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

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