Second-order topological magneto-optical effects in noncoplanar antiferromagnets

The second-order magneto-optical effects, represented by Voigt and Sch\"afer-Hubert are effective methods to detect the spin textures in antiferromagnets, whereas previous studies usually limited collinear antiferromagnets. In noncollinear characterized chirality have been revealed play a critical role many exciting physics. particular, first-order topological effects originated from scalar discovered recently. this work, using first-principles calculations group-theory analysis, we generalize cases, that is, taking noncoplanar $3Q$ state of $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Fe}}_{x}{\mathrm{Mn}}_{1\ensuremath{-}x}$ alloy as an example. conventional comparatively studied $1Q$ $2Q$ states alloy. addition, natural linear birefringence due crystal anisotropy is discussed strained $1Q, 2Q$, states, unique fingerprint for experimentally distinguishing identified. Our work brings insight into antiferromagnets also provides attractive material platform future experimental exploration.