Wess-Zumino-Berry phase interference in spin tunnelling at excited levels with a magnetic field

Macroscopic quantum coherence and spin-phase interference between excited l evels in single-domain ferromagnetic particles in a magnetic field along th e hard-anisotropy axis are studied. The system has a general structure of t he magnetocrystalline anisotropy, such as one showing a biaxial, trigonal, tetragonal, or hexagonal symmetry. This study not only yields the previousl y obtained spin-phase interference results for the ground-state tunnelling, but also provides a generalization of the Kramers degeneracy to coherent s pin tunnelling in low-lying excited states. These analytical results are fo und to be in good agreement with those from numerical diagonalization. We a lso discuss the transition from quantum to classical behaviour and the poss ible relevance to experiment.