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We devise a formalism to investigate in a systematic way the spectroscopicmagnetic excitations in molecular magnets. This consists in introducing abilinear spin Hamiltonian that allows for discrete coupling parametersaccounting for distinct spin coupling mechanisms among the constituent magneticions, as well as the influence of the nonmagnetic ions in the system. The modelis applied to explore the magnetic excitations of the trimeric magneticcompounds $\mathrm{A_3Cu_3(PO_4)_4}$ $\mathrm{(A\ =\ Ca,\ Sr,\ Pb)}$ and thetetrameric molecular magnet $\mathrm{Ni_4Mo_{12}}$. Our results are in a verygood agreement with the available experimental data: For all trimers$\mathrm{A_3Cu_3(PO_4)_4}$, calculations reveal the existence of one thinenergy band referring to the flatness of observed excitation peaks. Moreoverfor the tetramer $\mathrm{Ni_4Mo_{12}}$, we concluded that the magneticexcitations may be traced back to the specific geometry and complex chemicalstructure of the exchange bridges leading to the splitting and broadness of thepeaks centered about 0.5 meV and 1.7 meV.

A systematic approach to determine the spectral characteristics of molecular magnets