Low-Energy Magnetic Excitations of the Mn 12 -Acetate Spin Cluster Observed by Neutron Scattering

We studied ${\mathrm{Mn}}_{12}$-acetate by inelastic neutron scattering and diffraction. We separated the energy levels corresponding to the splitting of the lowest $S$ multiplet ( $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$ ground state). The irregular spacing of the transition energies unambiguously shows the presence of high-order terms in the spin Hamiltonian [ $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.457(2){\mathrm{cm}}^{\ensuremath{-}1}$, ${B}_{4}^{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2.33(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\ensuremath{-}1}$]. The relative intensity of the lowest energy peaks is very sensitive to the small transverse term that is responsible for quantum tunneling, providing the first determination of this term in zero magnetic field $[{B}_{4}^{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}3.0(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\ensuremath{-}1}]$.