  Using polarization-resolved Raman spectroscopy, we investigate layer number,
temperature, and magnetic field dependence of Raman spectra in one- to
four-layer $\mathrm{CrI_{3}}$. Layer-number-dependent Raman spectra show that
in the paramagnetic phase a doubly degenerated $E_{g}$ mode of monolayer
$\mathrm{CrI_{3}}$ splits into one $A_{g}$ and one $B_{g}$ mode in N-layer (N >
1) $\mathrm{CrI_{3}}$ due to the monoclinic stacking. Their energy separation
increases in thicker samples until an eventual saturation.
Temperature-dependent measurements further show that the split modes tend to
merge upon cooling but remain separated until 10 K, indicating a failed attempt
of the monoclinic-to-rhombohedral structural phase transition that is present
in the bulk crystal. Magnetic-field-dependent measurements reveal an additional
monoclinic distortion across the magnetic-field-induced layered
antiferromagnetism-to-ferromagnetism phase transition. We propose a structural
change that consists of both a lateral sliding toward the rhombohedral stacking
and a decrease in the interlayer distance to explain our experimental
observations.
