Fig. 1: Concept of NLMO effects.
From: Giant and controllable nonlinear magneto-optical effects in two-dimensional magnets

Magnets with non-centrosymmetric crystal structures exhibit both the crystal SHG and the MSHG due to the simultaneous breaking of \({{{\mathcal{P}}}}\), \({{{\mathcal{T}}}}\) and \({{{\mathcal{PT}}}}\) symmetries. The crystal SHG is unaffected by the magnetization direction reversal while the MSHG changes the sign. Thus, the two terms can constructively (left panel) or destructively (right panel) interfere with each other for the positive and negative magnetization directions, respectively, which leads to NLMO effects. The red and blue arrows represent magnetic orders related by \({{{\mathcal{T}}}}\) operation.