Magnetic Field Dependence of Macroscopic Quantum Tunneling and Coherence of Ferromagnetic Particle

Abstract

We calculate the quantum tunneling rate of a ferromagnetic particle of $\sim 100 Å$ diameter in a magnetic field of arbitrary angle. We consider the magnetocrystalline anisotropy with the biaxial symmetry and that with the tetragonal symmetry. Using the spin-coherent-state path integral, we obtain approximate analytic formulas of the tunneling rates in the small $ε(=1- H/H_c)$-limit for the magnetic field normal to the easy axis ($θ_H = π/2$), for the field opposite to the initial easy axis ($θ_H = π$), and for the field at an angle between these two orientations ($π/2 << θ_H << π$). In addition, we obtain numerically the tunneling rates for the biaxial symmetry in the full range of the angle $θ_H$ of the magnetic field ($π/2 < θ_H \leq π$), for the values of ε=0.01 and 0.001.