  We have investigated analytically quantum tunneling of large spin in the
biaxial spin system with the magnetic field applied along the hard and medium
anisotropy axes by using a purely quantum-mechanical approach. When the
magnetic field parallels the hard axis, the tunnel splittings of all the energy
level pairs are oscillatory as a function of the magnetic field. The quenching
points are completely determined by the coexistence of solutions of the Ince's
equation. When the magnetic field points the medium axis, the tunnel splitting
oscillations disappear due to no coexistence of solutions. These results
coincide the recent experimental observations in the nanomagnet Fe$_8$.

Mesoscale and Nanoscale Physics