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

Abstract

We calculate the quantum tunneling rate of a ferromagnetic particle of $\sim 100\mathring{A}$ 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 $\epsilon (=1-H/H_c)$-limit for the magnetic field normal to the easy axis (${\theta }_H=\pi /2$), for the field opposite to the initial easy axis (${\theta }_H=\pi$), and for the field at an angle between these two orientations ($\pi /2<<{\theta }_H<<\pi$). In addition, we obtain numerically the tunneling rates for the biaxial symmetry in the full range of the angle ${\theta }_H$ of the magnetic field ($\pi /2<{\theta }_H\le \pi$), for the values of ε=0.01 and 0.001.

25 pages of text (RevTex) and 4 figures (PostScript files), to be published in Phys. Rev. B

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