The recent discovery of 2D magnets has revealed various intriguing phenomena due to the coupling between spin and other degree of freedoms (such as helical photoluminescence, nonreciprocal SHG). Previous research on the spin-phonon coupling effect mainly focuses on the renormalization of phonon frequency. Here we demonstrate that the Raman polarization selection rules of optical phonons can be greatly modified by the magnetic ordering in 2D magnet CrI$_3$. For monolayer samples, the dominant A$rm_{1g}$ peak shows abnormally high intensity in the cross polarization channel at low temperature, which is forbidden by the selection rule based on the lattice symmetry. While for bilayer, this peak is absent in the cross polarization channel for the layered antiferromagnetic (AFM) state and reappears when it is tuned to the ferromagnetic (FM) state by an external magnetic field. Our findings shed light on exploring the emergent magneto-optical effects in 2D magnets.
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