Geometrical phase effects in biaxial nanomagnetic particles

The oscillations of tunnel splitting are obtained by geometrical analysis o f the topological Wess-Zumino phase on the basis of tunneling paths in biax ial nanomagnetic particles with magnetic field along the hard anisotropy ax is. This theory not only yields the previous quantum interference results f or the ground-state tunneling, but also gives the excited level splittings, all of which agree well with the numerical diagonalization. Furthermore, t he parity effect in the asymmetric double-well system, which was recently d iscovered in experiment, can be derived by similar arguments, and is also c ertified by using the complex periodic orbit theory. The possibility of imp roving the discrepancy with the experiment in the periods of oscillations i s discussed.