Magnetization quantum tunneling at excited levels for a biaxial spin system in an arbitrarily directed magnetic field

The quantum tunneling of the magnetization vector between excited levels are studied theoretically in single-domain ferromagnetic nanoparticles with biaxial crystal symmetry placed in an external magnetic field at an arbitrarily directed angle in the ZX plane. By applying the periodic instanton method in the spin-coherent-state path-integral representation, we calculate the tunnel splittings and the tunneling rates between excited levels in the low barrier limit for different angle ranges of the external magnetic field (theta(H)= pi/2, pi/2 much less than theta(H) much less than pi, and theta(H)=pi). The temperature dependences of the tunneling frequency and the decay rate are clearly shown for each case. Our results show that the tunnel splittings and the tunneling rates depend on the orientation of the external magnetic field distinctly, which provides a possible experimental test for magnetic quantum tunneling in nanometer-scale single-domain ferromagnets.