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We study Raman response of Heisenberg antiferromagnets on the$\mathbf{C}_\mathrm{5v}$ Penrose and $\mathbf{C}_\mathrm{8v}$ Ammann-Beenkerlattices within and beyond the Loudon-Fleury second-order perturbation schemeintending to explore optical features peculiar to quasiperiodic magnets. Withinthe Loudon-Fleury mechanism, we find one and only Raman-active mode of$\mathrm{E}_2$ symmetry without any dependence on linear incident and scatteredpolarizations. Beyond the Loudon-Fleury mechanism, two more symmetry species$\mathrm{A}_1$ and $\mathrm{A}_2$ are activated via dynamic ring exchange andchiral spin fluctuations, respectively, which can be extracted by the use ofcircular as well as linear polarizations. We employ Green's functions on onehand and configuration-interaction wavefunctions on the other hand to calculatethe multimagnon contributions to inelastic light scatterings. Demonstrating thegreat advantage of the configuration-interaction scheme, we reveal that a majorportion of the Shastry-Shraiman fourth-order Raman intensity is mediated bymultimagnon fluctuations.

Polarized Raman Response of Two-Dimensional Quasiperiodic Antiferromagnets: Configuration-Interaction versus Green's Function Approaches