  Many molecular magnetic clusters, such as single-molecule magnets, are
characterized by spin ground states with defined total spin S exhibiting
zero-field-splittings. In this work, the spectroscopic intensities of the
transitions within the ground-state multiplet are analyzed. In particular, the
effects of a mixing with higher-lying spin multiplets, which is produced by
anisotropic interactions and is neglected in the standard single-spin
description, are investigated systematically for the two experimental
techniques of inelastic neutron scattering (INS) and electron paramagnetic
resonance (EPR), with emphasis on the former technique. The spectroscopic
transition intensities are calculated analytically by constructing
corresponding effective spin operators perturbationally up to second order and
consequently using irreducible tensor operator techniques. Three main effects
of spin mixing are observed. Firstly, a pronounced dependence of the INS
intensities on the momentum transfer Q, with a typical oscillatory behavior,
emerges in first order, signaling the many-spin nature of the wave functions in
exchange-coupled clusters. Secondly, as compared to the results of a
first-order calculation, the intensities of the transitions within the spin
multiplet are affected differently by spin mixing. This allows one, thirdly, to
differentiate the higher-order contributions to the cluster magnetic anisotropy
which come from the single-ion ligand-field terms and spin mixing,
respectively. The analytical results are illustrated by means of the three
examples of an antiferromagnetic heteronuclear dimer, the Mn-[3 x 3] grid
molecule, and the single-molecule magnet Mn12.
