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

TL;DR

This paper investigates how magnetic fields influence quantum tunneling and coherence in ferromagnetic particles with biaxial and tetragonal anisotropy, providing analytical and numerical results for tunneling rates across various field orientations.

Contribution

It offers new analytical formulas and numerical calculations for quantum tunneling rates of ferromagnetic particles under arbitrary magnetic field angles and anisotropy symmetries.

Findings

Analytic formulas for tunneling rates in small epsilon limit.

Numerical tunneling rates for full angle range at specific epsilon values.

Dependence of tunneling rates on magnetic field orientation and anisotropy symmetry.

Abstract

We calculate the quantum tunneling rate of a ferromagnetic particle of $\sim 100 \AA$ 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 ($\pi/2 < \theta_H \leq \pi$), for the values of \epsilon =0.01 and 0.001.