Dynamical Effective Hamiltonian for Second Harmonic Generation in Quantum Magnets.

Although Second Harmonic Generation is a promising and widely used method recently for studying 2D magnetic materials that reveals different magnetic and electronic phases [1][2], the quantitative analysis of the full SHG tensor is currently challenging, because it requires accurate treatment of the ground and excited states, which can be influenced by many-body correlations. We thus developed an Ab-initio approach towards quantitative analysis of SHG in insulating magnets and so we can compute SHG response with respect to polarization angle at any wavelength of potential interest for experimental investigation. We benchmark our method using NiI₂, a multiferroic 2D van der Waals antiferromagnet, and showed SHG response for NiI₂ to compare our findings with existing experimental studies [3]. Real and imaginary parts are found to be distinct. We also identify the excitation pathways for d-d → LMCT or LMCT → d-d transitions to specify which spin couplings are in resonance or off-resonance with the incident light.

1. Sun, Z., Yi, Y., Song, T. et al. Giant nonreciprocal second-harmonic generation from antiferromagnetic bilayer CrI₃. Nature 572, 497–501(2019)

2. Liu, Q., Su, W., Gu, Y. et al. Surprising pressure-induced magnetic transformations from helimagnetic order to antiferromagnetic state in NiI₂. Nat Commun 16, 4221(2025)

3. Song, Qian, et al. Evidence for a single-layer van der Waals multiferroic.Nature 602.7898(2022): 601-605