Quantum tunneling of magnetization in a general magnetic field

We study macroscopic quantum tunneling and coherence in small ferromagnetic particles in the presence of magnetic fields with a general direction. Different structures of the tunnel barriers can be generated by the magnitude and direction of the magnetic field. We calculate the tunneling rate via instanton method and give the approximate analytic forms of the rate for the hexagonal and cubic symmetries. We also present the numerical results of the WKB exponent for cubic symmetry in a wide range of angles, and discuss their different features.