Properties of low-lying excited manifolds in the Mn12 acetate

Most experimental data on the single-molecule magnet Mn$_{12}$ acetate have been successfully explained by the assumption that the Mn$_{12}$ acetate has an effective ground-state spin of S=10. However, the effect of the low-lying excited manifolds caused by interactions between Mn spins has not been well understood. To investigate the features of the low-lying excited manifolds, the intramolecular exchange interactions are calculated using density-functional theory (DFT). With the calculated exchange parameters, the energy gap between the S=10 ground-state and the first excited-state manifold is calculated by diagonalization of the Heisenberg Hamiltonian. The upper limit on the energy gap is about 40.5 K which is likely to be overestimated due to incomplete treatment of the Coulomb potential within DFT. It is found that there are several S=9 low-energy excited-state manifolds above the S=10 ground-state manifold. The magnetic anisotropy barriers for the low-lying spin excitations are calculated using DFT. Based on the calculations, it is found that the anisotropy barriers for the low-lying excited manifolds are approximately the same as that for the ground-state manifold, which is applicable to other single-molecule magnets such as Mn$_4$.