Tuning inelastic light scattering via symmetry control in the two-dimensional magnet CrI₃

The coupling between spin and charge degrees of freedom in a crystal gives rise to magneto-optical effects with applications in the sensitive detection of local magnetic order, optical modulation and data storage. In two-dimensional magnets these effects manifest themselves in the large magneto-optical Kerr effect^1,2, spontaneous helical light emission^3,4 from ferromagnetic (FM) monolayers and electric-field induced Kerr rotation^5-7 and giant second-order non-reciprocal optical effects⁸ in antiferromagnetic (AFM) bilayers. Here we demonstrate the tuning of inelastically scattered light through symmetry control in atomically thin chromium triiodide (CrI₃). In monolayers, we found an extraordinarily large magneto-optical Raman effect from an A_1g phonon mode due to the emergence of FM order. The linearly polarized, inelastically scattered light rotates by ~40°, more than two orders of magnitude larger than the rotation from the magneto-optical Kerr effect under the same experimental conditions. In CrI₃ bilayers, the same phonon mode becomes Davydov-split into two modes of opposite parity, which exhibit divergent selection rules that depend on inversion symmetry and the underlying magnetic order. We demonstrate the magneto-electrical control over these selection rules by activating or suppressing Raman activity for the odd-parity phonon mode and the magneto-optical rotation of scattered light from the even-parity phonon mode. Our work underlines the unique opportunities provided by two-dimensional magnets to control the combined time-reversal and inversion symmetries to manipulate Raman optical selection rules and for exploring emergent magneto-optical effects and spin-phonon coupled physics.