First-principles study of the magneto-Raman effect in van der Waals layered magnets

Two-dimensional (2D) van der Waals magnetic materials (or 2D magnets), such as chromium triiodide (CrI₃), exhibit various fascinating phenomena due to the coupling between spin and other degrees of freedoms, such as large magneto-optical Kerr effect, helical photoluminescence, giant second-order non-reciprocal optical effects, etc. The spin-phonon coupling in 2D magnets can also give rise to various important effects including the renormalization of phonon frequency and the dramatic change in Raman intensity for certain Raman modes. Although the sensitivity of the Raman modes to the interlayer magnetic order has been experimentally explored for CrI₃, there are some fundamental questions unanswered. To fully reveal the underlying mechanism governing the dependence of Raman intensity on the interlayer magnetic order in CrI₃, we carried out density functional theory (DFT) simulations of magneto-Raman scattering that is capable of describing the magnetic-order-dependent Raman intensities. More specifically, the spin-dependent anti-symmetric off-diagonal terms in Raman tensors are quantitatively calculated, allowing us to directly capture the Raman polarization selection rules at different magnetic orders. Our simulated Raman spectra versus magnetic order not only match experimental data well, but also explain why only certain Raman modes are spin-sensitive while the majority of phonon modes are not. Moreover, we also predict a new spin-dependent Raman mode in CrI₃ that has not yet been studied experimentally. Finally, we apply our magneto-Raman simulation capability to study another hot 2D magnet, MnBi₂Te₄, and reveal its spin-dependent Raman modes. Our computational work will guide further experimental investigation into magneto-Raman scattering of a wide range of 2D magnets.