Non-Kramers degeneracy and oscillatory tunnel splittings in the biaxial spin system

We have investigated analytically quantum tunnelling of large spin in the biaxial spin system with the magnetic field applied along the hard and medium anisotropy axes by using Schrodinger's interpretation of quantum mechanics. When the magnetic field parallels the hard axis, the tunnel splittings of all the energy level pairs become oscillatory as a function of the magnetic field. The quenching points are completely determined by the coexistence of solutions of Ince's equation. When the magnetic field points to the medium axis, the tunnel splitting oscillations disappear due to the absence of coexistence of solutions. These results coincide with the recent experimental observations in the nanomagnet Fe-8.