Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule   Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion
  We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field. 
M. S. Foss-Feig and Jonathan R. Friedman