light polarizations at temperatures as indicated. The spectra are shifted for clarity. Blue and red solid lines are fits of Voigt profiles to the data. Two spectra were analyzed simultaneously in two scattering channels with the integrated intensity as the only independent parameter. (d)–(f) Phonon energies obtained from the Voigt profiles. Each $E_g$ mode splits into an $A_g$ and a $B_g$ mode above 180 K.

Figure 5

Raman-active phonons in ${\mathrm{CrI}}_3$ for (a) the monoclinic phase hosting $A_g$ and $B_g$ modes and for (b) the rhombohedral phase hosting $A_g$ and $E_g$ modes. Blue and violet spheres denote Cr and I atoms, respectively. Solid lines represent primitive unit cells. Arrow lengths are proportional to the square root of the interatomic forces. The given energies are calculated for zero temperature.