Macroscopic Quantum Phenomena in Small Ferromagnetic Particles

Small (radius ~50 A) ferromagnetic particles are candidates for macroscopic quantum tunneling and macroscopic quantum coherence. At low temperature, and in the presence of external magnetic fields, the magnetization can tunnel out of metastable easy directions, or between degenerate easy directions. A qualitative analysis shows that the tunneling rate can be made as large as 10 ^4-10^8 sec ^{-1} with suitable fields and reasonable material parameters. In order to calculate the tunneling rate more precisely, a path integral formalism for spin coherent states is used. The formalism for evaluating the van Vleck determinants for such path integrals is developed. The WKB exponent associated with the least action path and the prefactor related with the fluctuations about the classical path are calculated for various forms of the magnetocrystalline anisotropy. It is also shown that the coupling of the magnetization to the phonons is an extremely weak source of dissipation that, for practical purposes does not reduce the tunneling rate. Such dissipation is shown to have a spectral density J(omega)~omega ^3. A partial discussion for a nonuniform candidate tunneling configuration is given, based on the critical single-domain size from stability analysis.