Spin excitations in the molecule Mn$_{19}$ with a record ground-state spin $S$ = 83/2

In the magnetic molecule Mn$_{19}$, 12 Mn(III) and 7 Mn(II) ions are ferromagnetically coupled such as to yield a $S$ = 83/2 ground state. We recorded Q-band EPR and inelastic neutron scattering (INS) spectra on powder samples of Mn$_{19}$. The EPR data is well interpreted by the model of an isolated $S$ = 83/2 spin with uniaxial magnetic anisotropy, $H$ = \textit{DS}$_{z}^{2}$ + \textit{g$\mu $}$_{B}$\textbf{S}$\cdot $\textbf{B}. We find $D$ = 0.004 cm$^{{\-}1}$, hence Mn$_{19}$ is not a single-molecule magnet. The INS spectra show a broad feature I at ca. 0.25 meV, which exhibits an uncommon temperature dependence, and two peaks II and III at ca. 3.0 and 5.7 meV. The analysis of the INS data is complicated by the huge Hilbert space of Mn$_{19}$ of 6.8 10$^{13}$ states. Peaks II and III are assigned to discrete ferromagnetic spin waves. Understanding feature I is more difficult because it consists of many transitions which combine such as to yield a complex temperature dependence. Hence, its behavior cannot be described in a single-spin picture, but requires an inherent many-body description.