Geometrical phase effects in biaxial nanomagentic particles

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The oscillation of tunnel splitting are obtained by geometrical analysis of the topological Wess-Zumino phase on the basis of tunneling paths in biaxial nanomagnetic particles with magnetic field along the hard anisotropy axis. This theory not only just yields the previous quantum interference results for the ground state tunneling, but also gives the excited level splittings, all of which agree well with the numerical diagonalization. Furthermore, the parity effect in the asymmetric system which was recently discovered in experiment can be derived by similar arguments, and is also certified by using the complex periodic orbit theory. The possibility of improving the discrepancy with the experiment in the periods of oscillations is discussed.