The oscillation of tunnel splitting in the biaxial spin systems with the magnetic field along the hard anisotropy axis is analyzed within the particle-mapping approach, rather than in the $(\theta ,\phi )$ spin coherent-state representation. In our mapping procedure, the spin system with Hamiltonian $\mathcal{H}=-{\mathrm{DS}}_x^2{+ES}_z^2-{\mathrm{HS}}_z,$ where D and E are anisotropy constants satisfying $D,E>\mathrm{}0,$ and H is the magnetic field, is transformed into a particle moving in the restricted $S^1$ geometry whose wave function is subjected to the boundary condition involving an additional phase shift. We obtain from this boundary condition the values of the fields at which tunneling is quenched, by considering the destructive interference of two opposite Feynman propagators, without instanton approximation. We also show that the quenching fields are same for all energy levels. Furthermore, even if we consider another possible Hamiltonian for the biaxial system whose mapping potential has completely different tunneling pictures, the eigenvalue equation obtained by mapping yields just the energy splittings of original spin system numerically.

• Received 14 September 1999

DOI:https://doi.org/10.1103/PhysRevB.62.3014