Point-group selection rules and universal momentum-transfer dependencies for inelastic neutron scattering on molecular spin clusters

Recent significant progress in inelastic neutron scattering (INS) has rendered this technique even more useful for the characterization of magnetic systems, including molecular spin clusters. By so-called four-dimensional INS on single-crystal probes, excitation spectra can be recorded in large portions of momentum-transfer (Q) and energy-transfer (E) space. Spin-selection rules permit $\mathrm{\ensuremath{\Delta}}S=0,\ifmmode\pm\else\textpm\fi{}1$ transitions between different spin multiplets. Additional selection rules can be imposed by point-group symmetry but were not discussed yet. As most synthetic spin clusters with interesting magnetic properties have high molecular symmetry, a clear understanding of this issue will be helpful for interpreting INS spectra. Here we discuss point-group INS selection rules for magnetically isotropic or anisotropic spin clusters. Rings and a number of spin polyhedra with cubic or icosahedral symmetry are chosen as illustrative and relevant examples. These systems exhibit a significant number of point-group selection rules in isotropic spin models, and most of them maintain a smaller number of selection rules in anisotropic spin models. We also explain how the Q dependence of certain excitations depends exclusively on the point-group symmetry of the states involved in the transition, an aspect that had thus far only been detailed for spin rings. We provide the universal Q-dependent intensity functions (and their powder-averaged forms) for a set of polyhedra (cube, icosahedron, truncated tetrahedron, cuboctahedron, dodecahedron, icosidodecahedron, and truncated icosahedron). Overall, these results help to disentangle the relevant dynamical information contained in INS spectra from those features that are entirely determined by molecular symmetry.