Macroscopic magnetization tunneling and coherence: Calculation of tunneling-rate prefactors

The tunneling of the total magnetization of a small (100 - diameter) magnetic particle out of metastable easy directions or between degenerate easy directions is studied. The previously known Wentzel-Kramers-Brillouin exponents for the tunneling rates for these processes are supplemented by calculations of the prefactors, for various forms of the magnetocrystalline anisotropy. The calculations are done using spin-coherent-state path integrals. The formalism for evaluating fluctuation determinants for such path integrals is developed.