  The quantum interference effects induced by the Wess-Zumino term, or Berry
phase are studied theoretically in resonant quantum coherence of magnetization
vector between degenerate excited states in nanometer-scale single-domain
ferromagnets in the absence of an external magnetic field. By applying the
periodic instanton method in the spin-coherent-state path integral, we evaluate
the low-lying tunnel splittings between degenerate excited states of
neighboring wells. And the low-lying energy level spectrum of m-th excited
states are obtained with the help of the Bloch theorem in one-dimensional
periodic potential.
