Structural Monoclinicity and Its Coupling to Layered Magnetism in Few-Layer $\mathrm{CrI_{3}}$

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.