Exchange interactions and high-energy spin states inMn12-acetate

We perform inelastic neutron scattering measurements on the molecular nanomagnet ${\mathrm{Mn}}_{12}$-acetate to measure the excitation spectrum up to $45\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ $(500\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. We isolate magnetic excitations in two groups at $5--6.5\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ $(60--75\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and $8--10.5\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ $(95--120\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, with higher levels appearing only at $27\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.2em}{0ex}}(310\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and $31\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.2em}{0ex}}(360\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. From a detailed characterization of the transition peaks we show that all of the low-energy modes appear to be separate $S=9$ excitations above the $S=10$ ground state, with the peak at $27\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.2em}{0ex}}(310\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ corresponding to the first $S=11$ excitation. We consider a general model for the four exchange interaction parameters of the molecule. The static susceptibility is computed by high-temperature series expansion and the energy spectrum, matrix elements, and ground-state spin configuration by exact diagonalization. The theoretical results are matched with experimental observation by inclusion of cluster anisotropy parameters, revealing strong constraints on possible parameter sets. We conclude that only a model with dominant exchange couplings ${J}_{1}\ensuremath{\sim}{J}_{2}\ensuremath{\sim}5.5\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.2em}{0ex}}(65\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and small couplings ${J}_{3}\ensuremath{\sim}{J}_{4}\ensuremath{\sim}0.6\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.3em}{0ex}}(7\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ is consistent with the experimental data.