Ferromagnetic instanton interference in magnetic fields - Detailed calculation of tunneling-rate

Macroscopic quantum coherence and tunneling of small ferromagnetic particles in the presence of a magnetic field are investigated by using the instanton method. Both the Wentzel-Kramers-Brillouin exponent and the van Vleck fluctuation determinant are obtained for each case. The topological quenching at H = 0 for half-integral spin particles is evident and such effect can be destroyed by a large applied magnetic field. The oscillating relations of the tunneling rate with the weak applied magnetic field are clearly shown and the quenching of tunneling at some definite values of the field is predicted. The experiment condition for observing the topological quenching is suggested.