Magnetization of $Mn_{12}$ acetate in a slowly varying magnetic field: A quantum mechanical study

Beginning with a Heisenberg: spin Hamiltonian for the manganese ions in the Mn12Ac molecule, we find a number of model exact low-energy states of the system whose spectrum corresponds to the ordering of the states proposed from experiments. We also obtain the spatial symmetry classification of the low-lying states and find that none of the excitations below about 100 K have the same symmetry as the S = 10 ground state. This allows us to restrict ourselves to the S = 10 ground-state manifold in a time-dependent formalism to find the magnetization of the molecule in the presence of a slowly varying magnetic field at zero temperature. In our study, we consider the field sweep rate, fourth-order anisotropic spin interactions, and a transverse field. We study the effects of these parameters on the magnetization steps which are known to occur in the hysteresis plots in this system. We also study the weights of the different states at the magnetization plateaus as functions of these parameters. We find that the magnetization plateaus are reproduced even though there are a large number of states which can tunnel into each other